Non-Parametric Image Subtraction for MRI

第32卷 第4期光电工程V ol.32, No.4 2005年4月 Opto-Electronic Engineering April, 2005文章编号：1003-501X (2005) 04-0078-04一种视频序列的背景提取算法肖梅1，韩崇昭1，张雷2( 1. 西安交通大学电子与信息工程学院综合自动化研究所，陕西西安 710049；2. 长安大学太白山教学实习基地，陕西西安 710064 )摘要：针对传统背景提取算法的不足，提出一种新的视频序列背景提取方法。

根据高斯分布建模图像每个像素位置背景，判断观测值是否和背景匹配，据此决定采用递推更新背景或是批处理更新背景。

若高斯分布模型判断观测值和背景模型匹配，则更新高斯模型参数，并使用最小二乘法递推更新背景；对连续判断不匹配背景的像素则采取批处理方法更新背景。

实验表明，和其它背景提取算法相比，该算法提取的背景效果好，能有效去除噪声和消除前景的运动模糊。

关键词：背景构建；最小二乘法；目标识别；高斯模型中图分类号：TN911.73 文献标识码：ABackground subtraction for video image sequenceXIAO Mei1, HAN Chong-zhao1, ZHANG Lei2(1. School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China;2.Taibai Campus, Chang'an University, Xi'an 710064, China)Abstract:In view of the faults of traditional method, a new background subtraction method for video image sequence is proposed. The values of image pixel are modeled as a Gaussian model. Backgrounds are updated by recursion and batch process. First, we determine which pixel may match with Gaussian distribution, then update the parameters of Gaussian model and rebuild background based on least squares by recursion. The parameters of Gaussian distribution and backgrounds in rest pixel position are updated by batch process. The novel algorithm can not only eliminate foreground influence on background rebuild but also remove noises. The method proposed in the paper is effective and simple.Key words: Background construction；Least squares methods；Target recognition；Gaussian model引言正确地从视频流中提取运动目标是计算机视觉领域一个重要的研究问题，也是许多智能视频系统(如视频监视、交通自动监控等)的基础部分。

