of sparse data points

浙江大学2016 –2017 学年春夏学期《Artificial Intelligence》课程期末考试试卷课程号： 21191890 ，开课学院：_计算机科学与技术学院_考试试卷：A卷、B卷（请在选定项上打√）考试形式：闭、开卷（请在选定项上打√），允许带___________入场考试日期： 2017 年 6 月 25 日,考试时间： 120 分钟诚信考试，沉着应考，杜绝违纪。

考生姓名：_____________学号：_____________所属院系：_____________1.Fill in the blanks (30 points)1)Two common structures are used, namely first-in-first-out (FIFO queue) and last-in-first-out (LIFO queue). The breadth-first-search uses a __________queue, depth-first search uses a__________ queue.2)In alpha-beta pruning search, the algorithm maintains two values, alpha and beta, whichrepresents the maximum score that the maximizing player is assured of and the minimum score that the minimizing player is assured of respectively. At the beginning of alpha-beta search, alpha is set to __________ and beta is set to __________, i.e. both players start with their lowest possible score.3) A and B are two random variables. P(A) and P(B) are their probabilities. It is knownthat P(A)+P(B)=0.5, and P(A|B)P(B|A)=14. Then the P(A) is_______.4) In your 10-day vacation in Alaska, you kept the following log on the weather andwhether you saw a bear that day:(rain, bear) 1 day (¬rain, bear) 2 days (rain, ¬bear) 6 days (¬rain, ¬bear)1 daya) Compute the marginal probability P(bear ) = _______b) Compute the conditional probability P(¬bear|rain) = _______5) In the figure, the circles show a plot of a trainingdata set of 10 data points, the dash line shows the function f(x) used to generate the data and solid curve shows the higher order polynomial g(x) fitted to given 10 data points. The fitted curve passes exactly through each data point, so the value of RMS error E RMS = 0 and g(x) gives avery poor representation of the function f(x). This behavior is known as___________________ (please select over-fitting or under-fitting to fill in this blank).6) For a given likelihood function p(x n |θ), if we obtain a data set of observations X ={x 1,x 2,x 3} and these data points are independent and identically distributed (i.i.d.), then p (X |θ)=p(x 1,x 2,x 3|θ)= ____________.7) For multivariate Gaussian distribution N (x|μ, Σ) of the D dimensional input space x,we have __________ independent parameters for μ and Σ. If Σ is a diagonal matrix and 2σ∑=I , the number of total parameters reduces to __________.8) The Linear basis function models involve linear combinations of fixed nonlinearfunctions of the input variables. If given basis functions ϕ(x )=(ϕ0(x ),ϕ1(x ),ϕ2(x ))T, where ϕ0(x )=1 and the model parameters w =(w 0,w 1,w 2)T , then the linear basis function y (x , w ) = ____________.9)In general, a deep convolutional neural network consists of convolutional layer,pooling layer, fully-connected layer and classifier layer, the softmax is usuallyemployed at the __________ layer.10)Reinforcement learning mainly consists of policy, value function and model.A__________ maps a state to an action, and a value function is a prediction of future reward. In Q-value function, discount factor γ is usually used, the range of discount factor γ is __________.2. Multiple Choice (36 points, only one of the options is correct.)1)Consider three 2D points a = (0, 0), b = (0, 1), c = (1, 0). Run k-means with twoclusters. Let the initial cluster centers be (-1, 0), (0, 2). What clusters will k-means learn after one iteration? _____(A) {a}, {b, c}(B) {a, b}, {c}(C) {a, c}, {b}(D) none of the above2)The sigmoid function in a neural network is defined as g(x)=e x1+e x. There isanother commonly used activation function called the hyperbolic tangent function,which is defined as tanh(x)=e x−e−xe x+e−x. How are these two functions related?____________(A) tanℎ(x)=g(x)−1(B) tanℎ(x)=2g(x)−1(C) tanℎ(x)=g(2x)−1(D) tanℎ(x)=2g(2x)−13)Which nodes will be pruned along with their branches by alpha-beta pruning? _____(A) I (B) H, I (C) G, H, I (D) C, H, I4)Consider a 3-puzzle where, like in the usual 8-puzzle game, a tile canonly move to an adjacent empty space. Given the initial state which ofthe following state cannot be reached? _____(A) (B) (C) (D)5)Given two Gaussian distribution N(x|−1,1) and N(x|1,1), which of the followingformula is correct? ______________(A) N(0|−1,1)>N(0|1,1)(B) N(−1|−1,1)>N(−1|1,1)(C) N(0|−1,1)<N(0|1,1)(D) N(−1|−1,1)<N(−1|1,1)6)The Fisher’s criterion is defined to be _________(A)the separation of the projected class means.(B)the separation of the projected class variances.(C)the ratio of the between-class variance to the within-class variance.(D)the ratio of the within-class variance to the between-class variance.7)Suppose we have a data set {x1,…,x N} drawn from the mixture of two 2D Gaussians,which can be written as p(x)=0.5N(x|μ1,Σ1)+0.5N(x|μ2,Σ2). If Σ1=Σ2=σ2I in this model, which of the following figures is consistent with the distribution of data points p(x)? _______________(A) (B) (C) (D)8)Consider a polynomial curve fitting problem. If the fitted curve oscillates wildlythrough each point and achieve bad generalization by making accurate predictions for new data, we say this behavior is over-fitting. Which of the following methods cannot be used to control over-fitting? ________________(A)Use fewer training data(B)Add validation set, use Cross-validation(C)Add a regularization term to an error function(D)Use Bayesian approach with suitable prior9)AlexNet (one of popular multi-layer convolutional neural networks for imageclassification) is trained in a_________ setting, K-means clustering is employed in a _________ setting and Boosting for classification is implemented in a_________ setting , linear regression model for classification is realized in a _________ setting.(A) unsupervised, supervised, supervised, unsupervised(B) supervised, supervised, supervised, supervised(C) supervised, supervised, unsupervised, unsupervised(D) supervised, unsupervised, supervised, supervised10)In linear least square regression model, we can add a regularization term to an errorfunction (i.e., sum-of-squares) in order to control _________. The lasso regularizer will introduce____________ solution compared to quadratic regularizer.(A) over-fitting, dense (B) over-fitting, sparse(C) under-fitting, dense (D) under-fitting, sparse11)We can decompose the expected squared loss of one predict model as follows:expected loss = (bias)2 + variance + noiseIn general, one flexible model (i.e., under-fitting) model will introduce high_________ and one rigid model (i.e., overfitting) model will introduce high _______________.There is a tradeoff between a model's ability to minimize bias and variance.(A) variance, bias (B) bias, bias(C) variance, variance (D) bias, variance12)Which description is not correct in terms of supervised learning, semi-supervisedlearning, unsupervised learning and reinforcement learning?__________(A) Reinforcement learning is one of specific supervised learning methods.(B) Semi-supervised learning falls between unsupervised learning (without anylabeled training data) and supervised learning (with completely labeled training data).(C) Reinforcement learning is neither supervised learning nor unsupervised.(D) Deep reinforcement learning is a combination of deep learning and reinforcementlearning.13)In reinforcement learning, Q-learning defines a function Q(s, a) representing the_______________ when we perform action a in state s, and continue optimally from that point on. The Q-function can be learned iteratively by ______________.(A) The immediate reward plus discounted maximum future reward, Bellman equation(B) Discounted maximum future reward, Markov decision process(C) The immediate reward plus discounted maximum future reward, Markov decisionprocess(D) Discounted maximum future reward, Bellman equation14)When we use one deep convolutional neural network model to classify 101 concepts,which option is not correct in the following description?_________(A)The output of the last fully connected layer can be used as the learning features ofeach concept.(B)The dimension of the classification layer can be 101.(C)The convolutional kernels are pre-defined (i.e., data-independent).(D) Dropout is used to boost the performance.15)Which description is not correct in terms of deep learning?__________(A)Deep learning is essentially a method to learn the features of raw data.(B)Backpropagation is conducted to optimize the weights of deep neural networks sothat the neural network can learn how to correctly map arbitrary inputs to outputs.(C)The achieved performance of deep learning is due to its powerful representationability via many of non-linear mappings.(D)Deep convolutional neural network for classification is employed in an end-to-endmechanism via unsupervised learning.16) Which description is not correct about K-Means clustering?___________(A)K-means clustering can be used for image segmentation and image compression.(B)K is the number of clusters and is generally pre-defined.(C)Each data point can be assigned to more than one cluster.(D)If the dimension of each data points is D, the dimension of cluster centers is D.17)The number of pruned successors in alpha-beta pruning is highly dependent on _____.(A)The moving order(B)The initialized values of alpha and beta(C)The number of terminal nodes(D)Whether breadth-first search or depth-first search is employed18)What description is not correct in terms of AI?(A)Deep learning is one kind of machine learning methods.(B)Machine learning is deep learning.(C)Search is one kind of methods used in AI.(D)In general, LeNet-5 (one of deep convolutional neural networks) maps eachhandwriting images into 0-9 digital character concept space.3.Calculus and Analysis (34 points)1)(Game Playing, 8 points) As shown in the following figure, there is a MINMAXsearch tree with three layers. The utility values for the leaf nodes are respectively displayed at the bottom of the figure.(a) Fill in the blanks for the utility values associated with the tree nodes (i.e., B, C, D) as well as the root node A. (4 points)(b) Draw mark ‘//’ on some branches in the figure to show that they are pruned by the alpha-beta pruning algorithm. (4 points)2) (Boosting, 8 points ) Boosting is a powerful technique for combining multiple “base” classifiers to produce a form of committee whose performance can be significantly better than that of any of the base classifiers. Consider a two-class classification problem, in which the training data comprises 2D input vectors 1,...,N x x along with corresponding binary target variables 1,...,N t t where {1,1}n t ∈+-. Assume that we have trained three base classifiers 12(),()f f x x ,3()f x and the corresponding weighting coefficients 123,,ααα. Please answer:(a) The final classifier learned by boosting can be given by: (4 points)F final (x )=(b) If three base classifiers 12(),()f f x x ,3()f x are shown in the figure and1230.3,0.5,0.7ααα===. Each base classifier partitions the input space into tworegions separated by a linear decision boundary Ωi . The dark regio n with ‘+’ means the target value is +1 and the bright region with ‘-’ means the target value is -1. Three decision boundaries have been put together in the last right figure and separate the space into six sub-regions, please mark the final decision result in the figure with ‘+’ or ‘-’ for each sub -region.(4 points)3) (Image Restoration, 6 points ) Please share several key tricks that effectively improve the performance of your Image Restoration Algorithm in Project 2. (About 100~150 words).4)(Deep learning, 12 points)(a) Convolution is very important in deep convolutional neural network. Please calculate the convolved value of the center pixel in Figure (1) with the given convolutional kernel in Figure (2). (3 points)(b) Given a single depth slice in Figure (3), please give out the average-pooling value of this slice with 2×2 filters and stride 2. (3 points)(c) If we trained a deep convolutional neural network as follows in Figue (4). The sofmax is used to classify five concepts (e.g., car, airplane, truck, ship and person). If we input a car image into the trained deep model, please write out one of likely 5-dimensional outputs by the deep model. (3 points)Figure (4)(d) Please write down the trainable parameters in this model. (3 points)《Artificial Intelligence》Final Examination Answer SheetName： Student ID： Dept.： _1.Fill in the blanks (30 points, 2pt/per)1).______________________, _______________________2). _____________________, _______________________3)._____________________4). _____________________, _______________________5)._____________________6). _____________________7)._____________________, _______________________8)._____________________9)._____________________10).____________________ , _______________________2.Multiple Choice (36 points, 2pt/per)3. Calculus and Analysis (34 points)1) (Game Playing, 8 points)(a) (4 points)(b)(4 points)2) (Boosting, 8 points)(a) (4 points)F final(x)=(b) (4 points)3) (Image Restoration, 6 points)4) (Deep Learning, 12 points)(a)(3 points)(b)(3 points)(c)(3 points)(d)(3 points)。

收稿日期：２０２２－１０－１５基金项目：北京市自然科学基金项目（４２１２００１）引用格式：赵宇轩，贾克斌，陈嘉平．一种融合ＩＭＵ的手持旋轴激光雷达定位建图方法［Ｊ］．测控技术，２０２３，４２（１０）：３８－４３．ＺＨＡＯＹＸ，ＪＩＡＫＢ，ＣＨＥＮＪＰ．ＡＨａｎｄｈｅｌｄＲｏｔａｒｙＬｉＤＡＲＳＬＡＭＭｅｔｈｏｄＩｎｔｅｇｒａｔｅｄｗｉｔｈＩＭＵ［Ｊ］．Ｍｅａｓｕｒｅｍｅｎｔ＆ＣｏｎｔｒｏｌＴｅｃｈｎｏｌｏｇｙ，２０２３，４２（１０）：３８－４３．一种融合ＩＭＵ的手持旋轴激光雷达定位建图方法赵宇轩１，２，贾克斌１，２，陈嘉平１，２（１．北京工业大学信息学部，北京　１００１２４；２．先进信息网络北京实验室，北京　１００１２４）摘要：同步定位与建图（ＳｉｍｕｌｔａｎｅｏｕｓＬｏｃａｌｉｚａｔｉｏｎａｎｄＭａｐｐｉｎｇ，ＳＬＡＭ）是移动机器人与智能车辆实现环境感知、实时定位的关键技术。

随着科技的不断发展，具有便携、扫描范围广等优势的手持旋轴激光雷达应用愈加广泛。

为了解决手持旋轴激光雷达在运行过程中由于旋转引起的特征点稀疏导致定位建图质量差的问题，提出一种改进的ＳＬＡＭ算法。

在ＬＩＯ ＳＡＭ算法的基础上计算了一种表征点云强度信息的特征点，在提取几何特征边缘点与平面点时，将周围强度值变化较大的点作为一种新的特征点引入点云匹配。

同时，通过实时判断系统是否存在退化风险，从而动态调整滤波数值设置，保证了系统运行的稳定性。

实验结果表明，在手持旋轴激光雷达采集的户外场景数据下，经过改进的ＳＬＡＭ算法相比ＬＩＯ ＳＡＭ算法有更好的定位与建图效果。

关键词：同步定位与建图；激光雷达；惯性测量单元；特征提取中图分类号：ＴＰ２４２ 文献标志码：Ａ 文章编号：１０００－８８２９（２０２３）１０－００３８－０６ｄｏｉ：１０．１９７０８／ｊ．ｃｋｊｓ．２０２３．０３．２２８ＡＨａｎｄｈｅｌｄＲｏｔａｒｙＬｉＤＡＲＳＬＡＭＭｅｔｈｏｄＩｎｔｅｇｒａｔｅｄｗｉｔｈＩＭＵＺＨＡＯＹｕｘｕａｎ１牞２牞ＪＩＡＫｅｂｉｎ１牞２ 牞ＣＨＥＮＪｉａｐｉｎｇ１牞２牗１．ＦａｃｕｌｔｙｏｆＩｎｆｏｒｍａｔｉｏｎ牞ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ牞Ｂｅｉｊｉｎｇ１００１２４牞Ｃｈｉｎａ牷２．ＢｅｉｊｉｎｇＬａｂｏｒａｔｏｒｙｏｆＡｄｖａｎｃｅｄＩｎｆｏｒｍａｔｉｏｎＮｅｔｗｏｒｋ牞Ｂｅｉｊｉｎｇ１００１２４牞Ｃｈｉｎａ牘Ａｂｓｔｒａｃｔ牶Ｓｉｍｕｌｔａｎｅｏｕｓｌｏｃａｌｉｚａｔｉｏｎａｎｄｍａｐｐｉｎｇ牗ＳＬＡＭ牘ｉｓａｋｅｙｔｅｃｈｎｏｌｏｇｙｆｏｒｍｏｂｉｌｅｒｏｂｏｔｓａｎｄｉｎｔｅｌｌｉｇｅｎｔｖｅｈｉｃｌｅｓｔｏｒｅａｌｉｚｅｅｎｖｉｒｏｎｍｅｎｔａｗａｒｅｎｅｓｓａｎｄｒｅａｌ ｔｉｍｅｌｏｃａｌｉｚａｔｉｏｎ．Ｗｉｔｈｔｈｅｃｏｎｔｉｎｕｏｕｓｄｅｖｅｌｏｐｍｅｎｔｏｆｔｅｃｈ ｎｏｌｏｇｙ牞ｈａｎｄｈｅｌｄｒｏｔａｒｙＬｉＤＡＲ牞ｗｈｉｃｈｈａｓｔｈｅａｄｖａｎｔａｇｅｓｏｆｐｏｒｔａｂｉｌｉｔｙａｎｄｗｉｄｅｓｃａｎｎｉｎｇｒａｎｇｅ牞ｉｓｍｏｒｅａｎｄｍｏｒｅｗｉｄｅｌｙｕｓｅｄ．ＴｏｓｏｌｖｅｔｈｅｐｒｏｂｌｅｍｏｆｓｐａｒｓｅｆｅａｔｕｒｅｐｏｉｎｔｓｃａｕｓｅｄｂｙｒｏｔａｔｉｏｎｄｕｒｉｎｇｔｈｅｏｐｅｒａｔｉｏｎｏｆｈａｎｄｈｅｌｄｒｏｔａｒｙＬｉＤＡＲ牞ｗｈｉｃｈｌｅａｄｓｔｏｐｏｏｒｑｕａｌｉｔｙｏｆｌｏｃａｌｉｚａｔｉｏｎａｎｄｍａｐｐｉｎｇ牞ａｎｉｍｐｒｏｖｅｄＳＬＡＭａｌｇｏｒｉｔｈｍｉｓｐｒｏｐｏｓｅｄ．ＢａｓｅｄｏｎｔｈｅＬＩＯ ＳＡＭａｌｇｏｒｉｔｈｍ牞ａｆｅａｔｕｒｅｐｏｉｎｔｃｈａｒａｃｔｅｒｉｚｉｎｇｔｈｅｉｎｔｅｎｓｉｔｙｉｎｆｏｒｍａｔｉｏｎｏｆｔｈｅｐｏｉｎｔｃｌｏｕｄｉｓｃａｌｃｕｌａｔｅｄ牞ａｎｄｗｈｅｎｅｘｔｒａｃｔｉｎｇｔｈｅｇｅｏｍｅｔｒｉｃｆｅａｔｕｒｅｅｄｇｅｐｏｉｎｔｓａｎｄｐｌａｎｅｐｏｉｎｔｓ牞ｔｈｅｐｏｉｎｔｓｗｉｔｈｌａｒｇｅｃｈａｎｇｅｓｉｎｓｕｒｒｏｕｎｄｉｎｇｉｎｔｅｎｓｉｔｙｖａｌｕｅｓａｒｅｉｎｔｒｏｄｕｃｅｄａｓａｎｅｗｆｅａｔｕｒｅｃｌｏｕｄｆｏｒｐｏｉｎｔｃｌｏｕｄｍａｔｃ ｈｉｎｇ．Ａｔｔｈｅｓａｍｅｔｉｍｅ牞ｔｈｅｓｙｓｔｅｍｏｐｅｒａｔｉｏｎｓｔａｂｉｌｉｔｙｉｓｅｎｓｕｒｅｄｂｙｄｙｎａｍｉｃａｌｌｙａｄｊｕｓｔｉｎｇｔｈｅｆｉｌｔｅｒｉｎｇｐａｒａｍｅ ｔｅｒｓｅｔｔｉｎｇｓｂｙｊｕｄｇｉｎｇｗｈｅｔｈｅｒｔｈｅｓｙｓｔｅｍｈａｓｄｅｇｒａｄａｔｉｏｎｒｉｓｋｉｎｒｅａｌ ｔｉｍｅ．ＴｈｅｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｉｍｐｒｏｖｅｄＳＬＡＭａｌｇｏｒｉｔｈｍｈａｓｂｅｔｔｅｒｌｏｃａｌｉｚａｔｉｏｎａｎｄｍａｐ ｂｕｉｌｄｉｎｇｅｆｆｅｃｔｓｔｈａｎｔｈｅＬＩＯ ＳＡＭａｌｇｏｒｉｔｈｍｕｎ ｄｅｒｔｈｅｏｕｔｄｏｏｒｓｃｅｎｅｄａｔａｃｏｌｌｅｃｔｅｄｂｙｈａｎｄｈｅｌｄｒｏｔａｒｙＬｉＤＡＲ．Ｋｅｙｗｏｒｄｓ牶ＳＬＡＭ牷ＬｉＤＡＲ牷ＩＭＵ牷ｆｅａｔｕｒｅｅｘｔｒａｃｔｉｏｎ 随着同步定位与建图（ＳｉｍｕｌｔａｎｅｏｕｓＬｏｃａｌｉｚａｔｉｏｎａｎｄＭａｐｐｉ ｎｇ，ＳＬＡＭ）技术的不断发展，其已经广泛应用于２Ｄ／３Ｄ建图、智能机器人导航等领域［１］。