f in eo nIn fio nI n fTechnical Committee SD Card Associationf in eo nIn fi ne o n I nf in eo nIRevision HistoryDate Version Changes compared to previous issueApril 3, 2006 1.10 Simplified Version Initial ReleaseFebruary 8, 20072.00(1) Added method to change bus speed (Normal Speed up to 25MHzand High Speed up to 50 MHz)(2) Operational Voltage Requirement is extended to 2.7-3.6V(3) Combine sections 12 (Physical Properties) and 13 (MechanicalExtensions) and add miniSDIO to the new section 13 (Physical Properties)(4) Add Embedded SDIO ATA Standard Function Interface Code (5) Reference of Physical Ver2.00 supports SDHC combo card. (6) Some typos in Ver1.10 are fixed.f in eo nIn fi ne o n I nf in eo nI Release of SD Simplified SpecificationThe following conditions apply to the release of the SD simplified specification ("Simplified Specification") by the SD Card Association. The Simplified Specification is a subset of the complete SD Specification which is owned by the SD Card Association.Publisher:SD Association2400 Camino Ramon, Suite 375 San Ramon, CA 94583 USA Telephone: +1 (925) 275-6615 Fax: +1 (925) 886-4870 E-mail: office@Copyright Holder: The SD Card AssociationNotes:This Simplified Specification is provided on a non-confidential basis subject to the disclaimers below. Any implementation of the Simplified Specification may require a license from the SD Card Association or other third parties.Disclaimers:The information contained in the Simplified Specification is presented only as a standard specification for SD Cards and SD Host/Ancillary products and is provided "AS-IS" without any representations or warranties of any kind. No responsibility is assumed by the SD Card Association for any damages, any infringements of patents or other right of the SD Card Association or any third parties, which may result from its use. No license is granted by implication, estoppel or otherwise under any patent or other rights of the SD Card Association or any third party. Nothing herein shall be construed as an obligation by the SD Card Association to disclose or distribute any technical information, know-how or other confidential information to any third party.f in eo nIn fi ne o n I nf in eo nConventions Used in This DocumentNaming ConventionsSome terms are capitalized to distinguish their definition from their common English meaning. Words not capitalized have their common English meaning.Numbers and Number BasesHexadecimal numbers are written with a lower case “h” suffix, e.g., FFFFh and 80h. Binary numbers are written with a lower case “b” suffix (e.g., 10b).Binary numbers larger than four digits are written with a space dividing each group of four digits, as in 1000 0101 0010b.All other numbers are decimal.Key WordsMay: Indicates flexibility of choice with no implied recommendation or requirement.Shall: Indicates a mandatory requirement. Designers shall implement such mandatory requirements to ensure interchangeability and to claim conformance with the specification.Should: Indicates a strong recommendation but not a mandatory requirement. Designers should give strong consideration to such recommendations, but there is still a choice in implementation.Application NotesSome sections of this document provide guidance to the host implementers as follows: Application Note:This is an example of an application note.f in eo nIn fi ne o n I nf in eo nTable of Contents1. General Description.................................................................................................................................1 1.1 SDIO Features....................................................................................................................................1 1.2 Primary Reference Document.............................................................................................................1 1.3 Standard SDIO Functions....................................................................................................................1 2. SDIO Signaling Definition........................................................................................................................2 2.1 SDIO Card Types................................................................................................................................2 2.2 SDIO Card modes...............................................................................................................................2 2.2.1 SPI (Card mandatory support).....................................................................................................2 2.2.2 1-bit SD Data Transfer Mode (Card Mandatory Support).............................................................2 2.2.3 4-bit SD Data Transfer Mode (Mandatory for High-Speed Cards, Optional for Low-Speed).........2 2.3 SDIO Host Modes...............................................................................................................................2 2.4 Signal Pins..........................................................................................................................................3 3. SDIO Card Initialization............................................................................................................................4 3.1 Differences in I/O card Initialization.....................................................................................................4 3.2 The IO_SEND_OP_COND Command (CMD5).................................................................................10 3.3 The IO_SEND_OP_COND Response (R4)........................................................................................11 3.4 Special Initialization considerations for Combo Cards.......................................................................12 3.4.1 Re-initialize both I/O and Memory..............................................................................................12 3.4.2 Using a Combo Card as SDIO only or SD Memory only after Combo Initialization....................12 3.4.3 Acceptable Commands after Initialization..................................................................................12 3.4.4 Recommendations for RCA after Reset.....................................................................................12 3.4.5 Enabling CRC in SPI Combo Card.............................................................................................14 4. Differences with SD Memory Specification..........................................................................................15 4.1 SDIO Command List.........................................................................................................................15 4.2 Unsupported SD Memory Commands...............................................................................................15 4.3 Modified R6 Response......................................................................................................................16 4.4 Reset for SDIO..................................................................................................................................16 4.5 Bus Width..........................................................................................................................................16 4.6 Card Detect Resistor.........................................................................................................................17 4.7 Timings..............................................................................................................................................17 4.8 Data Transfer Block Sizes.................................................................................................................18 4.9 Data Transfer Abort...........................................................................................................................18 4.9.1 Read Abort.................................................................................................................................18 4.9.2 Write Abort.................................................................................................................................18 4.10 Changes to SD Memory Fixed Registers..........................................................................................18 4.10.1 OCR Register.............................................................................................................................19 4.10.2 CID Register...............................................................................................................................19 4.10.3 CSD Register.............................................................................................................................19 4.10.4 RCA Register.............................................................................................................................19 4.10.5 DSR Register.............................................................................................................................19 4.10.6 SCR Register.............................................................................................................................19 4.10.7 SD Status...................................................................................................................................19 4.10.8 Card Status Register..................................................................................................................19 5. New I/O Read/Write Commands............................................................................................................21 5.1 IO_RW_DIRECT Command (CMD52)..............................................................................................21 5.2 IO_RW_DIRECT Response (R5)......................................................................................................22 5.2.1 CMD52 Response (SD modes)..................................................................................................22 5.2.2 R5, IO_RW_DIRECT Response (SPI mode).............................................................................23 5.3 IO_RW_EXTENDED Command (CMD53). (24)f in eo nIn fi ne o n I nf in eo nI 5.3.2 Special Timing for CMD53 Multi-Block Read..............................................................................25 6. SDIO Card Internal Operation................................................................................................................26 6.1 Overview...........................................................................................................................................26 6.2 Register Access Time........................................................................................................................26 6.3 Interrupts...........................................................................................................................................26 6.4 Suspend/Resume..............................................................................................................................27 6.5 Read Wait..........................................................................................................................................27 6.6 CMD52 During Data Transfer............................................................................................................27 6.7 SDIO Fixed Internal Map...................................................................................................................27 6.8 Common I/O Area (CIA)....................................................................................................................28 6.9 Card Common Control Registers (CCCR).........................................................................................28 6.10 Function Basic Registers (FBR)........................................................................................................35 6.11 Card Information Structure (CIS).......................................................................................................37 6.12 Multiple Function SDIO Cards...........................................................................................................37 6.13 Setting Block Size with CMD53.........................................................................................................37 6.14 Bus State Diagram............................................................................................................................38 7. Embedded I/O Code Storage Area (CSA).............................................................................................39 7.1 CSA Access.......................................................................................................................................39 7.2 CSA Data Format..............................................................................................................................39 8. SDIO Interrupts.......................................................................................................................................40 8.1 Interrupt Timing.................................................................................................................................40 8.1.1 SPI and SD 1-bit Mode Interrupts ..............................................................................................40 8.1.2 SD 4-bit Mode............................................................................................................................40 8.1.3 Interrupt Period Definition ..........................................................................................................40 8.1.4 Interrupt Period at the Data Block Gap in 4-bit SD Mode (Optional)..........................................40 8.1.5 Inhibited Interrupts (Removed Section)......................................................................................40 8.1.6 End of Interrupt Cycles...............................................................................................................40 8.1.7 Terminated Data Transfer Interrupt Cycle ..................................................................................41 8.1.8 Interrupt Clear Timing.................................................................................................................41 9. SDIO Suspend/Resume Operation........................................................................................................42 10. SDIO Read Wait Operation.....................................................................................................................43 11. Power Control.........................................................................................................................................44 11.1 Power Control Overview....................................................................................................................44 11.2 Power Control support for SDIO Cards.............................................................................................44 11.2.1 Master Power Control ................................................................................................................44 11.2.2 Power Selection.........................................................................................................................45 11.2.3 High-Power Tuples.....................................................................................................................45 11.3 Power Control Support for the SDIO Host.........................................................................................45 11.3.1 Version 1.10 Host.......................................................................................................................45 11.3.2 Power Control Operation............................................................................................................46 12. High-Speed Mode...................................................................................................................................47 12.1 SDIO High-Speed Mode....................................................................................................................47 12.2 Switching Bus Speed Mode in a Combo Card...................................................................................47 13. SDIO Physical Properties......................................................................................................................48 13.1 SDIO Form Factors...........................................................................................................................48 13.2 Full-Size SDIO ..................................................................................................................................48 13.3 miniSDIO...........................................................................................................................................48 14. SDIO Power.............................................................................................................................................48 14.1 SDIO Card Initialization Voltages......................................................................................................48 14.2 SDIO Power Consumption................................................................................................................48 15. Inrush Current Limiting..........................................................................................................................50 16. CIS Formats.. (51)f in eo nIn fi ne o n I nf in eo nI 16.2 Basic Tuple Format and Tuple Chain Structure.................................................................................51 16.3 Byte Order Within Tuples ..................................................................................................................51 16.4 Tuple Version ....................................................................................................................................52 16.5 SDIO Card Metaformat......................................................................................................................52 16.6 CISTPL_MANFID: Manufacturer Identification String Tuple..............................................................53 16.7 SDIO Specific Extensions..................................................................................................................53 16.7.1 CISTPL_FUNCID: Function Identification Tuple.........................................................................53 16.7.2 CISTPL_FUNCE: Function Extension Tuple..............................................................................54 16.7.3 CISTPL_FUNCE Tuple for Function 0 (common).......................................................................54 16.7.4 CISTPL_FUNCE Tuple for Function 1-7....................................................................................55 16.7.5 CISTPL_SDIO_STD: Function is a Standard SDIO Function.....................................................58 16.7.6 CISTPL_SDIO_EXT: Tuple Reserved for SDIO Cards...............................................................58 Appendix A.....................................................................................................................................................59 A.1 SD and SPI Command List....................................................................................................................59 Appendix B.....................................................................................................................................................61 B.1 Normative References...........................................................................................................................61 Appendix C.....................................................................................................................................................62 C.1 Abbreviations and Terms...................................................................................................................62 Appendix D.. (64)f in eo nIn fi ne o n I nf in eo nI Table of TablesTable 3-1 OCR Values for CMD5.....................................................................................................................10 Table 4-1 Unsupported SD Memory Commands.............................................................................................16 Table 4-2 R6 response to CMD3.....................................................................................................................16 Table 4-3 SDIO R6 Status Bits.........................................................................................................................16 Table 4-4 Combo Card 4-bit Control................................................................................................................17 Table 4-5 Card Detect Resistor States.............................................................................................................17 Table 4-6 is blanked.........................................................................................................................................17 Table 4-7 SDIO Status Register Structure .......................................................................................................20 Table 5-1 Flag data for IO_RW_DIRECT SD Response..................................................................................23 Table 5-2 IO_RW_ EXTENDED command Op Code Definition.......................................................................24 Table 5-3 Byte Count Values ...........................................................................................................................25 Table 6-1 Card Common Control Registers (CCCR).......................................................................................29 Table 6-2 CCCR bit Definitions........................................................................................................................34 Table 6-3 Function Basic Information Registers (FBR)....................................................................................35 Table 6-4 FBR bit and field definitions.............................................................................................................36 Table 6-5 Card Information Structure (CIS) and reserved area of CIA.............................................................37 Table 11-1 Reference Tuples by Master Power Control and Power Select......................................................45 Table 16-1 Basic Tuple Format........................................................................................................................51 Table 16-2 Tuples Supported by SDIO Cards..................................................................................................52 Table 16-3 CISTPL_MANFID: Manufacturer Identification Tuple.....................................................................53 Table 16-4 CISTPL_FUNCID Tuple.................................................................................................................53 Table 16-5 CISTPL_FUNCE Tuple General Structure.....................................................................................54 Table 16-6 TPLFID_FUNCTION Tuple for Function 0 (common)....................................................................54 Table 16-7 TPLFID_FUNCTION Field Descriptions for Function 0 (common).................................................54 Table 16-8 TPLFID_FUNCTION Tuple for Function 1-7..................................................................................55 Table 16-9 TPLFID_FUNCTION Field Descriptions for Functions 1-7.............................................................57 Table 16-10 TPLFE_FUNCTION_INFO Definition...........................................................................................57 Table 16-11 TPLFE_CSA_PROPERTY Definition...........................................................................................57 Table 16-12 CISTPL_SDIO_STD: Tuple Reserved for SDIO Cards................................................................58 Table 16-13 CISTPL_SDIO_EXT: Tuple Reserved for SDIO Cards.................................................................58 Table A-14 SD Mode Command List................................................................................................................59 Table A-15 SPI Mode Command List (60)f in eo nIn fi ne o n I nf in eo nI Table of FiguresFigure 2-1 Signal connection to two 4-bit SDIO cards.......................................................................................3 Figure 3-1 SDIO response to non-I/O aware initialization..................................................................................4 Figure 3-2 Card initialization flow in SD mode (SDIO aware host)....................................................................7 Figure 3-3 Card initialization flow in SPI mode (SDIO aware host)....................................................................9 Figure 3-4 IO_SEND_OP_COND Command (CMD5).....................................................................................10 Figure 3-5 Response R4 in SD mode...............................................................................................................11 Figure 3-6 Response R4 in SPI mode..............................................................................................................11 Figure 3-7 Modified R1 Response....................................................................................................................11 Figure 3-8 Re-Initialization Flow for I/O Controller...........................................................................................13 Figure 3-9 Re-Initialization Flow for Memory controller ...................................................................................13 Figure 5-1 IO_RW_DIRECT Command...........................................................................................................21 Figure 5-2 R5 IO_RW_DIRECT Response (SD modes)..................................................................................22 Figure 5-3 IO_RW_DIRECT Response in SPI Mode.......................................................................................23 Figure 5-4 IO_RW_EXTENDED Command.....................................................................................................24 Figure 6-1 SDIO Internal Map..........................................................................................................................28 Figure 6-2 State Diagram for Bus State Machine (38)f in eo nIn fi ne o n I nf in eo nI 1. General DescriptionThe SDIO (SD Input/Output) card is based on and compatible with the SD memory card. This compatibility includes mechanical, electrical, power, signaling and software. The intent of the SDIO card is to provide high-speed data I/O with low power consumption for mobile electronic devices. A primary goal is that an SDIO card inserted into a non-SDIO aware host shall cause no physical damage or disruption of that host or it’s software. In this case, the SDIO card should simply be ignored. Once inserted into an SDIO aware host, the detection of the card proceeds via the normal means described in this specification with some extensions. In this state, the SDIO card is idle and draws a small amount of power (15 mA averaged over 1 second). During the normal initialization and interrogation of the card by the host, the card identifies itself as an SDIO card. The host software then obtains the card information in a tuple (linked list) format and determines if that card’s I/O function(s) are acceptable to activate. This decision is based on such parameters as power requirements or the availability of appropriate software drivers. If the card is acceptable, it is allowed to power up fully and start the I/O function(s) built into it.1.1 SDIO Features• Targeted for portable and stationary applications• Minimal or no modification to SD Physical bus is required • Minimal change to memory driver software• Extended physical form factor available for specialized applications • Plug and play (PnP) support• Multi-function support including multiple I/O and combined I/O and memory • Up to 7 I/O functions plus one memory supported on one card. • Allows card to interrupt host• Operational Voltage range: 2.7-3.6V (Operational Voltage is used for Initialization) • Application Specifications for Standard SDIO Functions. • Multiple Form Factors:• Full-Size SDIO • miniSDIO1.2 Primary Reference DocumentThis specification is based on and refers extensively to the SDA document:SD Memory Card SpecificationsPart 1 PHYSICAL LAYER SPECIFICATION Version 2.00 May 9, 2006The reader is directed to this document for more information on the basic operation of SD cards. In addition, other documents are referenced in this specification. A complete list can be found in appendix B.1.This specification can apply to any released versions of Physical Layer Specification after Version 2.00.1.3 Standard SDIO FunctionsAssociated with the base SDIO specification, there are several Application Specifications for Standard SDIO Functions. These common functions such as cameras, Bluetooth cards and GPS receivers have a standard register interface, a common operation method and a standard CIS extension. Implementation of the standard interfaces are optional for any card vendor, but compliance with the standard allows the use of standard drivers and applications which will increase the appeal of these cards to the consumer. Full information on these standard interfaces can be found in the Application Specifications for Standard SDIO Functions maintained by the SDA.。

THE PURE THEORY OF PUBLIC EXPENDITUREPaul A. Samuelson1. Assumptions. Except for Sax, Wicksell,Lindahl, Musgrave, and Bowen, economists have rather neglected the theory of optimal public expenditure, spending most of their energy on the theory of taxation. Therefore, I explicitly assume two categories of goods: ordinary private consumption goods ()n X X X ,,21 which can be parcelled out among different individuals ()s i ,,,,2,1 according to the relations ∑=si ij j X X and collective consumption goods ()m n n X X ++ ,1 which all enjoy incommon in the sense that each individual's consumption of such a good leads to no subtraction from any other individual's consumption of that good, so thati j n j n X X ++= simultaneously for each and every i th individual and each collectiveconsumptive good. I assume no mystical collective mind that enjoys collective consumption goods; instead I assume each individual has a consistent set of ordinal preferences with respect to his consumption of all goods (collective as well as private) which can be summarized by a regularly smooth and convex utility index()i m n i i i X X u u +=,,1 (any monotonic stretching of the utility index is of course also an admissible cardinal index of preference). I shall throughout follow the convention of writing the partial derivative of any function with respect to its j th argument by aj subscript, so that ij ii jX u u ∂∂= etc. Provided economic quantities can be divided into two groups, (1) outputs or goods which everyone always wants to maximize and(2) inputs or factors which everyone always wants to minimize, we are free to change the algebraic signs of the latter category and from then on to work only with "goods," knowing that the case of factor inputs is covered as well. Hence by this convention we are sure that 0 ij u always.To keep production assumptions at the minimum level of simplicity, I assume a regularly convex and smooth production-possibility schedule relating totals of alloutputs, private and collective; or ()0,,1=+m n X X F , with 0 j F 、and ratios n jF F determinate and subject to the generalized laws of diminishing returns.Feasibility considerations disregarded, there is a maximal (ordinal) utility frontier representing the Pareto-optimal points —of which there are an (s —I) fold infinity —with the property that from such a frontier point you can make one person better off only by making some other person worse off. If we wish to make normative judgments concerning the relative ethical desirability of different configurations involving some individuals being on a higher level of indifference and some on a lower, we must be presented with a set of ordinal interpersonal norms or with a social welfare function representing a consistent set of ethical preferences among all the possible states of the system. It is not a "scientific" task of the economist to "deduce" the form of this function; this can have as many forms as there are possible ethical views; for the present purpose, the only restriction placed on the social welfare function is that it shall always increase or decrease when any one person's ordinal preference increases or decreases, all others staying on their same indifference levels: mathematically, we narrow it to the class that any one of its indexes can be written ()s u u u U U ,,,21 = with 0 j U .2. Optimal Conditions. In terms of these norms, there is a "best state of the world" which is defined mathematically in simple regular cases by the marginal conditionsr j ir ijF F u u = ()n j r s i ,2,1,;,,2,1== or ()n j r s i ,2;1;,,2,1=== （1）r j n s i ir i j n F F u u +=+=∑1 ()n r m j ,2,1;,,2,1== or ()1;,,2,1==r s j （2）1=q kq i k i u U u U ()n k s q i ,2,1;,,2,1,== or ()1;,,2;1===k s i q （3） Equations (1) and (3) are essentially those given in the chapter on welfare economics in my Foundations of Economic Analysis. They constitute my version ofthe "new welfare economics." Alone (1) represents that subset of relations which defines the Pareto-optimal utility frontier and which by itself represents what I regard as the unnecessarily narrow version of what once was called the "new welfare economics."The new element added here is the set (2), which constitutes a pure theory of government expenditure on collective consumption goods. By themselves(1)and(2)define the (s —Ι) fold infinity of utility frontier points; only when a set of interpersonal normative conditions equivalent to (3) is supplied are we able to define an unambiguously "best" state.Since formulating the conditions (2)some years ago, I have learned from the published and unpublished writings of Richard Musgrave that their essential logic is contained in the "voluntary-exchange" theories of public finance of the Sax-Wicksell-Lindahl-Musgrave type, and I have also noted Howard Bowen's independent discovery of them in Bowen's writings of a decade ago. A graphical interpretation of these conditions in terms of vertical rather than horizontal addition of different individuals' marginal-rate-of-substitution schedules can be given; but what I must emphasize is that there is a different such schedule for each individual at each of the (s —Ι)fold infinity of different distributions of relative welfare along the utility frontier.3. Impossibility of decentralized spontaneous solution. So much for the involved optimizing equations that an omniscient calculating machine could theoretically solve if fed the postulated functions. No such machine now exists. But it is well known that an "analogue calculating machine" can be provided by competitive market pricing, (a) so long as the production functions satisfy the neoclassical assumptions of constant returns to scale and generalized diminishing returns and (b) so long as the individuals' indifference contours have regular convexity and, we may add, (c) so long as all goods are private. We can then insert between the right- and left-hand sides of (Ι) the equality with uniform market pricesr j p p and adjoin thebudget equations for each individuali i n n i L X p X p =++ 11 ()s i ,,2,1 = （1）1where L' is a lump-sum tax for each individual so selected in algebraic value as to lead to the "best" state of the world. Now note, if there were no collective consumption goods, then (Ι) and (r)‘can have their solution enormously simplified. Why? Because on the one hand perfect competition among productive enterprises would ensure that goods are produced at minimum costs and are sold at proper marginal costs, with all factors receiving their proper marginal productivities; and on the other hand, each individual, in seeking as a competitive buyer to get to the highest level of indifference subject to given prices and tax, would be led as if by an Invisible Hand to the grand solution of the social maximum position. Of course the institutional framework of competition would have to be maintained, and political decision making would still be necessary, but of a computationally minimum type, namely, algebraic taxes and transfers ()s L L L ,,,21 would have to be varied until society is swung to the ethical observer's optimum. The servant of the ethical observer would not have to make explicit decisions about each. person's detailed consumption and work; he need only decide about generalized purchasing power, knowing that each person can be counted on to allocate it optimally. In terms of communication theory and game terminology, each person is motivated to do the signalling of his tastes needed to define and reach the attainable-bliss point.Now all of the above remains valid even if collective consumption is not zero but is instead explicitly set at its optimum values as determined by (1)，(2)，and(3).However no decentralized pricing system can serve to determine optimally these Levels of collective consumption. Other kinds of "voting" or "signalling" would have to be tried. But, and this —is the point sensed by Wicksell but perhaps not fully appreciated by Lindahl, now it is in the selfish interest of each person to give false signals, to pretend to have less interest in a given collective consumption activity than he really has, etc. I must emphasize this: taxing according to a benefit theory of taxation can not at all solve the computational problem in the decentralized manner possible for the first category of "private" goods to which the ordinary marketpricing applies and which do not have the "external effects" basic to the very notion of collective consumption goods. Of course, utopian voting and signaling schemes can be imagined. ("Scandinavian consensus," Kant's "categorical imperative," and other devices meaningful only under conditions of "symmetry," etc.) The failure of market catallactics in no way denies the following truth: given sufficient knowledge the optimal decisions can always be found by scanning over all the attainable states of the world and selecting the one which according to the postulated ethical welfare function is best. The solution"exists"; the problem is how to "find" it.One could imagine every person in the community being indoctrinated to behave like a "parametric decentralized bureaucrat" who reveals his preferences by signalling in response to price parameters or Lagrangean multipliers, to questionnaires, or to other devices. But there is still this fundamental technical difference going to the heart of the whole problem of social economy: by departing from his indoctrinated rules, any one person can hope to snatch some selfish benefit in a way not possible under the self-policing competitive pricing of private goods; and the "external economies" or " jointness of demand" intrinsic to the very concept of collective goods and governmental activities makes it impossible for the grand ensemble of optimizing equations to have that special pattern of zeros which makes laissez-faire competition even theoretically possible as an analogue computer.4. Conclusion. To explore further the problem raised by public expenditure would take us into the mathematical domain of "sociology" or "welfare politics," which Arrow, Duncan Black, and others have just begun to investigate. Political economy can be regarded as one special sector of this general domain, and it may turn out to be pure luck that within the general domain there happened to be a subsector with the "simple" properties of traditional economics.汉语翻译公共支出纯理论1、假设：除了萨克斯、维克塞尔、林达尔、马斯格雷夫和鲍恩,经济学家们宁愿忽视最优公共支出理论，而将他们的大量精力用于税收理论。

计算机视觉笔试题库及答案一、选择题1. 在计算机视觉中，下面哪项不属于主要的图像特征描述算法？A. SIFT（尺度不变特征变换）B. HOG（方向梯度直方图）C. CNN（卷积神经网络）D. PCA（主成分分析）答案：D2. 以下哪种方法常用于图像分割任务？A. Canny边缘检测B. Haar特征检测C. 高斯滤波D. 彩色空间转换答案：A3. 在目标检测中，以下哪个算法是基于特征的分类器？A. YOLO（You Only Look Once）B. R-CNN（Region-CNN）C. SSD（Single Shot MultiBox Detector）D. Faster R-CNN答案：B4. 下面哪项是计算机视觉中的经典任务？A. 图像风格迁移B. 图像超分辨率C. 图像分类D. 图像降噪答案：C5. 在图像配准中，以下哪种方法可以用于检测图像之间的特征点匹配？A. SURF（加速稳健特征）B. RANSAC（随机抽样一致性）C. ORB（旋转差异二进制）D. Homography（单应性矩阵）答案：A二、填空题1. 在卷积神经网络中，通过不断迭代调整网络参数以使损失函数达到最小值的方法称为_____________。