目录File文件 (1)Edit 编辑 (2)View 视图 (2)Plot 绘图 (3)Column 列 (3)Worksheet 工作表 (4)Analysis 分析 (4)Statistics 统计分析 (5)Image 图像 (6)Tools 工具 (9)Format 格式 (9)Windows 窗口 (10)Help 帮助 (10)File文件New 新建 (18)Project项目 (18)Worksheet 工作簿 (19)Matrix 矩阵 (20)Graph 图形 (21)Prom Template 从模板创建 (21)Excel (22)Layout 布局页 (22)Notes 记事本 (23)Function Plot 函数绘图 (24)Open 打开 (27)Open Excel 打开Excel文件 (27)Open Sample OPJ 打开示例项目 (28)Append 追加 (28)Close 关闭 (28)Save Project 保存项目 (28)Save Project As 项目另存为 (28)Save Window As 窗口另存为 (29)Save Template As 模板另存为 (29)Save Workbook as Analysis Template 工作簿另存为分析模板 (30)Save Project as Analysis Template项目另存为分析模板 (30)Import 导入 (30)Import Wizard 导入向导 (31)Customize 定制............................................................................................................. .. (31)Export 导出 (33)Batch Processing 批处理 (34)Database Import数据库导入 (35)Edit 编辑Copy (full precision) 精确复制 (37)Copy (including label rows) 带标识符行复制 (37)Paste Transpose 转置粘贴 (37)Paste Link 粘贴链接 (38)Paste Link Transpose粘贴链接转置 (38)Paste Special 特殊粘贴 (38)Merge (Embedded) Graphs 合并(嵌入)图形 (39)Button Edit Mode 按钮编辑模式 (39)View 视图Toolbars 工具栏 (41)Status Bar 状态栏 (41)Command Window 命令窗口 (42)Code Builder 代码创建器 (42)Quick Help 快速帮助 (43)Project Explorer 项目浏览器 (43)View Windows 视窗 (43)Results Log 结果记录 (44)View Mode (45)Messages Log 信息记录 (46)Actively Update Plots 即时更新图形 (46)Page Break Preview Lines 分页预览线 (46)Print View打印视图 (47)Page 页面视图 (47)Window 窗口视图 (47)Zoom In 放大 (48)Zoom Out 缩小 (49)Whole Page 满页 (49)Show 显示 (49)Show Data Information 显示数据信息 (51)Data Mode 数据模式 (52)Show Column/Row 显示列/行 (52)Show X/Y 显示X/Y (53)Image Mode 图像模式 (53)Show Image Thumbnails 显示缩略图 (53)Plot 绘图Line 线条 (54)Symbol 符号 (55)Line + Symbol 线条+符号 (56)Column/Bar/Pie 柱/条/饼 (56)Multi-Curve 多曲线 (57)3D XYY 三维XYY图 (59)3D XYZ 三维XYZ图 (60)3D Surface 三维曲面图 (60)3D Wire/Bar/Symbol 三维线/柱/符号 (61)Statistics 统计 (62)Area 面积 (65)Contour 等高线图 (65)Specialized 专业图 (66)Stock 股票 (68)Template Library 模板库 (70)Column 列Set as X 设为X (72)Set as Label 设为标记符号 (72)Disregard Column 忽略此列 (73)Set as Y Error 设为Y的误差 (73)Set as Categorical 设为分类数据 (73)Setting Column Values 设定列数值 (74)Fill Column with 填充列 (74)Add New Columns 添加新列 (75)Set Sampling Interval 设置采样间隔 (76)Move Columns 移动列 (76)Show X Column 显示X列 (77)Slide Show of Dependent Graphs 幻灯放映 (77)Add Sparklines 添加拆线图 (79)Worksheet 工作表Sort Range 排序范围 (80)Sort Columns列排序 (81)Sort Worksheet 工作表排序 (81)Clear Worksheet 清除工作表 (81)Worksheet Script 工作表脚本 (81)Worksheet Query 工作表查询 (82)Reset Column Short Names 重置列短名 (83)Split Worksheet 拆分工作表 (84)Split Workbooks 拆分工作簿 (84)Pivot Table 数据透视表 (84)Stack Column 堆列 (85)Unstack Column 拆堆列 (87)Remove Duplicated rows 删除重复行 (87)Reduce Rows 减少行 (88)Transpose 转置 (89)Convert to XYZ 转换为XYZ (90)Convert to Matrix转换为矩阵 (93)Analysis 分析Mathematics 数学运算 (97)Interpolate/Extrapolate Y from X 由X内插/外推求Y (98)Trace Interpolate 迹线外推 (98)Interpolate/Extrapolate 内插/外推 (99)3D Interpolation 三维内插 (100)XYZ Trace Interpolation XYZ 迹线内插 (101)XYZ Surface Area XYZ表面积 (102)Set Column Values 设置列值 (102)Normalize Column. 归一化列 (102)Simple Math 简单数学运算 (103)Differetiate 微分 (104)Integrate 积分 (105)Polygon Area 多边形面积 (105)Average Multiple Curves 多曲线平均 (106)Data Manipulation 数据处理 (106)Subtract Reference Data 与参考值相减 (107)Reduce Duplicate X data 归纳重复的X数据 (108)Reduce by Group 按组归纳 (108)Reduce to Evenly Spaced X 归纳为均匀间隔的X (110)Linear Fit 线性拟合 (112)Fit Linear with X Error 带X误差的线性拟合 (114)Polynomial Fit 多项式拟合 (115)Multiple Linear Regression所谓多元线性回归 (115)Nonlinear Curve Fit 非线性曲线拟合 (117)Nonlinear Surface Fit 非线性表面拟合 (118)Simulate Curve 模拟曲线 (118)Simulate Surface 模拟表面 (119)Exponential Fit 指数拟合 (121)Sigmoidal Fit 反曲拟合 (122)Compare Datasets 比较数据集 (122)Compare Models 比较模型 (123)Signal Processing 信号处理 (125)Smooth 平滑 (125)FFT Filters FFT滤波 (126)FFT (127)Wavelet 小波分析 (129)Convolution 卷积 (132)Deconvolution 反卷积 (133)Coherence 相干性 (134)Correlation 相关性 (135)Hibert Transform希尔伯特变换 (135)Envelope 包络线 (136)Decimation 抽取 (136)Peaks and Baseline 峰和基线 (137)Multiple Peak Fit 多重峰拟合 (138)Single Peak Fit 单峰拟合 (141)Peak Analyzer 峰分析器 (141)Batch Peak Analysis Using Theme 使用主题批量分析 (147)Statistics 统计分析Descriptive Statistics 描述统计 (149)Correlations Coefficient 相关系数 (149)Statistics on Columns 列统计 (151)Statistics on Rows 和统计 (152)Discrete Frequency 离散频率 (154)Frequency Counts 频率计数 (155)Normality Test 正态性检验 (157)2D Frequency Counts/Binning 二维频率计数/分区 (159)Hypothesis Testing 假设检验 (160)One-Sample t-Test 单样本t-检验 (161)Pair-Sample t-Test 配对样本t-检验 (162)Two-Sample t-Test 双样本t-检验 (164)One-Sample Test for Variances 单样本方差检验 (167)Two-Sample Test for Variances 双样本方差检验 (169)ANOV A 方差分析 (170)One-Way ANOV A 单因素方差分析 (170)Two-Way ANOV A 双因素方差分析 (172)One-Way Repeated Measures ANOVA 单因素重复测量方差分析 (174)Two-Way Repeated Measures ANOV A 双因素重复测量方差分析 (176)NonParametric Tests 非参数检验 (178)One-Sample Wilcoxon Signed Rank Test单样本Wilcoxon符号秩检验 (179)Paired Sample Sign Test 配对样本符号检验 (180)Paired Sample Wilcoxon Signed Rank Test配对样本Wilcoxon符号秩检验 (181)Two-Sample Kolmogorov-Smirnov Test 双样本KS检验 (183)Mann-Whitney Test Mann-Whitney检验 (185)Kruskal-Wallis ANOV AKruskal-Wallis方差分析 (187)Moods Median Test 中位数检验 (188)Friedman ANOV A Friedman方差分析 (189)(NPH) K independent Samples K个独立样本 (191)(NPH) Paired Samples 配对样本 (193)(NPH) Two Independent Samples 两个独立样本 (195)Survival Analysis 生存分析 (197)Kaplan-Meier Estimator卡普兰-迈耶估计量 (198)Cox Model Estimator比例风险模型 (199)Weilbull fit Weibull拟合 (201)Multivariate Analysis 多元分析 (203)Principal Component Analysis 主成分分析 (203)K-Means Cluster Analysis K-均值聚类分析 (204)Hierarchical Cluster Analysis 层次聚类分析 (206)Discriminant Analysis 判别分析 (208)Power and Sample Size 功效和样本大小分析 (212)(PSS) One-Sample t-test 单样本t-检验 (212)(PSS) Two-Sample t-test 双样本t-检验 (213)(PSS)Paired t-test 配对样本t-检验 (214)(PSS)One-Way ANOV A 单因素方差分析 (215)ROC Curve受试者工作特征曲线 (216)Image 图像Image adjustments 图像调整 (220)Brightness 亮度 (221)Contrast 对比度 (221)Gamma伽玛值 (221)Hue 色调 (222)Invert 图像色彩翻转 (222)Saturation 饱和度 (223)Histcontrast 直方图对比度 (223)Histequalize 直方图均衡 (223)Auto Level 自动色阶 (224)Color Level 色阶调整 (224)Function LUT 函数搜寻表 (225)Leveling 层次调整 (226)Balance 色彩平衡 (227)Color Replace 颜色替换 (228)Arithmetic transformation 算术变换 (228)Alpha Blend 透明混合 (229)Simple Math 简单数学运算 (230)Math Function 数学函数 (232)Pixel Logic 像素逻辑 (233)Subtract Background 减背景 (234)Extract to XYZ 图像转数据 (235)Morphological Filter 形态学过滤 (236)Replace Background 背景替换 (238)Subtract Interpolated Background 内插背景减影 (238)Conversion 转换 (239)Convert to Data 转成数值 (239)Color to Gray 转换成灰度图....................................................................................... 240 Convert to Image 转换成图像. (241)Binary 转换成二值图 (242)Dynamic Binary 转换成动态二值图 (243)Threshold 阈值 (244)RGB Merge 三原色合并 (245)RGB Splist 三原色拆分 (246)Image Scale 图像比例尺 (247)Geometric Transforms 几何变换 (248)Flip 翻转 (248)Rotate 旋转 (248)Shear 修剪 (249)Resize 调整尺寸 (251)AutoTrim 自动修整 (251)Offset 图像偏移 (252)Spatial Filtering 空间过滤 (254)Average 平均过滤 (255)Gaussian 高斯过滤 (255)Median 中值过滤 (256)Noise 噪音 (257)Edge 边缘.................................................................................................................... 258 Sharpen 锐化................................................................................................................ 258 Unsharpen Mask USM 锐化. (259)User Filter 用户滤镜 (260)Graph 图形 (262)Layer Contents 图层内容 (262)Plot Setup 绘图设置 (263)Add Plot to Layer 层中加图 (263)Add Error Bars 添加误差条 (264)Add Function Graph 添加函数曲线 (265)Rescale to Show All 重置坐标显示全部 (266)Layer Management 图层管理 (266)Add Axis Scrollbar 添加坐标滚动条 (266)New Layer (Axes) 新图层(坐标) (267)Extract to Graphs 提取图层 (268)Apply Palette to Color Map 应用调色板 (270)Merge Graph Windows (271)Speed Mode (271)Update Legend 更新图例 (272)New Legend 新图例 (273)New Enhanced Legend (273)New Table (274)New Color Scale (274)New XY Scaler 新XY比例尺............................................................................................ 275 Set Active Layer By Layer Icon Only ................................................................................... 275 Fit Layer to Graph 图层适合图形....................................................................................... 276 Fit Page to Layers 页面适合图层. 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C-DBSCAN:Density-Based Clustering with ConstraintsCarlos Ruiz1,Myra Spiliopoulou2,and Ernestina Menasalvas11Facultad de Informatica,Universidad Politecnica,Madrid,Spaincruiz@cettico.fi.upm.es,emenasalvas@fi.upm.es 2Faculty of Computer Science,Otto-von-Guericke-Universit¨a t Magdeburg,Germanymyra@iti.cs.uni-magdeburg.deAbstract.Density-based clustering methods are of particular interest for ap-plications where the anticipated groups of data instances are expected to dif-fer in size or shape,arbitrary shapes are possible and the number of clusters isnot known a priori.In such applications,background knowledge about group-membership or non-membership of some instances may be available and itsexploitation so interesting.Recently,such knowledge is being expressed as con-straints and exploited in constraint-based clustering.In this paper,we enhance thedensity-based algorithm DBSCAN with constraints upon data instances–“Must-Link”and“Cannot-Link”constraints.We test the new algorithm C-DBSCAN onartificial and real datasets and show that C-DBSCAN has superior performanceto DBSCAN,even when only a small number of constraints is available.Keywords:constraint-based clustering,semi-supervised clustering,instance-level constraints,clustering with constraints,background knowledge.1IntroductionIn the last years,clustering with instance-level constraints has received a lot of attention, because it allows the incorporation of domain knowledge to the knowledge discovery process[1].Constraint-based clustering exploits the fact that many applications deliver background information in the form of a small set of labeled data,i.e.records that should belong to the same cluster or be in distinct clusters.Such information can be exploited to guide the clustering of the non-labeled data.Examples of constraint-based clustering include the detection of road lanes from GPS data[2]and helping the nav-igation of a Sony Aibo Robot[3].Constraints improve clustering quality[2],enhance computational performance[3]and prevent the construction of empty clusters[4].Most works on constraint-based clustering have been designed for partitioning al-gorithms[2]and hierarchical algorithms[5].In this study,we apply the principle of constraint-driven cluster formation upon density-based clustering and show that in-stance-level constraints enhance performance with respect to cluster quality.Density-based algorithms identify dense data areas of separated by sparse areas.“Density”may refer to a high concentration of proximal data points or to the closeness of a data point to the mean of a Gaussian.We concentrate on one prominent example of density-based clustering,DBSCAN[6],which discovers neighbourhoods of proximal points in a metric space.DBSCAN requires no background knowledge on the number A.An et al.(Eds.):RSFDGrC2007,LNAI4482,pp.216–223,2007.c Springer-Verlag Berlin Heidelberg2007C-DBSCAN:Density-Based Clustering with Constraints217Fig.1.(a)DS1(b)DS2(c)DS3(d)DS4.Samples where DBSCAN does not perform well. or shape of clusters nor on the data distribution.However,it performs poorly if the clus-ters are diffuse,partially overlapping,connected by“bridges”or having very different densities.These shortcomings are depicted in the examples of Fig1(artificial data).We extend DBSCAN into Constraint-driven DBSCAN“C-DBSCAN”.Wefirst par-tition the data space into subspaces and then enforce“instance-level constraints”on the data,i.e.constraints that dictate whether some points may appear in the same cluster or not.We use these constraints to drive cluster construction and show experimentally, that the clusterings produced are of higher quality than DBSCAN clusters.The rest of the paper is organized as follows:Section2discusses related literature. We describe C-DBSCAN in Section3.Section4contains ourfirst experiments that compare C-DBSCAN with the DBSCAN for various datasets and sets of constraints. Section5summarizes our results and proposes directions for further research.2Related WorkClustering with constraints[7,8],also referred to as semi-supervised clustering[9],is a relatively new research direction,in which background knowledge in the form of constraints is used to enhance the clustering process.An overview of the types of con-straints proposed in literature can be found in[7].In this study,we focus on“instance-level constraints”:They express background knowledge on the cluster membership of some data instances,i.e.that some instances must appear in the same cluster(“Must-Link”constraints)or in separate clausters(“Cannot-Link”constraints)[2].There are two approaches for constraint enforcement.In thefirst one,the objective function is modified into one that satisfies as many constraints as possible[2,10,11,3,5]. In the second one,sometimes called“distance-based”,the algorithm is trained on the data involved in constraints,learns a new metric and uses it for clustering[12,13,14].A challenging aspect is the interplay between achieving a feasible solution(i.e.en-suring convergence)and satisfying all constraints.Davidson et al have proven in[3]that the satisfaction of all Must-Link and Cannot-Link constraints when clustering with K-means is an NP-complete problem;Cannot-Link constraints may prevent the algorithm from converging.When hierarchical clustering is used instead,constraint satisfaction becomes a P-complete problem[5].In this study,we enhance a density-based algo-rithm with constraints,i.e.an algorithm that focusses on local optima,similarly to a hierarchical algorithm.This allows us to build clusters that satisfy all constraints.A number of successful density-based clustering algorithms can be found in the lit-erature,starting with DBSCAN in1996[6].DBSCAN has been designed for large and noisy datasets and is able to discover clusters of arbitrary shapes:DBSCAN introduced218 C.Ruiz,M.Spiliopoulou,and E.Menasalvasthe concept of“neighbourhood”as a region of given radius(i.e.a sphere)and containing a minimum number of data points.Connected neighbourhoods form clusters,thus de-parting from the notion of spherical cluster[6].The idea of dense neighbourhood has inspired further research on density-based clustering algorithms,including[15,16,17]. In this study,we have opted for the DBSCAN as a reference representative.3Instance-Level Constraints for Density-Based