答案：反向传播（Backpropagation）2. 图像分割通常可以将图像中的每个像素点标记为不同的___________________。

答案：目标或背景（Object or Background）3. 使用Canny边缘检测算法，可以得到__________________。

答案：图像的边缘信息4. 在目标检测中，非极大值抑制（Non-Maximum Suppression）用于__________________。

答案：从重叠的边界框中选择最佳的检测结果5. 在图像配准中，单应性矩阵（Homography Matrix）可以用于_________________。

答案：将一个图像在透视变换下转换到另一个图像上的映射关系三、简答题1. 请简要介绍一下SIFT算法的基本原理及应用领域。

Core ModuleGeometry Creation and Editing• Lens primitives (rectangular or circular apertures)• Spline sweep and patch surfaces• Polyline sweeps and extrusions• Conic trough and revolved reflectors• Cylinders, blocks, spheres, toroids, and skinned solids• Union, intersection, subtraction boolean operations• Object trim operation• Move, rotate, scale, align• Copy, rectangular, and circular pattern copy• Multiple and partial immersion and cementing for solid objects• Pickups for parametric modeling• Grouping of model entitiesOptical Properties• Specular reflection/transmission/TIR with Fresnel losses• Diffuse transmission/reflection• Scatter models: mixed diffuse, narrow angle, and angle of incidence (AOI)• Volume scattering (Mie, user defined)• Scattering aim regions• User-defined coatings• Probabilistic ray splitting and importance sampling• Constant or varying optical density or transmittance vs. length• Index of refraction (constant, interpolated, standard dispersion formulas)• Surface patterns of 2D or 3D elements• Photorealistic rendering (Illumination Module needed for lit appearance)User Interface and Other Features• ActiveX interface for macro programming in MS Excel, VB, VC++, Matlab, Mathematica, and others • OpenGL-rendered graphics• Tabbed windows and editable spreadsheets• Multiple design views and navigation windows• Point-and-click, copy-and-paste, moving and resizing of windows• Extensive help featuresPoint-and-Shoot Ray Tracing• Parallel, diverging, or converging sets of rays• Individual rays, 2D ray fans, 3D ray grids• Sequential and non-sequential ray propagationLibraries• LED sources• Display films• Application and feature examplesIllumination ModulePowerful illumination analysis capabilities, such as photorealistic renderings that show the luminance effects of light sources in the model, simulate real-world conditions and reduce the need for physical prototypes.Illumination Analysis• Photorealistic Rendering• Photometric or radiometric analysis using forward and backward ray tracing• Illuminance, luminance, luminous intensity• Line charts, raster, contour, and surface charts• Colorimetric analysis: 1931 and 1976 CIE coordinates, correlated color temperature• RGB output display, CIE chromaticity chart• Post-processing of output data• Receiver data filtering using over a dozen filter types• Encircled and ensquared energy• Spectral power distribution• Multi-CPU processingSources and Receivers• Point sources• Volume and surface emitters (spheres, cylinders, blocks, toroids)• User-defined spatial, volume, and angular distributions• Source emittance aim regions• Spectral distributions: Blackbody, Gaussian, continuous, discrete, and user defined• Angular and spatial importance sampling• Ray data sources and Radiant Imaging source model support• Surface and far field receivers• Angular and spatial luminance meters• Receiver aperture sub-samplingOptimization ModuleThe Optimization Module gives designers tremendous flexibility to choose from hundreds of system parameters to designate as variables, constraints, and performance criteria in order to achieve the desired system performance.Illumination Optimization• Optimize illumination uniformity and/or flux on a receiver• Match target illumination distributions• Collimate and focus merit functions for non-sequential rays• Lagrange constraint handling• User-defined variables, constraints, and performance criteria• Vary any floating point model parameter• User-defined combinations of parameters• Bounded and unbounded variables• Backlight pattern optimization utility• Parameter sensitivity utility• Point-and-shoot ray merit functionsAdvanced Design ModuleThe Advanced Design Module leverages proprietary algorithms from Synopsys’ LucidShape products that automatically calculate and construct optical geometries based on user-defined illuminance and intensity patterns. This unique, functional approach gives designers the freedom to focus on overall design objectives rather than the implementation details of complex optical components.• Freeform Design features for modeling freeform reflective and refractive surfaces that are automatically shaped to form the resulting light pattern.• MacroFocal Reflector tool for designing multi-surface segmented reflectors, with different spreads for each facet.• Procedural Rectangle Lens tool for designing surfaces with pillowed optical arrays.• LED Lens tool for creating various types of freeform LED collimator lenses.Advanced Physics Module• Designers can take advantage of programming extensions to develop custom optical parts and advanced illumination subsystems using:• Phosphor particle modeling (single and multiple)• Gradient Index (GRIN) materials - used in copiers, scanners, and fiber optic telecommunication systems.• User-defined optical properties (UDOPs) - such as proprietary polarization components, scatterers, coatings, and other specialty optical materials.• Birefringent (uniaxial) materials - used in advanced applications such as AR/VR headsets and biomedical instruments.The results for UDOPs and birefringent materials can be packaged into a portable format and exchanged with your project team, customers, suppliers, and subcontractors.SOLIDWORKS Link ModuleThe SOLIDWORKS Link Module enables you to link SOLIDWORKS 3D opto-mechanical models to LightTools, where you can assign optical properties and use the Optimization Module to optimize your design. This module provides complete parametric interoperability between LightTools models and SOLIDWORKS.Data Exchange ModulesSupporting features for the Data Exchange Modules include the ability to group and simplify imported geometry and perform geometry repairs to maintain CAD model integrity and improve ray trace speed.Translators• SAT version 1.0 through 7.0• STEP AP 203 and AP 214• IGES version 5.3, including surfaces and solids• Parasolid• CATIA V4 and V5 (import and export)• Grouping and simplification of imported surfaces• Geometry repairLightTools SmartStart Library ModuleProvides access to a library of materials and media commonly used in the design of automotive lighting systems. Includes refractive index and absorption data as well as pre-defined volume scatter and BSDF materials.Imaging Path Module• Sequential ray tracing• Paraxial solves• Image path view• Spot diagram and transverse aberration plotsDistributed Simulation ModuleThe Distributed Simulation Module allows you to distribute Monte Carlo ray tracing over multiple computers to speed simulations of complex optical models.©2022 Synopsys, Inc. All rights reserved. Synopsys is a trademark of Synopsys, Inc. in the United States and other countries. A list of Synopsys trademarks isavailable at /copyright.html . All other names mentioned herein are trademarks or registered trademarks of their respective owners.。

常用英语词汇 -andrew Ng课程average firing rate均匀激活率intensity强度average sum-of-squares error均方差Regression回归backpropagation后向流传Loss function损失函数basis 基non-convex非凸函数basis feature vectors特点基向量neural network神经网络batch gradient ascent批量梯度上涨法supervised learning监察学习Bayesian regularization method贝叶斯规则化方法regression problem回归问题办理的是连续的问题Bernoulli random variable伯努利随机变量classification problem分类问题bias term偏置项discreet value失散值binary classfication二元分类support vector machines支持向量机class labels种类标记learning theory学习理论concatenation级联learning algorithms学习算法conjugate gradient共轭梯度unsupervised learning无监察学习contiguous groups联通地区gradient descent梯度降落convex optimization software凸优化软件linear regression线性回归convolution卷积Neural Network神经网络cost function代价函数gradient descent梯度降落covariance matrix协方差矩阵normal equations DC component直流重量linear algebra线性代数decorrelation去有关superscript上标degeneracy退化exponentiation指数demensionality reduction降维training set训练会合derivative导函数training example训练样本diagonal对角线hypothesis假定，用来表示学习算法的输出diffusion of gradients梯度的弥散LMS algorithm “least mean squares最小二乘法算eigenvalue特点值法eigenvector特点向量batch gradient descent批量梯度降落error term残差constantly gradient descent随机梯度降落feature matrix特点矩阵iterative algorithm迭代算法feature standardization特点标准化partial derivative偏导数feedforward architectures前馈构造算法contour等高线feedforward neural network前馈神经网络quadratic function二元函数feedforward pass前馈传导locally weighted regression局部加权回归fine-tuned微调underfitting欠拟合first-order feature一阶特点overfitting过拟合forward pass前向传导non-parametric learning algorithms无参数学习算forward propagation前向流传法Gaussian prior高斯先验概率parametric learning algorithm参数学习算法generative model生成模型activation激活值gradient descent梯度降落activation function激活函数Greedy layer-wise training逐层贪心训练方法additive noise加性噪声grouping matrix分组矩阵autoencoder自编码器Hadamard product阿达马乘积Autoencoders自编码算法Hessian matrix Hessian矩阵hidden layer隐含层hidden units隐蔽神经元Hierarchical grouping层次型分组higher-order features更高阶特点highly non-convex optimization problem高度非凸的优化问题histogram直方图hyperbolic tangent双曲正切函数hypothesis估值，假定identity activation function恒等激励函数IID 独立同散布illumination照明inactive克制independent component analysis独立成份剖析input domains输入域input layer输入层intensity亮度/灰度intercept term截距KL divergence相对熵KL divergence KL分别度k-Means K-均值learning rate学习速率least squares最小二乘法linear correspondence线性响应linear superposition线性叠加line-search algorithm线搜寻算法local mean subtraction局部均值消减local optima局部最优解logistic regression逻辑回归loss function损失函数low-pass filtering低通滤波magnitude幅值MAP 极大后验预计maximum likelihood estimation极大似然预计mean 均匀值MFCC Mel 倒频系数multi-class classification多元分类neural networks神经网络neuron 神经元Newton’s method牛顿法non-convex function非凸函数non-linear feature非线性特点norm 范式norm bounded有界范数norm constrained范数拘束normalization归一化numerical roundoff errors数值舍入偏差numerically checking数值查验numerically reliable数值计算上稳固object detection物体检测objective function目标函数off-by-one error缺位错误orthogonalization正交化output layer输出层overall cost function整体代价函数over-complete basis超齐备基over-fitting过拟合parts of objects目标的零件part-whole decompostion部分-整体分解PCA 主元剖析penalty term处罚因子per-example mean subtraction逐样本均值消减pooling池化pretrain预训练principal components analysis主成份剖析quadratic constraints二次拘束RBMs 受限 Boltzman 机reconstruction based models鉴于重构的模型reconstruction cost重修代价reconstruction term重构项redundant冗余reflection matrix反射矩阵regularization正则化regularization term正则化项rescaling缩放robust 鲁棒性run 行程second-order feature二阶特点sigmoid activation function S型激励函数significant digits有效数字singular value奇怪值singular vector奇怪向量smoothed L1 penalty光滑的L1 范数处罚Smoothed topographic L1 sparsity penalty光滑地形L1 稀少处罚函数smoothing光滑Softmax Regresson Softmax回归sorted in decreasing order降序摆列source features源特点Adversarial Networks抗衡网络sparse autoencoder消减归一化Affine Layer仿射层Sparsity稀少性Affinity matrix亲和矩阵sparsity parameter稀少性参数Agent 代理 /智能体sparsity penalty稀少处罚Algorithm 算法square function平方函数Alpha- beta pruningα - β剪枝squared-error方差Anomaly detection异样检测stationary安稳性（不变性）Approximation近似stationary stochastic process安稳随机过程Area Under ROC Curve／ AUC Roc 曲线下边积step-size步长值Artificial General Intelligence/AGI通用人工智supervised learning监察学习能symmetric positive semi-definite matrix Artificial Intelligence/AI人工智能对称半正定矩阵Association analysis关系剖析symmetry breaking对称无效Attention mechanism注意力体制tanh function双曲正切函数Attribute conditional independence assumptionthe average activation均匀活跃度属性条件独立性假定the derivative checking method梯度考证方法Attribute space属性空间the empirical distribution经验散布函数Attribute value属性值the energy function能量函数Autoencoder自编码器the Lagrange dual拉格朗日对偶函数Automatic speech recognition自动语音辨别the log likelihood对数似然函数Automatic summarization自动纲要the pixel intensity value像素灰度值Average gradient均匀梯度the rate of convergence收敛速度Average-Pooling均匀池化topographic cost term拓扑代价项Backpropagation Through Time经过时间的反向流传topographic ordered拓扑次序Backpropagation/BP反向流传transformation变换Base learner基学习器translation invariant平移不变性Base learning algorithm基学习算法trivial answer平庸解Batch Normalization/BN批量归一化under-complete basis不齐备基Bayes decision rule贝叶斯判断准则unrolling组合扩展Bayes Model Averaging／ BMA 贝叶斯模型均匀unsupervised learning无监察学习Bayes optimal classifier贝叶斯最优分类器variance 方差Bayesian decision theory贝叶斯决议论vecotrized implementation向量化实现Bayesian network贝叶斯网络vectorization矢量化Between-class scatter matrix类间散度矩阵visual cortex视觉皮层Bias 偏置 /偏差weight decay权重衰减Bias-variance decomposition偏差 - 方差分解weighted average加权均匀值Bias-Variance Dilemma偏差–方差窘境whitening白化Bi-directional Long-Short Term Memory/Bi-LSTMzero-mean均值为零双向长短期记忆Accumulated error backpropagation积累偏差逆传Binary classification二分类播Binomial test二项查验Activation Function激活函数Bi-partition二分法Adaptive Resonance Theory/ART自适应谐振理论Boltzmann machine玻尔兹曼机Addictive model加性学习Bootstrap sampling自助采样法／可重复采样Bootstrapping自助法Break-Event Point／ BEP 均衡点Calibration校准Cascade-Correlation级联有关Categorical attribute失散属性Class-conditional probability类条件概率Classification and regression tree/CART分类与回归树Classifier分类器Class-imbalance类型不均衡Closed -form闭式Cluster簇/ 类/ 集群Cluster analysis聚类剖析Clustering聚类Clustering ensemble聚类集成Co-adapting共适应Coding matrix编码矩阵COLT 国际学习理论会议Committee-based learning鉴于委员会的学习Competitive learning竞争型学习Component learner组件学习器Comprehensibility可解说性Computation Cost计算成本Computational Linguistics计算语言学Computer vision计算机视觉Concept drift观点漂移Concept Learning System /CLS观点学习系统Conditional entropy条件熵Conditional mutual information条件互信息Conditional Probability Table／ CPT 条件概率表Conditional random field/CRF条件随机场Conditional risk条件风险Confidence置信度Confusion matrix混杂矩阵Connection weight连结权Connectionism 连结主义Consistency一致性／相合性Contingency table列联表Continuous attribute连续属性Convergence收敛Conversational agent会话智能体Convex quadratic programming凸二次规划Convexity凸性Convolutional neural network/CNN卷积神经网络Co-occurrence同现Correlation coefficient有关系数Cosine similarity余弦相像度Cost curve成本曲线Cost Function成本函数Cost matrix成本矩阵Cost-sensitive成本敏感Cross entropy交错熵Cross validation交错考证Crowdsourcing众包Curse of dimensionality维数灾害Cut point截断点Cutting plane algorithm割平面法Data mining数据发掘Data set数据集Decision Boundary决议界限Decision stump决议树桩Decision tree决议树／判断树Deduction演绎Deep Belief Network深度信念网络Deep Convolutional Generative Adversarial NetworkDCGAN深度卷积生成抗衡网络Deep learning深度学习Deep neural network/DNN深度神经网络Deep Q-Learning深度Q 学习Deep Q-Network深度Q 网络Density estimation密度预计Density-based clustering密度聚类Differentiable neural computer可微分神经计算机Dimensionality reduction algorithm降维算法Directed edge有向边Disagreement measure不合胸怀Discriminative model鉴别模型Discriminator鉴别器Distance measure距离胸怀Distance metric learning距离胸怀学习Distribution散布Divergence散度Diversity measure多样性胸怀／差别性胸怀Domain adaption领域自适应Downsampling下采样D-separation（ Directed separation）有向分别Dual problem对偶问题Dummy node 哑结点General Problem Solving通用问题求解Dynamic Fusion 动向交融Generalization泛化Dynamic programming动向规划Generalization error泛化偏差Eigenvalue decomposition特点值分解Generalization error bound泛化偏差上界Embedding 嵌入Generalized Lagrange function广义拉格朗日函数Emotional analysis情绪剖析Generalized linear model广义线性模型Empirical conditional entropy经验条件熵Generalized Rayleigh quotient广义瑞利商Empirical entropy经验熵Generative Adversarial Networks/GAN生成抗衡网Empirical error经验偏差络Empirical risk经验风险Generative Model生成模型End-to-End 端到端Generator生成器Energy-based model鉴于能量的模型Genetic Algorithm/GA遗传算法Ensemble learning集成学习Gibbs sampling吉布斯采样Ensemble pruning集成修剪Gini index基尼指数Error Correcting Output Codes／ ECOC纠错输出码Global minimum全局最小Error rate错误率Global Optimization全局优化Error-ambiguity decomposition偏差 - 分歧分解Gradient boosting梯度提高Euclidean distance欧氏距离Gradient Descent梯度降落Evolutionary computation演化计算Graph theory图论Expectation-Maximization希望最大化Ground-truth实情／真切Expected loss希望损失Hard margin硬间隔Exploding Gradient Problem梯度爆炸问题Hard voting硬投票Exponential loss function指数损失函数Harmonic mean 调解均匀Extreme Learning Machine/ELM超限学习机Hesse matrix海塞矩阵Factorization因子分解Hidden dynamic model隐动向模型False negative假负类Hidden layer隐蔽层False positive假正类Hidden Markov Model/HMM 隐马尔可夫模型False Positive Rate/FPR假正例率Hierarchical clustering层次聚类Feature engineering特点工程Hilbert space希尔伯特空间Feature selection特点选择Hinge loss function合页损失函数Feature vector特点向量Hold-out 留出法Featured Learning特点学习Homogeneous 同质Feedforward Neural Networks/FNN前馈神经网络Hybrid computing混杂计算Fine-tuning微调Hyperparameter超参数Flipping output翻转法Hypothesis假定Fluctuation震荡Hypothesis test假定考证Forward stagewise algorithm前向分步算法ICML 国际机器学习会议Frequentist频次主义学派Improved iterative scaling/IIS改良的迭代尺度法Full-rank matrix满秩矩阵Incremental learning增量学习Functional neuron功能神经元Independent and identically distributed/独Gain ratio增益率立同散布Game theory博弈论Independent Component Analysis/ICA独立成分剖析Gaussian kernel function高斯核函数Indicator function指示函数Gaussian Mixture Model高斯混杂模型Individual