ClusteringOur constraint-based algorithm builds upon DBSCAN[6].DBSCAN identifies neigh-bourhoods around core points,i.e.points having at least MinPts neighbours within a radius E ps.Points within the same neighbourhood are density-reachable,those in overlapping neighbourhoods are density-connected.A cluster is a maximal group of overlapping neighbourhoods.C-DBSCAN extends DBSCAN in three steps:Wefirst apply a KD-Tree[18]to divide the data space into dense partitions,similarly to DESCRY[17].We enforce Cannot-Link constraints within each tree leaf,thus producing“local clusters”.Next, we merge adjacent local clusters,thereby enforcing the Must-Link constraints.Finally, we merge adjacent clusters hierarchically,while enforcing the remaining Cannot-Link constraints.3.1Partitioning the Data SpaceFor the partitioning step(cf.Algorithm1),we use the KD-Tree construction algorithm [18],which divides the data space iteratively into cubes by splitting planes that are perpendicular to the axes.Each cube becomes a node and is further partitioned,as long as it contains a minimum number of data points(the MinPts threshold of DBSCAN). The result is an unbalanced tree:small leaves capture locally dense subareas while large ones cover the less dense subareas.With this partitioning,thin bridges between dense subareas are avoided.Instead of connecting arbitrary adjacent neighbourhoods to build clusters,only neighbourhoods within the same node are considered atfirst.They are merged into“local clusters”,subject to the instance-level concstraints described below.3.2Introducing Instance-Level ConstraintsC-DBSCAN supports two types of constraints among data instances/points:A Must-Link constraint for the data points x and y states that they must be assigned to the same cluster.A Cannot-Link constraint states that they must be assigned to different clusters. Creating Local Clusters under Cannot-Link Constraints.Step2of C-DBSCAN(cf.Al-gorithm1)groups density-reachable points into“local clusters”while enforcing Cannot-Link constraints.The leaf nodes of the KD-Tree are traversed:If there is a Cannot-Link constraint involving data points within the same leaf,then each data point of the leaf becomes a singleton local cluster.If there is no Cannot-Link constraints, the conventional DBSCAN is invoked for each data point p in the leaf:It is checked whether there is a neighbourhood with at least MinPts points in a radius E ps around p.C-DBSCAN:Density-Based Clustering with Constraints219Algorithm1.C-DBSCANData:A set of instances,D.A set of must-link constraints,ML,and a set of cannot-link constraints,CL.Result:The set D partitioned into clusters that satisfy ML and CL.beginStep1:Partitioning the data space.kdtree:=BuildKDTree(D).Step2:Creating local clusters under Cannot-Link constraints.repeatfor(all unlabeled points in a leaf X)doSelect an arbitrary point p i from X.X pi ←all points in X that are within Eps radius of p i.if(X pi contains less than MinPts points)thenLabel p i as NOISE.else if(exists a Cannot-Link constraint in CL among points in X pi )thenCreate a local cluster for each point in X.Break.elseLabel p i as bel X pias LOCAL CLUSTER.until(all leaves of the kdtree have been processed)Step3a:Merging local clusters under Must-Link constraints.for(each constraint m∈ML)doJoin clusters involved in constraint m into cluster Y.Label Y as CORE LOCAL CLUSTER.Step3b:Merging clusters under Cannot-Link constraints.for(each core(local)cluster Y)dowhile(number of local clusters NLC decreases)doclosestCluster←closest local cluster to Y.if( Cannot-Link constraint in CL between points of Y and closestCluster)thenY←Y∪bel Y as CORE CLUSTER.NLC-=1.endIf the neighbourhood has too few points,then p is a noise point and is ignored.Oth-erwise,all data points that are density-reachable from it become members of the same local cluster.Merging Local Clusters under Must-Link Constraints.Must-Link constraints are en-forced in Step3a(cf.Algorithm1).If the data points involved in a Must-Link constraint belong to different local clusters,the clusters are merged into a“core local cluster”.At the end of Step3a,points that should appear together belong either to the same core lo-cal cluster(by constraint enforcement)or are already members of the same local cluster –one of the data points is a core point and the other is density-reachable from it. Merging Clusters under Cannot-Link Constraints.In Step3b(cf.Algorithm1),we further merge local clusters(also:singleton local clusters and core local clusters output220 C.Ruiz,M.Spiliopoulou,and E.Menasalvasby Step3a)to enforce Cannot-Link constraints that are not satisfied yet.For cluster merging,we use hierarchical agglomerative clustering with single linkage,but only consider density-reachable data points when we compute distances.Moreover,we let the core local clusters drive the merging process,in the sense that we do not consider arbitrary clusters as candidates but only the local clusters that are close to each core local cluster.For each such pair of candidates,we check whether they contain data points involved in a Cannot-Link constraint.If this is the case,the clusters are not merged.The algorithm stops when the number of clusters does not change any more. Discussion on Constraint Enforcement.Most constraint-based clustering algorithms make a best effort to enforce all constraints.C-DBSCAN ensures that all constraints are satisfied:Step3a enforces all Must-Link constraints;Step2enforces Cannot-Link constraints within the same KD-tree node;Step3b enforces the remaining Cannot-Link constraints by preventing the merging of clusters.This is achieved at the cost of building many small clusters,since each Cannot-Link constraint results in a singleton local cluster.We believe that some of those singleton clusters can be merged with other ones without constraint violation,so we intend to work on heuristics to this purpose. 4Experimental ResultsWe have studied the impact of constraints on the clustering results by applying C-DBSCAN and the original DBSCAN on four artificial and three real datasets with a priori known clusters.The artificial datasets contain data,for which DBSCAN is known to perform poorly(cf.Section1and Fig.1).The real datasets are from the Ma-chine Learning Repository UCI[19].They are depicted in Fig.2and summarized in Table1.In a real scenario,constraints are derived by studying a small subset of the data;they are the result of human insight.Our datasets do not contain such constraints,so we have generated some randomly.We show that even random constraints do increase cluster quality.For each dataset,we have generated a percentage x%=5%,10%,15%...100% of records involved in Must-Link constraints.The Cannot-Link constraints were derived from the Must-Link constraints and are thus interdependent.However,this only means that the percentage of independent constraints is smaller than x%.4.1Evaluation methodThe datasets we use are labeled,so we can compute cluster quality towards the known classes.For this,we use the Rand Index measure[22],which takes as input twoTable1.Data sets used in the experimentsArtificial data sets Real data setsDS1(2classes,bridge between clusters)Iris[19](3classes,2overlapped)DS2(3classes,2overlapped,bridge)Cure[20](5classes,4overlapped,2by2) DS3(2classes,bridge)Chameleon[21](2classes,bridge)DS4(7gaussian clusters,4overlapped,2by2,bridge,different notions of densityC-DBSCAN:Density-Based Clustering with Constraints 221Fig.2.(a)IRIS (b)CURE (c)CHAMELEONpartitionings ζ1and ζ2,computes the number of “agreements”and “disagreements”among them,and takes the highest value 1if the partitionings are identical.The “agree-ments”are the number a of data points that appear together in the same partition for both ζ1and in ζ2plus the number b of data points that appear in di fferent partition for both ζ1and ζ2.The “disagreements”are the number c of data points that appear in the same partition of ζ1and in di fferent partitions of ζ2plus the number d of data points that appear in the same partition of ζ2and in di fferent partitions of ζ1.Then:Rand (ζ1,ζ2)=agreements agreements +disagreements =a +b a +b +c +d4.2Results Using Artificial and Known Data SetsWe show the performance of C-DBSCAN for the artificial datasets DS1,...,DS4in Fig.3and for the datasets IRIS,CURE and CHAMELEON in Fig.4.In both figures,the horizontal axis depicts the percentage of data points involved in constraints.The vertical axis shows the Rand Index value of each clustering towards the classes (the true partitioning).The Rand Index for DBSCAN is constant.We have placed this value at point Zero of the axes:Deviations from this point reflect the impact of the con-straints.The curves show that C-DBSCAN improves DBSCAN and achieves very good partitionings,reaching RandIndex values of more than 0.8for all datasets.We see that a small number of arbitrary,labeled records su ffices to guide C-DBSCAN towards a good partitioning and that no more constraints are necessary (saturation at 10%).This result strengthens the findings of [2,10]that a small amount of domain information is su fficient to achieve high performance.Fig.3.Rand Index values for C-DBSCAN with di fferent constraint-sets -Artificial datasets222 C.Ruiz,M.Spiliopoulou,and E.MenasalvasFig.4.Rand Index values for C-DBSCAN with different constraint-sets-Real datasets5ConclusionsConstraint-based clustering methods exploit background knowledge to guide the group-ing of data into clusters.We have presented C-DBSCAN,a constraint-based extension of the density-based algorithm DBSCAN[6].C-DBSCAN enforces Must-Link and Cannot-Link constraints among data points and,Differently from best-effort constraint-based clustering algorithms,it guarantees that all constraints are satisfied.Ourfirst experiments show that even constraints improve the clustering quality substantially,no-tably on datasets where the original DBSCAN performs poorly.We have observed that few constraints suffice to improve quality.We intend to study next the impact of constraint type(Must-Link vs Cannot-Link)on quality and the in-terplay of constraint type and number of constraints,using larger and more complex datasets.Further,we want to design heuristics that minimize the number of singleton clusters built by C-DBSCAN by merging clusters,while still satisfying all constraints.A direct comparison of C-DBSCAN to other algorithms,like constraint-based K-means,would not be informative,since the relative behaviour of the basic algorithms for different data distributions is already well studied.However,we plan to study whether C-DBSCAN exploits constraints more effectively than other constraint-based algorithms.References1.Kopanas,I.,Avouris,N.M.,Daskalaki,S.:The Role of Domain Knowledge in a Large ScaleData Mining Projects.In:SETN’02:Proc.of the Methods and Applications of Artificial Intelligence,Second Hellenic Conf.on AI.V olume2308of LNCS,Springer.(2002)2.Wagstaff,K.,Cardie,C.,Rogers,S.,Schroedl,S.:Constrained K-means Clustering withBackground Knowledge.In:ICML’01:Proc.of18th Int.Conf.on Machine Learning.(2001) 577–5843.Davidson,I.,Ravi,S.S.:Clustering with Constraints:Feasibility 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numpy 数值归一化的方法## Navigating the Landscape of NumPy Normalization Ah, NumPy normalization –a cornerstone of data preprocessing in the realm of machine learning and data science. It's like preparing a canvas before painting a masterpiece, ensuring that our data is well-balanced and ready for the algorithms to work their magic. And just like there are various artistic styles, NumPy offers a diverse palette of normalization techniques, each with its own nuances and applications. One of the most common methods is **min-max scaling**, which elegantly transforms our data to fit within a specific range, typically between 0 and 1. It's like taking a hike in the mountains and scaling the heights to a comfortable level ground. This technique is particularly useful when dealing with algorithms sensitive to the scale of features, such as k-nearest neighbors or support vector machines. But sometimes, we might encounter treacherous outliers in our data – those extreme values that can skew the entire picture. In such cases, **standardization** comes to the rescue. This method, also known as Z-score normalization, centers the data around zero and scales it based on the standard deviation. It's like bringing order to a bustling marketplace, ensuring that every voice is heard equally, regardless of its initial volume. Standardization is a popular choice for algorithms like linear regression and principal component analysis, which thrive on data with a mean of zero and unit variance. Now, imagine we have data points scattered across a vast expanse, forming clusters of varying densities. This is where **L1 and L2 normalization** step in, like cartographers mapping uncharted territories. L1 normalization, also known as Manhattan normalization, scales features based on the sum of their absolute values, while L2 normalization, or Euclidean normalization, considers the square root of the sum of squared values. These methods are particularly handy when dealing with sparse data or when we want to emphasize the direction of the data points rather than their magnitudes. Of course, our journey doesn't end here. We have **max normalization**, which scales features based on their maximum absolute value, bringing them within the range of -1 and 1. This technique is particularly useful when we want to preserve the relationships between features while ensuring they fall within a specific range. And for situations where we need to downplay the influence of extreme values whilemaintaining the overall distribution, we have **robust scaling**, a technique based on percentiles that proves resilient to outliers. Choosing the right normalization technique is akin to selecting the perfect brushstroke for your painting. It depends on the nature of your data, the algorithms you're using, and the specific goals you want to achieve. Each method has its strengths and weaknesses, and understanding these nuances is key to unlocking the full potential of your data analysis. So, as you embark on your data exploration journey, remember that the art of normalization is a valuable tool in your arsenal, enabling you to transform raw data into insightful masterpieces.。