learner个体学习器Induction归纳Inductive bias归纳偏好Inductive learning归纳学习Inductive Logic Programming／ ILP归纳逻辑程序设计Information entropy信息熵Information gain信息增益Input layer输入层Insensitive loss不敏感损失Inter-cluster similarity簇间相像度International Conference for Machine Learning/ICML国际机器学习大会Intra-cluster similarity簇内相像度Intrinsic value固有值Isometric Mapping/Isomap等胸怀映照Isotonic regression平分回归Iterative Dichotomiser迭代二分器Kernel method核方法Kernel trick核技巧Kernelized Linear Discriminant Analysis／KLDA核线性鉴别剖析K-fold cross validation k折交错考证／k 倍交错考证K-Means Clustering K–均值聚类K-Nearest Neighbours Algorithm/KNN K近邻算法Knowledge base 知识库Knowledge Representation知识表征Label space标记空间Lagrange duality拉格朗日对偶性Lagrange multiplier拉格朗日乘子Laplace smoothing拉普拉斯光滑Laplacian correction拉普拉斯修正Latent Dirichlet Allocation隐狄利克雷散布Latent semantic analysis潜伏语义剖析Latent variable隐变量Lazy learning懒散学习Learner学习器Learning by analogy类比学习Learning rate学习率Learning Vector Quantization/LVQ学习向量量化Least squares regression tree最小二乘回归树Leave-One-Out/LOO留一法linear chain conditional random field线性链条件随机场Linear Discriminant Analysis／ LDA 线性鉴别剖析Linear model线性模型Linear Regression线性回归Link function联系函数Local Markov property局部马尔可夫性Local minimum局部最小Log likelihood对数似然Log odds／ logit对数几率Logistic Regression Logistic回归Log-likelihood对数似然Log-linear regression对数线性回归Long-Short Term Memory/LSTM 长短期记忆Loss function损失函数Machine translation/MT机器翻译Macron-P宏查准率Macron-R宏查全率Majority voting绝对多半投票法Manifold assumption流形假定Manifold learning流形学习Margin theory间隔理论Marginal distribution边沿散布Marginal independence边沿独立性Marginalization边沿化Markov Chain Monte Carlo/MCMC马尔可夫链蒙特卡罗方法Markov Random Field马尔可夫随机场Maximal clique最大团Maximum Likelihood Estimation/MLE极大似然预计／极大似然法Maximum margin最大间隔Maximum weighted spanning tree最大带权生成树Max-Pooling 最大池化Mean squared error均方偏差Meta-learner元学习器Metric learning胸怀学习Micro-P微查准率Micro-R微查全率Minimal Description Length/MDL最小描绘长度Minimax game极小极大博弈Misclassification cost误分类成本Mixture of experts混杂专家Momentum 动量Moral graph道德图／正直图Multi-class classification多分类Multi-document summarization多文档纲要One shot learning一次性学习Multi-layer feedforward neural networks One-Dependent Estimator／ ODE 独依靠预计多层前馈神经网络On-Policy在策略Multilayer Perceptron/MLP多层感知器Ordinal attribute有序属性Multimodal learning多模态学习Out-of-bag estimate包外预计Multiple Dimensional Scaling多维缩放Output layer输出层Multiple linear regression多元线性回归Output smearing输出调制法Multi-response Linear Regression／ MLR Overfitting过拟合／过配多响应线性回归Oversampling 过采样Mutual information互信息Paired t-test成对 t查验Naive bayes 朴实贝叶斯Pairwise 成对型Naive Bayes Classifier朴实贝叶斯分类器Pairwise Markov property成对马尔可夫性Named entity recognition命名实体辨别Parameter参数Nash equilibrium纳什均衡Parameter estimation参数预计Natural language generation/NLG自然语言生成Parameter tuning调参Natural language processing自然语言办理Parse tree分析树Negative class负类Particle Swarm Optimization/PSO粒子群优化算法Negative correlation负有关法Part-of-speech tagging词性标明Negative Log Likelihood负对数似然Perceptron感知机Neighbourhood Component Analysis/NCA Performance measure性能胸怀近邻成分剖析Plug and Play Generative Network即插即用生成网Neural Machine Translation神经机器翻译络Neural Turing Machine神经图灵机Plurality voting相对多半投票法Newton method牛顿法Polarity detection极性检测NIPS 国际神经信息办理系统会议Polynomial kernel function多项式核函数No Free Lunch Theorem／ NFL 没有免费的午饭定理Pooling池化Noise-contrastive estimation噪音对照预计Positive class正类Nominal attribute列名属性Positive definite matrix正定矩阵Non-convex optimization非凸优化Post-hoc test后续查验Nonlinear model非线性模型Post-pruning后剪枝Non-metric distance非胸怀距离potential function势函数Non-negative matrix factorization非负矩阵分解Precision查准率／正确率Non-ordinal attribute无序属性Prepruning 预剪枝Non-Saturating Game非饱和博弈Principal component analysis/PCA主成分剖析Norm 范数Principle of multiple explanations多释原则Normalization归一化Prior 先验Nuclear norm核范数Probability Graphical Model概率图模型Numerical attribute数值属性Proximal Gradient Descent/PGD近端梯度降落Letter O Pruning剪枝Objective function目标函数Pseudo-label伪标记Oblique decision tree斜决议树Quantized Neural Network量子化神经网络Occam’s razor奥卡姆剃刀Quantum computer 量子计算机Odds 几率Quantum Computing量子计算Off-Policy离策略Quasi Newton method拟牛顿法Radial Basis Function／ RBF 径向基函数Random Forest Algorithm随机丛林算法Random walk随机闲步Recall 查全率／召回率Receiver Operating Characteristic/ROC受试者工作特点Rectified Linear Unit/ReLU线性修正单元Recurrent Neural Network循环神经网络Recursive neural network递归神经网络Reference model 参照模型Regression回归Regularization正则化Reinforcement learning/RL加强学习Representation learning表征学习Representer theorem表示定理reproducing kernel Hilbert space/RKHS重生核希尔伯特空间Re-sampling重采样法Rescaling再缩放Residual Mapping残差映照Residual Network残差网络Restricted Boltzmann Machine/RBM受限玻尔兹曼机Restricted Isometry Property/RIP限制等距性Re-weighting重赋权法Robustness稳重性 / 鲁棒性Root node根结点Rule Engine规则引擎Rule learning规则学习Saddle point鞍点Sample space样本空间Sampling采样Score function评分函数Self-Driving自动驾驶Self-Organizing Map／ SOM自组织映照Semi-naive Bayes classifiers半朴实贝叶斯分类器Semi-Supervised Learning半监察学习semi-Supervised Support Vector Machine半监察支持向量机Sentiment analysis感情剖析Separating hyperplane分别超平面Sigmoid function Sigmoid函数Similarity measure相像度胸怀Simulated annealing模拟退火Simultaneous localization and mapping同步定位与地图建立Singular Value Decomposition奇怪值分解Slack variables废弛变量Smoothing光滑Soft margin软间隔Soft margin maximization软间隔最大化Soft voting软投票Sparse representation稀少表征Sparsity稀少性Specialization特化Spectral Clustering谱聚类Speech Recognition语音辨别Splitting variable切分变量Squashing function挤压函数Stability-plasticity dilemma可塑性 - 稳固性窘境Statistical learning统计学习Status feature function状态特点函Stochastic gradient descent随机梯度降落Stratified sampling分层采样Structural risk构造风险Structural risk minimization/SRM构造风险最小化Subspace子空间Supervised learning监察学习／有导师学习support vector expansion支持向量展式Support Vector Machine/SVM支持向量机Surrogat loss代替损失Surrogate function代替函数Symbolic learning符号学习Symbolism符号主义Synset同义词集T-Distribution Stochastic Neighbour Embeddingt-SNE T–散布随机近邻嵌入Tensor 张量Tensor Processing Units/TPU张量办理单元The least square method最小二乘法Threshold阈值Threshold logic unit阈值逻辑单元Threshold-moving阈值挪动Time Step时间步骤Tokenization标记化Training error训练偏差Training instance训练示例／训练例Transductive learning直推学习Transfer learning迁徙学习Treebank树库algebra线性代数Tria-by-error试错法asymptotically无症状的True negative真负类appropriate适合的True positive真切类bias 偏差True Positive Rate/TPR真切例率brevity简洁，简洁；短暂Turing Machine图灵机[800 ] broader宽泛Twice-learning二次学习briefly简洁的Underfitting欠拟合／欠配batch 批量Undersampling欠采样convergence收敛，集中到一点Understandability可理解性convex凸的Unequal cost非均等代价contours轮廓Unit-step function单位阶跃函数constraint拘束Univariate decision tree单变量决议树constant常理Unsupervised learning无监察学习／无导师学习commercial商务的Unsupervised layer-wise training无监察逐层训练complementarity增补Upsampling上采样coordinate ascent同样级上涨Vanishing Gradient Problem梯度消逝问题clipping剪下物；剪报；修剪Variational inference变分推测component重量；零件VC Theory VC维理论continuous连续的Version space版本空间covariance协方差Viterbi algorithm维特比算法canonical正规的，正则的Von Neumann architecture冯· 诺伊曼架构concave非凸的Wasserstein GAN/WGAN Wasserstein生成抗衡网络corresponds相切合；相当；通讯Weak learner弱学习器corollary推论Weight权重concrete详细的事物，实在的东西Weight sharing权共享cross validation交错考证Weighted voting加权投票法correlation互相关系Within-class scatter matrix类内散度矩阵convention商定Word embedding词嵌入cluster一簇Word sense disambiguation词义消歧centroids质心，形心Zero-data learning零数据学习converge收敛Zero-shot learning零次学习computationally计算(机)的approximations近似值calculus计算arbitrary任意的derive获取，获得affine仿射的dual 二元的arbitrary任意的duality二元性；二象性；对偶性amino acid氨基酸derivation求导；获取；发源amenable 经得起查验的denote预示，表示，是的标记；意味着，[逻]指称axiom 公义，原则divergence散度；发散性abstract提取dimension尺度，规格；维数architecture架构，系统构造；建筑业dot 小圆点absolute绝对的distortion变形arsenal军械库density概率密度函数assignment分派discrete失散的人工智能词汇discriminative有辨别能力的indicator指示物，指示器diagonal对角interative重复的，迭代的dispersion分别，散开integral积分determinant决定要素identical相等的；完整同样的disjoint不订交的indicate表示，指出encounter碰到invariance不变性，恒定性ellipses椭圆impose把强加于equality等式intermediate中间的extra 额外的interpretation解说，翻译empirical经验；察看joint distribution结合概率ennmerate例举，计数lieu 代替exceed超出，越出logarithmic对数的，用对数表示的expectation希望latent潜伏的efficient奏效的Leave-one-out cross validation留一法交错考证endow 给予magnitude巨大explicitly清楚的mapping 画图，制图；映照exponential family指数家族matrix矩阵equivalently等价的mutual互相的，共同的feasible可行的monotonically单一的forary首次试试minor较小的，次要的finite有限的，限制的multinomial多项的forgo 摒弃，放弃multi-class classification二分类问题fliter过滤nasty厌烦的frequentist最常发生的notation标记，说明forward search前向式搜寻na?ve 朴实的formalize使定形obtain获取generalized归纳的oscillate摇动generalization归纳，归纳；广泛化；判断（依据不optimization problem最优化问题足）objective function目标函数guarantee保证；抵押品optimal最理想的generate形成，产生orthogonal(矢量，矩阵等 ) 正交的geometric margins几何界限orientation方向gap 裂口ordinary一般的generative生产的；有生产力的occasionally有时的heuristic启迪式的；启迪法；启迪程序partial derivative偏导数hone 怀恋；磨property性质hyperplane超平面proportional成比率的initial最先的primal原始的，最先的implement履行permit同意intuitive凭直觉获知的pseudocode 伪代码incremental增添的permissible可同意的intercept截距polynomial多项式intuitious直觉preliminary预备instantiation例子precision精度人工智能词汇perturbation不安，搅乱theorem定理poist 假定，假想tangent正弦positive semi-definite半正定的unit-length vector单位向量parentheses圆括号valid 有效的，正确的posterior probability后验概率variance方差plementarity增补variable变量；变元pictorially图像的vocabulary 词汇parameterize确立的参数valued经估价的；可贵的poisson distribution柏松散布wrapper 包装pertinent有关的总计 1038 词汇quadratic二次的quantity量，数目；重量query 疑问的regularization使系统化；调整reoptimize从头优化restrict限制；限制；拘束reminiscent回想旧事的；提示的；令人联想的（ of ）remark 注意random variable随机变量respect考虑respectively各自的；分其他redundant过多的；冗余的susceptible敏感的stochastic可能的；随机的symmetric对称的sophisticated复杂的spurious假的；假造的subtract减去；减法器simultaneously同时发生地；同步地suffice知足scarce罕有的，难得的split分解，分别subset子集statistic统计量successive iteratious连续的迭代scale标度sort of有几分的squares 平方trajectory轨迹temporarily临时的terminology专用名词tolerance容忍；公差thumb翻阅threshold阈，临界。