SPSS（统计）名词解释2007-11-13 16:29:16| 分类：学习| 标签：|举报|字号大中小订阅Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型Arcing, 弧/弧旋Arcsine transformation, 反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP 统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法/Duncan新法Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数标准Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换文案。

形式与功能：走线amrish穆克，妮可斯塔尔，塔伦电影2008年11月18日1摘要艺术四是一个空间，是受几个相互竞争的利益。

它的设计是期望提供的机会，为个人移动方便从一头到另一头，保持一般维修费用是可行的和允许的活动范围从讲座，打雪仗。

本文提出了一个数学模型，提供了一种智能设计四路网络。

我们的核心模型是一个成本函数，其中评价可行性的一个给定的路径配置。

探索一套可行的路径配置我们写一个算法，随机生成样品本集。

然后在此基础上改进的搜索通过构建一个优化算法灵感来自马尔可夫链蒙特卡洛方法。

我们相信，这一改进的搜索找到一个地方最小路径配置，因为它似乎稳定摄动下。

2内容我问题的声明4二艺术四边形为图4三路径长度6四非正式路径诱导人的行为7五成本函数8六假设：9七算法寻找最优路径配置9八结果：10九推荐方案11未来工作15×西安书目163第一部分问题陈述我们的任务是重新设计艺术四通道使用一个数学模型，将帮助我们确定一个首选的设计。

除了一般的事实，尽量减少总长度的路径和最大限度的地区连续的草坪是可取的，我们要求道路维修成本是成正比的，道路总长度。

_美化成本取决于一些连续的草坪，创造了非官方的路径（因行人离开铺设路径到达目的地迅速）和几何连续的草坪。

_如果两点之间的路径是15%长于直线的点线连接，一行人离开道路，跨越四。

_平均步行可能离开的路径，如果它意味着节省10%以上的总长度的路径。

第二部分艺术作为一个图图论是一个重要的工具，在探索的问题，尽量减少总长度的路径和最大限度的地区连续的草坪是可取的，我们要求其范围从确定神经网络的线虫线虫发现失败的原因在电力grids1。

通过制定我们的走道设计问题的语言，我们可以很容易地提取关键结构和功能之间的关系。

我们描述的艺术四边形（现称为艺术四或简单的四）作为一个图的10个节点，这是最常见的入境和出境点的四（见下面的图1）。

看[ 1 ]4图1：康奈尔艺术四让节点集是一个=集合的。

样条插值法自适应滤波English:Spline interpolation is a widely used method for filling in missing or noisy data points in a dataset. It involves fitting a smooth curve or spline to the given data points in order to estimate the values at the missing or noisy points. However, standard spline interpolation techniques do not always produce satisfactory results, especially when dealing with datasets that have irregular or non-uniform sampling intervals. In such cases, adaptive filtering techniques can be employed to improve the accuracy of the spline interpolation.Adaptive filtering in spline interpolation involves adjusting the parameters of the fitting algorithm based on the characteristics of the dataset. One approach is to vary the degree of the spline based on the local density of data points. For regions with densely spaced data points, a higher degree spline can be used to capture the finer details and provide a more accurate estimation. Conversely, for regions with sparser data points, a lower degree spline can be employed to avoid overfitting. This adaptability allows the spline interpolation to better handle datasets with varying data densities.Another aspect of adaptive filtering in spline interpolation is the consideration of noise levels in the data. Noisy data points can significantly impact the accuracy of the interpolation. Therefore, it is necessary to detect and filter out the noise before performing the spline interpolation. This can be achieved by employing noise detection algorithms, such as the use of statistical measures like mean, standard deviation, or median absolute deviation. Once the noisy points have been identified, they can either be removed or replaced with more reliable estimates, such as the average of nearby points. This preprocessing step helps to reduce the impact of noise on the spline interpolation results.To summarize, adaptive filtering in spline interpolation improves the accuracy of the interpolation by adjusting the parameters based on the local data density and considering the noise levels in the dataset. This approach allows the spline interpolation to adapt to irregular or non-uniformly sampled data and provides more reliable estimates at missing or noisy data points.中文翻译:样条插值法是一种广泛应用于填补数据集中缺失或噪声数据点的方法。

2021年2月图 学 学 报 February2021第42卷第1期JOURNAL OF GRAPHICS V ol.42No.1融合稀疏点云补全的3D目标检测算法徐晨1,2，倪蓉蓉1,2，赵耀1,2(1. 北京交通大学信息科学研究所，北京 100044；2. 现代信息科学与网络技术北京市重点实验室，北京 100044)摘要：基于雷达点云的3D目标检测方法有效地解决了RGB图像的2D目标检测易受光照、天气等因素影响的问题。

但由于雷达的分辨率以及扫描距离等问题，激光雷达采集到的点云往往是稀疏的，这将会影响3D目标检测精度。

针对这个问题，提出一种融合稀疏点云补全的目标检测算法，采用编码、解码机制构建点云补全网络，由输入的部分稀疏点云生成完整的密集点云，根据级联解码方式的特性，定义了一个新的复合损失函数。

除了原有的折叠解码阶段的损失之外，还增加了全连接解码阶段存在的损失，以保证解码网络的总体误差最小，从而使得点云补全网络生成信息更完整的密集点云Y detail，并将补全的点云应用到3D目标检测任务中。

实验结果表明，该算法能够很好地将KITTI数据集中稀疏的汽车点云补全，并且有效地提升目标检测的精度，特别是针对中等和困难等级的数据效果更佳，提升幅度分别达到6.81%和9.29%。

关键词：目标检测；雷达点云；点云补全；复合损失函数；KITTI中图分类号：TP 391 DOI：10.11996/JG.j.2095-302X.2021010037文献标识码：A 文章编号：2095-302X(2021)01-0037-073D object detection algorithm combined with sparse point cloud completionXU Chen1,2, NI Rong-rong1,2, ZHAO Yao1,2(1. Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China;2. Beijing Key Laboratory of Modern Information Science and Network Technology, Beijing 100044, China)Abstract: The 3D object detection method based on radar point cloud effectively solves the problem that the 2D object detection based on RGB images is easily affected by such factors as light and weather. However, due to such issues as radar resolution and scanning distance, the point clouds collected by lidar are often sparse, which will undermine the accuracy of 3D object detection. To address this problem, an object detection algorithm fused with sparse point cloud completion was proposed. A point cloud completion network was constructed using encoding and decoding mechanisms. A complete dense point cloud was generated from the input partial sparse point cloud.According to the characteristics of the cascade decoder method, a new composite loss function was defined. In addition to the loss in the original folding-based decoder stage, the compound loss function also added the loss in the fully connected decoder stage to ensure that the total error of the decoder network was minimized. Thus, the收稿日期：2020-05-27；定稿日期：2020-08-28Received：27 May，2020；Finalized：28 August，2020基金项目：国家重点研发计划项目(2018YFB1201601)；国家自然科学基金项目(61672090)；中央高校基本科研业务费专项资金(2018JBZ001) Foundation items：National Key Research and Development Program (2018YFB1201601); National Natural Science Foundation of China (61672090);Special Fund for Fundamental Research Funds for Central Universities (2018JBZ001)第一作者：徐晨(1995–)，男，河北张家口人，硕士研究生。

小学上册英语第二单元期末试卷(含答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.Which of these is a popular fruit?A. SpinachB. CarrotC. StrawberryD. Broccoli答案:C2.Which animal is known for its ability to fly?A. DogB. BirdC. FishD. Lion答案:B Bird3.I like to ___ (explore/hike) in the woods.4.The _____ (食物链) starts with plants as producers.5.What do we call the fluffy white substance that falls from the sky in winter?A. RainB. HailC. SnowD. Sleet答案: C6._____ (perennial) flowers return each spring.7.What animal is known as the king of the jungle?A. TigerB. LionC. BearD. Elephant答案:B8.The process of separating mixtures based on boiling points is called ______.9.The ______ is known for his inventions.10.My ________ (玩具名称) helps me learn numbers.11.My dad is a very _______ (形容词) person. 他总是 _______ (动词).12.The __________ (十字军东征) were a series of religious wars in the Middle Ages.13. A reaction that requires a catalyst is called a ______ reaction.14.I enjoy helping my parents cook dinner on ______ (周末).15.The reaction between an acid and a base produces ______.16.The turtle is very ___ (slow).17.The candy is very ___ (sweet/sour).18.I enjoy watching _____ fly in the sky.19.The city of Cairo is located near the _______.20.What do we call a person who plays a musical instrument?A. PerformerB. MusicianC. ComposerD. Conductor答案:B21.My _____ (老师) shows us how to care for plants in class. 我的老师在课堂上教我们如何照顾植物。

折线统计图的英语作文Line Graphs: A Visual Representation of Time-Series Data.In the realm of data visualization, line graphs emerge as a powerful tool for showcasing the evolution of data points over time. Their simple yet effective design allows viewers to quickly discern trends, patterns, and relationships within a time-series dataset.Structure and Elements of a Line Graph.A line graph comprises the following key elements:X-axis (Horizontal Axis): Represents the independent variable, typically representing time.Y-axis (Vertical Axis): Represents the dependent variable, indicating the data values being plotted.Data Points: Individual data values plotted on the graph as points or symbols (e.g., circles, squares, triangles).Line: Connects the data points to form a continuous line, depicting the trend of the data over time.Types of Line Graphs.Line graphs can be classified based on the nature of the data and the purpose of the visualization:Simple Line Graph: Represents a single time-series dataset.Multi-Series Line Graph: Compares multiple time-series datasets on the same graph.Stacked Line Graph: Visualizes the cumulative contribution of different categories or components within a single time-series dataset.Smoothed Line Graph: Uses mathematical techniques to smooth out fluctuations and highlight the overall trend of the data.Creating an Effective Line Graph.Effective line graphs adhere to the following principles:Clear and concise: Use a straightforward design with minimal distractions.Accurate and reliable: Ensure that the data points and line representation accurately reflect the underlying data.Appropriate scale: Choose a scale that allows for easy comparison and interpretation of the data values.Relevant labels: Provide clear labels for both axes and any additional elements on the graph.Meaningful colors: Use colors that differentiatebetween different data series or categories, enhancing readability.Contextual information: Include a title and any necessary annotations to provide context for the graph.Applications of Line Graphs.Line graphs find widespread use in various fields, including:Economics: Tracking economic indicators such as GDP, unemployment rates, and stock prices.Science: Visualizing the results of experiments, such as changes in temperature, concentration, or reaction rates over time.Healthcare: Monitoring patient data, such as temperature, heart rate, and medication effectiveness.Marketing: Analyzing sales trends, customer engagement,and campaign performance.Education: Illustrating historical events, scientific concepts, and the progression of knowledge.Advantages and Limitations of Line Graphs.Advantages:Easy to understand and interpret.Effective for visualizing trends and patterns over time.Comparatively less complex to create than other types of graphs.Limitations:Limited in their ability to show complex relationships or multiple dimensions of data.Can be misleading if the data points are too sparse or the time interval is too large.May not be suitable for datasets with high volatility or numerous data points.Conclusion.Line graphs remain a versatile and essential tool for visualizing and analyzing time-series data. Theirsimplicity and effectiveness make them accessible to a wide audience, allowing for the quick identification of trends and patterns. By adhering to best practices and considering the appropriate type of line graph, users can harness the power of line graphs to effectively communicate their data insights.。