目录第一部分 (3)第二部分 (12)Letter A (12)Letter B (14)Letter C (15)Letter D (17)Letter E (19)Letter F (20)Letter G (21)Letter H (22)Letter I (23)Letter K (24)Letter L (24)Letter M (26)Letter N (27)Letter O (29)Letter P (29)Letter R (31)Letter S (32)Letter T (35)Letter U (36)Letter W (37)Letter Z (37)第三部分 (37)A (37)B (38)C (38)D (40)E (40)F (41)G (41)H (42)L (42)J (43)L (43)M (43)N (44)O (44)P (44)Q (45)R (46)S (46)U (47)V (48)第一部分[ ] intensity 强度[ ] Regression 回归[ ] Loss function 损失函数[ ] non-convex 非凸函数[ ] neural network 神经网络[ ] supervised learning 监督学习[ ] regression problem 回归问题处理的是连续的问题[ ] classification problem 分类问题处理的问题是离散的而不是连续的回归问题和分类问题的区别应该在于回归问题的结果是连续的，分类问题的结果是离散的。

[ ]discreet value 离散值[ ] support vector machines 支持向量机,用来处理分类算法中输入的维度不单一的情况（甚至输入维度为无穷）[ ] learning theory 学习理论[ ] learning algorithms 学习算法[ ] unsupervised learning 无监督学习[ ] gradient descent 梯度下降[ ] linear regression 线性回归[ ] Neural Network 神经网络[ ] gradient descent 梯度下降监督学习的一种算法，用来拟合的算法[ ] normal equations[ ] linear algebra 线性代数原谅我英语不太好[ ] superscript上标[ ] exponentiation 指数[ ] training set 训练集合[ ] training example 训练样本[ ] hypothesis 假设，用来表示学习算法的输出，叫我们不要太纠结H的意思，因为这只是历史的惯例[ ] LMS algorithm “least mean squares” 最小二乘法算法[ ] batch gradient descent 批量梯度下降，因为每次都会计算最小拟合的方差，所以运算慢[ ] constantly gradient descent 字幕组翻译成“随机梯度下降” 我怎么觉得是“常量梯度下降”也就是梯度下降的运算次数不变，一般比批量梯度下降速度快，但是通常不是那么准确[ ] iterative algorithm 迭代算法[ ] partial derivative 偏导数[ ] contour 等高线[ ] quadratic function 二元函数[ ] locally weighted regression局部加权回归[ ] underfitting欠拟合[ ] overfitting 过拟合[ ] non-parametric learning algorithms 无参数学习算法[ ] parametric learning algorithm 参数学习算法[ ] other[ ] activation 激活值[ ] activation function 激活函数[ ] additive noise 加性噪声[ ] autoencoder 自编码器[ ] Autoencoders 自编码算法[ ] average firing rate 平均激活率[ ] average sum-of-squares error 均方差[ ] backpropagation 后向传播[ ] basis 基[ ] basis feature vectors 特征基向量[50 ] batch gradient ascent 批量梯度上升法[ ] Bayesian regularization method 贝叶斯规则化方法[ ] Bernoulli random variable 伯努利随机变量[ ] bias term 偏置项[ ] binary classfication 二元分类[ ] class labels 类型标记[ ] concatenation 级联[ ] conjugate gradient 共轭梯度[ ] contiguous groups 联通区域[ ] convex optimization software 凸优化软件[ ] convolution 卷积[ ] cost function 代价函数[ ] covariance matrix 协方差矩阵[ ] DC component 直流分量[ ] decorrelation 去相关[ ] degeneracy 退化[ ] demensionality reduction 降维[ ] derivative 导函数[ ] diagonal 对角线[ ] diffusion of gradients 梯度的弥散[ ] eigenvalue 特征值[ ] eigenvector 特征向量[ ] error term 残差[ ] feature matrix 特征矩阵[ ] feature standardization 特征标准化[ ] feedforward architectures 前馈结构算法[ ] feedforward neural network 前馈神经网络[ ] feedforward pass 前馈传导[ ] fine-tuned 微调[ ] first-order feature 一阶特征[ ] forward pass 前向传导[ ] forward propagation 前向传播[ ] Gaussian prior 高斯先验概率[ ] generative model 生成模型[ ] gradient descent 梯度下降[ ] Greedy layer-wise training 逐层贪婪训练方法[ ] grouping matrix 分组矩阵[ ] Hadamard product 阿达马乘积[ ] Hessian matrix Hessian 矩阵[ ] hidden layer 隐含层[ ] hidden units 隐藏神经元[ ] Hierarchical grouping 层次型分组[ ] higher-order features 更高阶特征[ ] highly non-convex optimization problem 高度非凸的优化问题[ ] histogram 直方图[ ] hyperbolic tangent 双曲正切函数[ ] hypothesis 估值，假设[ ] identity activation function 恒等激励函数[ ] IID 独立同分布[ ] illumination 照明[100 ] inactive 抑制[ ] independent component analysis 独立成份分析[ ] input domains 输入域[ ] input layer 输入层[ ] intensity 亮度/灰度[ ] intercept term 截距[ ] KL divergence 相对熵[ ] KL divergence KL分散度[ ] k-Means K-均值[ ] learning rate 学习速率[ ] least squares 最小二乘法[ ] linear correspondence 线性响应[ ] linear superposition 线性叠加[ ] line-search algorithm 线搜索算法[ ] local mean subtraction 局部均值消减[ ] local optima 局部最优解[ ] logistic regression 逻辑回归[ ] loss function 损失函数[ ] low-pass filtering 低通滤波[ ] magnitude 幅值[ ] MAP 极大后验估计[ ] maximum likelihood estimation 极大似然估计[ ] mean 平均值[ ] MFCC Mel 倒频系数[ ] multi-class classification 多元分类[ ] neural networks 神经网络[ ] neuron 神经元[ ] Newton’s method 牛顿法[ ] non-convex function 非凸函数[ ] non-linear feature 非线性特征[ ] norm 范式[ ] norm bounded 有界范数[ ] norm constrained 范数约束[ ] normalization 归一化[ ] numerical roundoff errors 数值舍入误差[ ] numerically checking 数值检验[ ] numerically reliable 数值计算上稳定[ ] object detection 物体检测[ ] objective function 目标函数[ ] off-by-one error 缺位错误[ ] orthogonalization 正交化[ ] output layer 输出层[ ] overall cost function 总体代价函数[ ] over-complete basis 超完备基[ ] over-fitting 过拟合[ ] parts of objects 目标的部件[ ] part-whole decompostion 部分-整体分解[ ] PCA 主元分析[ ] penalty term 惩罚因子[ ] per-example mean subtraction 逐样本均值消减[150 ] pooling 池化[ ] pretrain 预训练[ ] principal components analysis 主成份分析[ ] quadratic constraints 二次约束[ ] RBMs 受限Boltzman机[ ] reconstruction based models 基于重构的模型[ ] reconstruction cost 重建代价[ ] reconstruction term 重构项[ ] redundant 冗余[ ] reflection matrix 反射矩阵[ ] regularization 正则化[ ] regularization term 正则化项[ ] rescaling 缩放[ ] robust 鲁棒性[ ] run 行程[ ] second-order feature 二阶特征[ ] sigmoid activation function S型激励函数[ ] significant digits 有效数字[ ] singular value 奇异值[ ] singular vector 奇异向量[ ] smoothed L1 penalty 平滑的L1范数惩罚[ ] Smoothed topographic L1 sparsity penalty 平滑地形L1稀疏惩罚函数[ ] smoothing 平滑[ ] Softmax Regresson Softmax回归[ ] sorted in decreasing order 降序排列[ ] source features 源特征[ ] sparse autoencoder 消减归一化[ ] Sparsity 稀疏性[ ] sparsity parameter 稀疏性参数[ ] sparsity penalty 稀疏惩罚[ ] square function 平方函数[ ] squared-error 方差[ ] stationary 平稳性（不变性）[ ] stationary stochastic process 平稳随机过程[ ] step-size 步长值[ ] supervised learning 监督学习[ ] symmetric positive semi-definite matrix 对称半正定矩阵[ ] symmetry breaking 对称失效[ ] tanh function 双曲正切函数[ ] the average activation 平均活跃度[ ] the derivative checking method 梯度验证方法[ ] the empirical distribution 经验分布函数[ ] the energy function 能量函数[ ] the Lagrange dual 拉格朗日对偶函数[ ] the log likelihood 对数似然函数[ ] the pixel intensity value 像素灰度值[ ] the rate of convergence 收敛速度[ ] topographic cost term 拓扑代价项[ ] topographic ordered 拓扑秩序[ ] transformation 变换[200 ] translation invariant 平移不变性[ ] trivial answer 平凡解[ ] under-complete basis 不完备基[ ] unrolling 组合扩展[ ] unsupervised learning 无监督学习[ ] variance 方差[ ] vecotrized implementation 向量化实现[ ] vectorization 矢量化[ ] visual cortex 视觉皮层[ ] weight decay 权重衰减[ ] weighted average 加权平均值[ ] whitening 白化[ ] zero-mean 均值为零第二部分Letter