全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：英语作文让真情自然流露关于王鹤棣的故事全文共3篇示例，供读者参考篇1The Inspiring Story of Wang Hedi: A Tale of Resilience and HopeAs a student, I have often found solace and motivation in the stories of individuals who have overcome incredible adversities.One such tale that has profoundly impacted me is the remarkable journey of Wang Hedi, a Chinese woman whose unwavering spirit and determination in the face of unimaginable challenges have left an indelible mark on my soul.Born in a small village in Shandong Province, Wang Hedi's life was far from ordinary. At the tender age of 24, she suffered a devastating spinal cord injury that left her paralyzed from the neck down. In an instant, her world turned upside down, and the dreams she had nurtured for a lifetime seemed to shatter around her.Yet, despite the overwhelming odds, Wang Hedi refused to surrender. Her indomitable spirit and an unquenchable thirst for life fueled her every step, even when those steps were confined to the boundaries of her wheelchair. With unwavering determination, she embarked on a journey of self-discovery, realizing that her disability did not define her worth or limit her potential.As I delved deeper into Wang Hedi's story, I found myself in awe of her resilience. Undeterred by her physical limitations, she pursued her passion for education, ultimately earning a bachelor's degree in computer science. Her academic achievements were a testament to the power of the human mindand the inextinguishable flame of ambition that burned within her.But Wang Hedi's journey did not end there. Driven by a desire to inspire others and contribute to society, she embarked on a career as a motivational speaker and writer. With her words, she touched countless lives, challenging societal perceptions of disability and encouraging others to embrace their unique strengths and overcome their limitations.One aspect of Wang Hedi's story that particularly resonated with me was her unyielding optimism in the face of adversity. Despite the countless obstacles that life threw her way, she maintained a positive outlook and an infectious enthusiasm that inspired all who crossed her path. Her smile, radiant and genuine, was a beacon of hope, reminding us that true joy and fulfillment can transcend even the most daunting of circumstances.As a student grappling with the pressures of academic life and the uncertainties of the future, Wang Hedi's story has been a constant source of inspiration. Her unwavering determination to pursue her dreams, regardless of the challenges, has taught me the value of perseverance and the importance of never giving up.Through her actions and her words, Wang Hedi has conveyed a powerful message: that our limitations are oftenself-imposed, and that our true strength lies in our ability to embrace our challenges and use them as stepping stones towards growth and self-discovery.In the midst of my own struggles, I often find myself reflecting on Wang Hedi's extraordinary journey. Her story has instilled in me a newfound appreciation for the gift of life and the boundless potential that lies within each of us, waiting to be unleashed.As I continue to navigate the winding paths of my academic and personal life, Wang Hedi's story will remain a guiding light, reminding me that true greatness is not measured by our physical abilities or the circumstances we are born into, but by the courage and resilience we display in the face of adversity.In a world that often emphasizes external markers of success, Wang Hedi's tale serves as a powerful reminder that true triumph lies in the unconquerable spirit within us – a spirit that transcends physical limitations and transforms every obstacle into an opportunity for growth and self-discovery.Wang Hedi's story is not merely a narrative of one woman's triumph over adversity; it is a testament to the indomitable human spirit, a celebration ofthe resilience that resides within each of us, and a clarion call to embrace our challenges and forge our own paths towards personal fulfillment and societal impact.As I reflect on her journey, I am filled with a profound sense of gratitude and inspiration. Gratitude for the countless individuals like Wang Hedi who have paved the way for others, and inspiration to embrace my own challenges with unwavering determination and an unshakable belief in my ability to make a positive difference in the world.Wang Hedi's story is a gift, a beacon of hope that illuminates the boundless potential within us all. It is a reminder that our circumstances do not define our destiny, and that true greatness lies in the resilience of the human spirit. As I embark on my own journey, I carry her tale with me, a constant companion that inspires me to dream bigger, persevere harder, and embrace the challenges that life presents as opportunities for growth and self-discovery.In the end, Wang Hedi's story is not just her own; it is a universal narrative of hope, courage, and the inextinguishable flame of the human spirit. It is a tale that transcends borders and cultures, touching the hearts and minds of all who bear witness to its power. And for me, as a student navigating thecomplexities of life, it serves as a constant reminder that our true potential is limitless, and that the path to greatness begins with the courage to embrace our challenges and the determination to forge our own destinies.篇2The Name That Sparked My JourneyWang Hedi. A simple name, but one that has profound meaning for me and my pursuit of understanding the human experience through the lens of history. This ordinary-sounding name first reached my ears in a rather underwhelming way - just a brief mention by my high school history teacher as we rushed through the modern era in our textbook. But those two words, casually uttered, awakened something inside me that has driven my academic path ever since.You see, Wang Hedi was a young woman, just a girl really, who got caught up in the tumultuous events of the Cultural Revolution in 1960s China. From the sparse details provided, she was persecuted and ultimately executed by the revoluionary authorities, punished for merely being a member of the urban intelligentsia class. A mind filled with potential and dreams, snuffed out for no justifiable reason. I remember feeling astartling sense of injustice and sadness upon hearing her name and fate, even though it was relayed so matter-of-factly by my teacher before we moved on to the next topic.In that fleeting moment, Wang Hedi became more than just a random name or vague statistic - she represented the many individuals whose lives were forever altered or ended during such turbulent periods in history, when ideological fervor outweighed human reason and decency. I couldn't shake the thought of who she was as a person - her hopes, her fears, her loved ones. What did her smile look like? What dreams did she have for the future? All that human potential, just...gone.From then on, I became somewhat obsessed with learning more about Wang Hedi and the Cultural Revolution in an effort to better understand how such tragedies could occur. I pored over books, essays, documentaries - anything that could provide more context around this brief life that had touched me so deeply. The more I learned, the more I understood how complex historical events and societal shifts can be, with a multitude of perspectives and human stories underlying the broad strokes of the past that we too often take at face value.My quest to truly know Wang Hedi's narrative unlocked a passion for giving a voice to those who had theirs permanentlysilenced. I found myself drawn to analyzing human rights movements, revolutions, and conflicts throughout history - not just reciting facts and dates, but striving to capture the profoundly personal impacts on the individuals caught up in the churn of those events. Every name, every person, had a rich life story to illuminate.As I progressed through my studies, diving deeper into 20th century Chinese history and the socio-political forces that led to the Cultural Revolution, Wang Hedi's name remained my talisman. When I would get bogged down in dense academic texts, I would refocus by asking myself - what would Wang Hedi, that passionate young woman with so much unrealized potential, want us to understand? How could I amplify her perspective and those of the innocents like her? It drove me to always strive for a more nuanced, humane understanding of the past and present.Even now, as I prepare to enter my PhD program focused on East Asian cultural studies, the mere utterance of "Wang Hedi" fills me with a sense of purpose and responsibility. While I will never truly know the specific details of her life, she has become emblematic of the millions throughout history who suffered unjustly at the hands of oppressive regimes, cultural purges, and unchecked abuses of power and ideology.In my studies and writings, I aim to shed light on the stories of those like Wang Hedi - the marginalized voices, the persecuted innocents, the ones whose human experiences risk being flattened and simplified into mere statistics and footnotes.I will continue asking the questions she can no longer ask and striving to understand all the nuances and complex contexts that led to her untimely demise. Her name compels me to empathize, to humanize, to never treat past events and human lives as emotionless data points.Ultimately, Wang Hedi's story, her very name, taught me that genuine understanding of history stems from fully connecting to the personal journeys underlying those broad narratives. The human experience, in all its complicated beauty and tragedy, must be the beating heart driving our intellectual pursuits into the past. Only through developing such empathetic frameworks can we aspire to build a better future - one where innocent dreamers like Wang Hedi are never persecuted for who they are, but rather are celebrated for their hopes, their potential, their very humanity.So while her journey was mercilessly cut short, Wang Hedi's legacy endures through the immense impact her name had in sparking my path as a student of the human spirit through thelens of history. With every analysis, every paragraph, every lecture I give, I strive to honor the individual lives, stories, and truths that lie beyond just the names and dates. Wang Hedi's dying words may have been silenced, but I will ensure her voice echoes through my life's work of amplifying the human experience woven through our collective past.篇3My Encounter with Wang Hedi - A Story of InspirationAs students, we often find ourselves caught up in the whirlwind of academic demands, extracurricular activities, and the pressures of everyday life. It's easy to become consumed by the pursuit of success, losing sight of the essence of what truly matters. However, my encounter with Wang Hedi, a remarkable individual, taught me a profound lesson about the power of resilience, compassion, and the indomitable human spirit.It was a crisp autumn day when our class was scheduled for a field trip to a local community center. Little did I know that this ordinary outing would profoundly impact my perspective on life. Upon arriving, we were greeted by the warm smiles of the center's staff and introduced to their special guest speaker –Wang Hedi.At first glance, Wang Hedi appeared like any other elderly woman, her face etched with the lines of a lifetime of experiences. However, as she began to share her story, a captivating aura enveloped the room, and we were all instantly transfixed.Wang Hedi recounted her harrowing experiences during the tumultuous years of World War II. Born into a humble family in a small village, she witnessed firsthand the devastation and suffering that war can bring. Her voice wavered as she described the loss of her parents and the constant fear that plagued her childhood. Despite the weight of her circumstances, she persevered, her determination fueled by an unwavering desire to survive and create a better future for herself.As she spoke, I found myself drawn into her narrative, my heart swelling with admiration for her courage and resilience. In the face of unimaginable adversity, Wang Hedi chose to embrace hope, refusing to let the darkness of her past define her. She emphasized the importance of education, which became her beacon of light, guiding her towards a path of personal growth and empowerment.With unwavering determination, Wang Hedi pursued her studies, often in secret and under the constant threat of discovery. She spoke of the countless sacrifices she made,working tirelessly to support herself while continuing her education. Her eyes sparkled as she recounted the joy she felt upon receiving her hard-earned diploma, a symbol of her triumph over the challenges that had once seemed insurmountable.But Wang Hedi's story did not end there. She went on to become a teacher, dedicating her life to imparting knowledge and instilling values of compassion and perseverance in the younger generation. Her gentle demeanor and infectious positivity touched the lives of countless students, inspiring them to chase their dreams and never give up, no matter the obstacles.As her captivating tale drew to a close, a profound silence fell over the room. We were all left in awe, our perspectives forever altered by the depth of her experiences and the resilience she embodied.In that moment, I realized the true power of the human spirit – the ability to rise above adversity, to find strength in the face of insurmountable odds, and to use one's experiences as a catalyst for positive change. Wang Hedi's story was a testament to the transformative impact that a single life can have, a reminder that even in the darkest of times, hope can prevail.As I reflected on her words, I couldn't help but feel a profound sense of gratitude for the sacrifices made by those who came before us. Their struggles paved the way for the freedoms and opportunities we enjoy today. Wang Hedi's unwavering determination to pursue education, despite the risks, resonated deeply with me, reminding me of the privilege I have to learn and grow without fear.Her message transcended the confines of her personal narrative, becoming a call to action for all of us. She encouraged us to embrace empathy, to stand against injustice, and to use our voices to create positive change in the world around us. Her unwavering belief in the power of education inspired me to approach my studies with renewed vigor, recognizing the transformative potential that knowledge holds.As I left the community center that day, I carried with me a newfound appreciation for the resilience of the human spirit and the profound impact that a single life can have. Wang Hedi's story had become a guiding light, reminding me to never take the privileges I enjoy for granted and to use my education as a tool to make a positive difference in the world.In the months and years that followed, I found myself drawn to stories of resilience and perseverance, seeking inspirationfrom the lives of those who had overcome incredible odds. I developed a deeper empathy for those who had endured hardships, and a burning desire to use my knowledge and skills to create positive change.Wang Hedi's story has become a permanent part of my journey, a constant reminder of the power of hope, determination, and the indomitable human spirit. Her unwavering courage in the face of adversity continues to inspire me, fueling my passion for learning and driving me to make a meaningful impact on the world around me.As I embark on the next chapter of my life, I carry with me the lessons learned from Wang Hedi's remarkable tale. Her story has taught me that even in the darkest of times, the human spirit can persevere, and that education is a powerful tool for personal growth and positive change. I am forever grateful for the opportunity to have encountered such an extraordinary individual, whose life has left an indelible mark on my soul.。

ｄｏｉ：１０．３９６９／ｊ．ｉｓｓｎ．１００３－３１０６．２０２４．０２．０２４引用格式：张清宇，崔丽珍，李敏超，等．倾斜地面３Ｄ点云快速分割算法［Ｊ］．无线电工程，２０２４，５４（２）：４４７－４５６．［ＺＨＡＮＧＱｉｎｇｙｕ，ＣＵＩＬｉｚｈｅｎ，ＬＩＭｉｎｃｈａｏ，ｅｔａｌ．ＡＦａｓｔＳｅｇｍｅｎｔａｔｉｏｎＡｌｇｏｒｉｔｈｍｆｏｒ３ＤＰｏｉｎｔＣｌｏｕｄｏｎＩｎｃｌｉｎｅｄＧｒｏｕｎｄ［Ｊ］．ＲａｄｉｏＥｎｇｉｎｅｅｒｉｎｇ，２０２４，５４（２）：４４７－４５６．］倾斜地面３Ｄ点云快速分割算法张清宇，崔丽珍，李敏超，马宝良（内蒙古科技大学信息工程学院，内蒙古包头０１４０１０）摘　要：依赖于平面拟合或局部几何特征区分地面障碍物的方法广泛应用于自动驾驶领域，但是在具有倾斜地形或稀疏数据的情况下，性能会降低。

在倾斜地形场景中，利用激光雷达（ＬｉＤＡＲ）提供的点云数据，通过地面点云的３Ｄ投影与直线拟合，利用栅格地图方法降低计算复杂度，实现地面点云的分割。

针对非地面的点云集合，利用ＳＬＲ聚类算法处理，通过设定强度特征阈值在垂直方向区分地面点与非地面点，并对扫描到的障碍物地面分类。

通过实验分析，提出的算法较其他地面点云分割算法，一方面在倾斜地形上具有更好的建图效果，另一方面ＳＬＲ聚类算法处理后的强度特征在Ｘ、Ｙ、Ｚ三个方向覆盖范围更精确，如在Ｘ方向相较于快速地面分割算法平均提高了４４．０％，相较于添加了栅格地图的算法平均提高了４０．１％。

关键词：倾斜地面；激光雷达；点云分割；栅格地图；聚类中图分类号：ＴＮ９５文献标志码：Ａ开放科学（资源服务）标识码（ＯＳＩＤ）：文章编号：１００３－３１０６（２０２４）０２－０４４７－１０ＡＦａｓｔＳｅｇｍｅｎｔａｔｉｏｎＡｌｇｏｒｉｔｈｍｆｏｒ３ＤＰｏｉｎｔＣｌｏｕｄｏｎＩｎｃｌｉｎｅｄＧｒｏｕｎｄＺＨＡＮＧＱｉｎｇｙｕ，ＣＵＩＬｉｚｈｅｎ，ＬＩＭｉｎｃｈａｏ，ＭＡＢａｏｌｉａｎｇ（ＳｃｈｏｏｌｏｆＩｎｆｏｒｍａｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇ，ＩｎｎｅｒＭｏｎｇｏｌｉａＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，Ｂａｏｔｏｕ０１４０１０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｔｈｅｍｅｔｈｏｄｓｔｈａｔｒｅｌｙｏｎｐｌａｎｅｆｉｔｔｉｎｇｏｒｌｏｃａｌｇｅｏｍｅｔｒｉｃｆｅａｔｕｒｅｓｔｏｄｉｓｔｉｎｇｕｉｓｈｇｒｏｕｎｄｏｂｓｔａｃｌｅｓａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｔｈｅｆｉｅｌｄｏｆａｕｔｏｍａｔｉｃｄｒｉｖｉｎｇ，ｂｕｔｔｈｅｉｒｐｅｒｆｏｒｍａｎｃｅｃｏｕｌｄｂｅｒｅｄｕｃｅｄｉｎｔｈｅｃａｓｅｏｆｓｌｏｐｉｎｇｔｅｒｒａｉｎｏｒｓｐａｒｓｅｄａｔａ．Ｉｎａｓｌｏｐｉｎｇｔｅｒｒａｉｎｓｃｅｎｅ，ｔｈｅｐｏｉｎｔｃｌｏｕｄｄａｔａｐｒｏｖｉｄｅｄｂｙＬｉＤＡＲ，ｔｈｅｇｒｉｄｍａｐｍｅｔｈｏｄｔｈｒｏｕｇｈ３Ｄｐｒｏｊｅｃｔｉｏｎａｎｄｌｉｎｅｆｉｔｔｉｎｇｏｆｔｈｅｇｒｏｕｎｄｐｏｉｎｔｃｌｏｕｄａｒｅｕｓｅｄｔｏｒｅｄｕｃｅｔｈｅｃｏｍｐｕｔａｔｉｏｎａｌｃｏｍｐｌｅｘｉｔｙａｎｄｒｅａｌｉｚｅｔｈｅｓｅｇｍｅｎｔａｔｉｏｎｏｆｔｈｅｇｒｏｕｎｄｐｏｉｎｔｃｌｏｕｄ．Ｆｏｒｔｈｅｃｏｌｌｅｃｔｉｏｎｏｆｎｏｎ ｇｒｏｕｎｄｐｏｉｎｔｃｌｏｕｄｓ，ＳＬＲｃｌｕｓｔｅｒｉｎｇａｌｇｏｒｉｔｈｍｉｓｕｓｅｄｔｏｐｒｏｃｅｓｓ．Ｇｒｏｕｎｄｐｏｉｎｔｓａｎｄｎｏｎ ｇｒｏｕｎｄｐｏｉｎｔｓａｒｅｄｉｓｔｉｎｇｕｉｓｈｅｄｉｎｔｈｅｖｅｒｔｉｃａｌｄｉｒｅｃｔｉｏｎｂｙｓｅｔｔｉｎｇｔｈｅｉｎｔｅｎｓｉｔｙｆｅａｔｕｒｅｔｈｒｅｓｈｏｌｄ，ａｎｄｔｈｅｓｃａｎｎｅｄｏｂｓｔａｃｌｅｇｒｏｕｎｄｉｓｃｌａｓｓｉｆｉｅｄ．Ｔｈｒｏｕｇｈｅｘｐｅｒｉｍｅｎｔａｌａｎａｌｙｓｉｓ，ｔｈｅｐｒｏｐｏｓｅｄａｌｇｏｒｉｔｈｍｈａｓｂｅｔｔｅｒｍａｐｐｉｎｇｅｆｆｅｃｔｔｈａｎｏｔｈｅｒｇｒｏｕｎｄｐｏｉｎｔｃｌｏｕｄｓｅｇｍｅｎｔａｔｉｏｎａｌｇｏｒｉｔｈｍｓｉｎｓｌｏｐｉｎｇｔｅｒｒａｉｎ．Ｏｎｔｈｅｏｔｈｅｒｈａｎｄ，ｔｈｅｉｎｔｅｎｓｉｔｙｆｅａｔｕｒｅｓｐｒｏｃｅｓｓｅｄｂｙＳＬＲｃｌｕｓｔｅｒｉｎｇａｌｇｏｒｉｔｈｍａｒｅｍｏｒｅａｃｃｕｒａｔｅｉｎｔｈｅｃｏｖｅｒａｇｅｏｆＸ，ＹａｎｄＺｄｉｒｅｃｔｉｏｎｓ．Ｆｏｒｅｘａｍｐｌｅ，ｉｎｔｈｅＸｄｉｒｅｃｔｉｏｎ，ｃｏｍｐａｒｅｄｗｉｔｈｔｈｅｆａｓｔｇｒｏｕｎｄｓｅｇｍｅｎｔａｔｉｏｎａｌｇｏｒｉｔｈｍ，ｔｈｅａｖｅｒａｇｅｉｎｃｒｅａｓｅｉｓ４４．０％；ｃｏｍｐａｒｅｄｗｉｔｈｔｈｅａｌｇｏｒｉｔｈｍｗｉｔｈｇｒｉｄｍａｐ，ｔｈｅａｖｅｒａｇｅｉｎｃｒｅａｓｅｉｓ４０．１％．Ｋｅｙｗｏｒｄｓ：ｓｌｏｐｉｎｇｔｅｒｒａｉｎ；ＬｉＤＡＲ；ｐｏｉｎｔｃｌｏｕｄｓｅｇｍｅｎｔａｔｉｏｎ；ｇｒｉｄｍａｐ；ｃｌｕｓｔｅｒｉｎｇ收稿日期：２０２３－０５－１０基金项目：国家自然科学基金（６２２６１０４２）；内蒙古自治区科技计划项目（２０２２ＹＦＳＨ００５１）ＦｏｕｎｄａｔｉｏｎＩｔｅｍ：ＮａｔｉｏｎａｌＮａｔｕｒａｌＳｃｉｅｎｃｅＦｏｕｎｄａｔｉｏｎｏｆＣｈｉｎａ（６２２６１０４２）；ＩｎｎｅｒＭｏｎｇｏｌｉａＡｕｔｏｎｏｍｏｕｓＲｅｇｉｏｎＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙＰｒｏｇｒａｍ（２０２２ＹＦＳＨ００５１）０　引言近年来，随着自动驾驶领域的迅速发展，不断的探索与创新也产生了许多新的技术问题，尤其需要进一步提高对环境的可靠感知。

小学下册英语第2单元寒假试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What do bees make?A. MilkB. HoneyC. BreadD. SugarB2.The _____ (植物) can grow in various climates.3.The ______ (植物的物种多样性) is crucial for resilience.4.The _______ (The Holocaust) resulted in the genocide of millions during WWII.5.What do we call the melting of snow and ice?A. PrecipitationB. EvaporationC. RunoffD. ThawingD6.The process of fermentation can produce __________ and alcohol.7. A _____ (蝌蚪) starts as a tadpole before becoming a frog.8.The teacher _______ (教) us math and science.9.The Milky Way has a supermassive black hole at its ______.10.The process of evaporation is the transition from liquid to _____.11.How many players are on a field hockey team?A. 10B. 11C. 12D. 1312.Many _______ bloom in summer.13.I have a collection of ______ (邮票) from many different countries.14.The _____ (植物图谱) can serve as an educational tool.15.What is 11 - 5?A. 5B. 6C. 7D. 816. A ______ is a geographical region defined by its features.17.The country known for its beautiful coastline is ________ (希腊).18.My favorite color is _______ (我最喜欢的颜色是_______).19.My grandmother tells the best __________ (故事).20.The kids are _____ in the park. (running)21.The three states of matter are solid, liquid, and _______. (气体)22.I enjoy learning about ________ in science class.23.glacial) landforms were shaped by ice. The ____24.The study of the history of Earth through rock layers is known as ______.25.My teacher is very ______.26.I want to ______ how to ride a bike. (learn)27.She is a lawyer, ______ (她是一名律师), who helps people.28.Which animal can fly?A. DogB. CatC. BirdD. FishC Bird29.I love to take care of _______ (我喜欢照顾_______).30.My grandma enjoys baking ____ (cakes) for birthdays.31.What is the color of the sky on a clear day?A. GreenB. BlueC. YellowD. GrayB32.I want to _______ (尝试) new foods.33.What is the opposite of hot?A. WarmB. CoolC. ColdD. FreezingC34. A ______ is a large area of low-lying land.35.I enjoy visiting ______ (动物园) to learn about conservation efforts.36.What is the name of the famous mountain range in Asia?A. RockiesB. AndesC. HimalayasD. AlpsC37.I need to _____ (finish/start) my homework.38.What do you call the person who teaches you in school?A. DoctorB. TeacherC. ChefD. EngineerB39.I have a stuffed ________ that I sleep with.40.What do we call the act of creating new things?A. InventionB. ExplorationC. InnovationD. DiscoveryC41.The _____ (种植技术) keeps improving to help farmers.42.The __________ (历史的身份认同) shapes group dynamics.43.What is the name of the famous statue in New York City?A. Christ the RedeemerB. Statue of LibertyC. DavidD. Venus de MiloB44.I enjoy learning about science with my ________ (玩具名称).45.Where do fish live?A. TreesB. SkyC. WaterD. LandC46. A __________ is a reaction that produces solid precipitates.47.Metallic elements are usually good ______ of heat.48.How many points is a touchdown worth in American football?A. 5B. 6C. 7D. 849.The __________ is an area characterized by low rainfall and sparse vegetation. (沙漠)50.The teacher, ______ (老师), encourages us to ask questions.51.The ________ is a small but mighty creature.52. A ______ (有机) garden avoids synthetic chemicals.53.War led to the formation of NATO and ________ (华沙条约组织). The Cold54.The spider spins its web to catch ______ (昆虫).55.Which animal is known as the king of the jungle?哪个动物被称为丛林之王？A. TigerB. LionC. BearD. ElephantB56.The __________ is a famous area known for its technology.57.The sandwich is ________ good.58.What is the color of an apple?A. BlueB. GreenC. RedD. All of the aboveD59.I can ______ (唱) very well.60.The ancient Greeks engaged in ________ to settle disputes.pounds can be broken down into simpler substances through _____ (chemical reactions).62.Space is a vacuum, meaning it has very little _______.63.The chemical symbol for aluminum is ______.64.What do we call the natural process of decay and breakdown of organic material?A. DecompositionB. MetabolismC. FermentationD. PhotosynthesisA Decomposition65. A ____ is a friendly creature that loves to be with friends.66.I have a toy _______ that can light up and glow.67.What is the name of the process by which plants release oxygen?A. PhotosynthesisB. RespirationC. GerminationD. Pollination68.Which insect is known for its ability to make honey?A. AntB. BeeC. FlyD. MosquitoB69.Metals can conduct __________.70. A reaction that occurs when a solid dissolves in a liquid is called a ______ reaction.71.The _____ (蚂蚁) sometimes help plants by protecting them.72.One thing I love about my friend is their ______. They always know how to make me ______, even on tough days. We enjoy doing many activities together, such as______ and ______.73.She is ___ her lunch. (packing)74.I love to _____ (play/study) sports.75.The library is ________ (安静).76.The rooster crows at _________ (黎明).77.I enjoy _______ (一起看电影)。

llamaindex 索引类型## English Response.The llamaindex indexing type is a hybrid indexing technique that combines locality-sensitive hashing (LSH) with a variant of Locality-Sensitive Binary Codes (LSBC) called CSI (Compact Sparse Index). It was developed by OpenAI to improve the accuracy and efficiency of nearest neighbor search in large-scale datasets.Key Features of llamaindex Indexing:Efficient Nearest Neighbor Search: llamaindex excels at finding similar items in a dataset, making it ideal for tasks like image retrieval, document search, and recommendation systems.Hybrid Approach: It combines the strengths of LSH and CSI, which allows it to handle both dense and sparse data effectively.Scalable: llamaindex is designed for large-scale datasets, with support for billions of data points.Fast Indexing and Querying: It offers fast indexing and querying times, making it practical for real-world applications.How llamaindex Works:1. Data Preprocessing: The data is zunächst preprocessed to extract features and reduce dimensionality, which helps improve the indexing efficiency.2. LSH Hashing: The preprocessed data is then hashed using LSH, which assigns similar data points to the same or nearby hash bins.3. CSI Code Generation: Each hash bin is converted intoa compact sparse index (CSI) code, which is a binary vector with only a small number of non-zero elements.4. Nearest Neighbor Search: To search for similar items, the query is converted into a CSI code and compared to the stored CSI codes. The items with the most similar codes are the nearest neighbors.Advantages of llamaindex Indexing:Improved Accuracy: llamaindex typically achieveshigher accuracy in nearest neighbor search compared toother indexing methods.Extended Applicability: It can handle both dense and sparse data, making it versatile for various applications.Computational Efficiency: The hybrid approach of llamaindex reduces computational costs and speeds up the indexing and querying processes.Scalability: Its ability to handle large datasets makes it suitable for practical applications with massive data volumes.Applications of llamaindex Indexing:llamaindex indexing has a wide range of applications, including:Image Retrieval: Finding similar images in large image databases.Document Search: Retrieving documents with similar content from vast collections.Clustering: Grouping similar data points into clusters for analysis and classification.Recommendation Systems: Suggesting personalized recommendations based on user preferences.Machine Learning: Enhancing the performance of machine learning algorithms by utilizing nearest neighbor information.## 中文回答：llamaindex 索引类型。