A[ ] Accumulated error backpropagation 累积误差逆传播[ ] Activation Function 激活函数[ ] Adaptive Resonance Theory/ART 自适应谐振理论[ ] Addictive model 加性学习[ ] Adversarial Networks 对抗网络[ ] Affine Layer 仿射层[ ] Affinity matrix 亲和矩阵[ ] Agent 代理/ 智能体[ ] Algorithm 算法[ ] Alpha-beta pruning α-β剪枝[ ] Anomaly detection 异常检测[ ] Approximation 近似[ ] Area Under ROC Curve／AUC Roc 曲线下面积[ ] Artificial General Intelligence/AGI 通用人工智能[ ] Artificial Intelligence/AI 人工智能[ ] Association analysis 关联分析[ ] Attention mechanism 注意力机制[ ] Attribute conditional independence assumption 属性条件独立性假设[ ] Attribute space 属性空间[ ] Attribute value 属性值[ ] Autoencoder 自编码器[ ] Automatic speech recognition 自动语音识别[ ] Automatic summarization 自动摘要[ ] Average gradient 平均梯度[ ] Average-Pooling 平均池化Letter B[ ] Backpropagation Through Time 通过时间的反向传播[ ] Backpropagation/BP 反向传播[ ] Base learner 基学习器[ ] Base learning algorithm 基学习算法[ ] Batch Normalization/BN 批量归一化[ ] Bayes decision rule 贝叶斯判定准则[250 ] Bayes Model Averaging／BMA 贝叶斯模型平均[ ] Bayes optimal classifier 贝叶斯最优分类器[ ] Bayesian decision theory 贝叶斯决策论[ ] Bayesian network 贝叶斯网络[ ] Between-class scatter matrix 类间散度矩阵[ ] Bias 偏置/ 偏差[ ] Bias-variance decomposition 偏差-方差分解[ ] Bias-Variance Dilemma 偏差–方差困境[ ] Bi-directional Long-Short Term Memory/Bi-LSTM 双向长短期记忆[ ] Binary classification 二分类[ ] Binomial test 二项检验[ ] Bi-partition 二分法[ ] Boltzmann machine 玻尔兹曼机[ ] Bootstrap sampling 自助采样法／可重复采样／有放回采样[ ] Bootstrapping 自助法[ ] Break-Event Point／BEP 平衡点Letter C[ ] Calibration 校准[ ] Cascade-Correlation 级联相关[ ] Categorical attribute 离散属性[ ] Class-conditional probability 类条件概率[ ] Classification and regression tree/CART 分类与回归树[ ] Classifier 分类器[ ] Class-imbalance 类别不平衡[ ] Closed -form 闭式[ ] Cluster 簇/类/集群[ ] Cluster analysis 聚类分析[ ] Clustering 聚类[ ] Clustering ensemble 聚类集成[ ] Co-adapting 共适应[ ] Coding matrix 编码矩阵[ ] COLT 国际学习理论会议[ ] Committee-based learning 基于委员会的学习[ ] Competitive learning 竞争型学习[ ] Component learner 组件学习器[ ] Comprehensibility 可解释性[ ] Computation Cost 计算成本[ ] Computational Linguistics 计算语言学[ ] Computer vision 计算机视觉[ ] Concept drift 概念漂移[ ] Concept Learning System /CLS 概念学习系统[ ] Conditional entropy 条件熵[ ] Conditional mutual information 条件互信息[ ] Conditional Probability Table／CPT 条件概率表[ ] Conditional random field/CRF 条件随机场[ ] Conditional risk 条件风险[ ] Confidence 置信度[ ] Confusion matrix 混淆矩阵[300 ] Connection weight 连接权[ ] Connectionism 连结主义[ ] Consistency 一致性／相合性[ ] Contingency table 列联表[ ] Continuous attribute 连续属性[ ] Convergence 收敛[ ] Conversational agent 会话智能体[ ] Convex quadratic programming 凸二次规划[ ] Convexity 凸性[ ] Convolutional neural network/CNN 卷积神经网络[ ] Co-occurrence 同现[ ] Correlation coefficient 相关系数[ ] Cosine similarity 余弦相似度[ ] Cost curve 成本曲线[ ] Cost Function 成本函数[ ] Cost matrix 成本矩阵[ ] Cost-sensitive 成本敏感[ ] Cross entropy 交叉熵[ ] Cross validation 交叉验证[ ] Crowdsourcing 众包[ ] Curse of dimensionality 维数灾难[ ] Cut point 截断点[ ] Cutting plane algorithm 割平面法Letter D[ ] Data mining 数据挖掘[ ] Data set 数据集[ ] Decision Boundary 决策边界[ ] Decision stump 决策树桩[ ] Decision tree 决策树／判定树[ ] Deduction 演绎[ ] Deep Belief Network 深度信念网络[ ] Deep Convolutional Generative Adversarial Network/DCGAN 深度卷积生成对抗网络[ ] Deep learning 深度学习[ ] Deep neural network/DNN 深度神经网络[ ] Deep Q-Learning 深度Q 学习[ ] Deep Q-Network 深度Q 网络[ ] Density estimation 密度估计[ ] Density-based clustering 密度聚类[ ] Differentiable neural computer 可微分神经计算机[ ] Dimensionality reduction algorithm 降维算法[ ] Directed edge 有向边[ ] Disagreement measure 不合度量[ ] Discriminative model 判别模型[ ] Discriminator 判别器[ ] Distance measure 距离度量[ ] Distance metric learning 距离度量学习[ ] Distribution 分布[ ] Divergence 散度[350 ] Diversity measure 多样性度量／差异性度量[ ] Domain adaption 领域自适应[ ] Downsampling 下采样[ ] D-separation （Directed separation）有向分离[ ] Dual problem 对偶问题[ ] Dummy node 哑结点[ ] Dynamic Fusion 动态融合[ ] Dynamic programming 动态规划Letter E[ ] Eigenvalue decomposition 特征值分解[ ] Embedding 嵌入[ ] Emotional analysis 情绪分析[ ] Empirical conditional entropy 经验条件熵[ ] Empirical entropy 经验熵[ ] Empirical error 经验误差[ ] Empirical risk 经验风险[ ] End-to-End 端到端[ ] Energy-based model 基于能量的模型[ ] Ensemble learning 集成学习[ ] Ensemble pruning 集成修剪[ ] Error Correcting Output Codes／ECOC 纠错输出码[ ] Error rate 错误率[ ] Error-ambiguity decomposition 误差-分歧分解[ ] Euclidean distance 欧氏距离[ ] Evolutionary computation 演化计算[ ] Expectation-Maximization 期望最大化[ ] Expected loss 期望损失[ ] Exploding Gradient Problem 梯度爆炸问题[ ] Exponential loss function 指数损失函数[ ] Extreme Learning Machine/ELM 超限学习机Letter F[ ] Factorization 因子分解[ ] False negative 假负类[ ] False positive 假正类[ ] False Positive Rate/FPR 假正例率[ ] Feature engineering 特征工程[ ] Feature selection 特征选择[ ] Feature vector 特征向量[ ] Featured Learning 特征学习[ ] Feedforward Neural Networks/FNN 前馈神经网络[ ] Fine-tuning 微调[ ] Flipping output 翻转法[ ] Fluctuation 震荡[ ] Forward stagewise algorithm 前向分步算法[ ] Frequentist 频率主义学派[ ] Full-rank matrix 满秩矩阵[400 ] Functional neuron 功能神经元Letter G[ ] Gain ratio 增益率[ ] Game theory 博弈论[ ] Gaussian kernel function 高斯核函数[ ] Gaussian Mixture Model 高斯混合模型[ ] General Problem Solving 通用问题求解[ ] Generalization 泛化[ ] Generalization error 泛化误差[ ] Generalization error bound 泛化误差上界[ ] Generalized Lagrange function 广义拉格朗日函数[ ] Generalized linear model 广义线性模型[ ] Generalized Rayleigh quotient 广义瑞利商[ ] Generative Adversarial Networks/GAN 生成对抗网络[ ] Generative Model 生成模型[ ] Generator 生成器[ ] Genetic Algorithm/GA 遗传算法[ ] Gibbs sampling 吉布斯采样[ ] Gini index 基尼指数[ ] Global minimum 全局最小[ ] Global Optimization 全局优化[ ] Gradient boosting 梯度提升[ ] Gradient Descent 梯度下降[ ] Graph theory 图论[ ] Ground-truth 真相／真实Letter H[ ] Hard margin 硬间隔[ ] Hard voting 硬投票[ ] Harmonic mean 调和平均[ ] Hesse matrix 海塞矩阵[ ] Hidden dynamic model 隐动态模型[ ] Hidden layer 隐藏层[ ] Hidden Markov Model/HMM 隐马尔可夫模型[ ] Hierarchical clustering 层次聚类[ ] Hilbert space 希尔伯特空间[ ] Hinge loss function 合页损失函数[ ] Hold-out 留出法[ ] Homogeneous 同质[ ] Hybrid computing 混合计算[ ] Hyperparameter 超参数[ ] Hypothesis 假设[ ] Hypothesis test 假设验证Letter I[ ] ICML 国际机器学习会议[450 ] Improved iterative scaling/IIS 改进的迭代尺度法[ ] Incremental learning 增量学习[ ] Independent and identically distributed/i.i.d. 独立同分布[ ] Independent Component Analysis/ICA 独立成分分析[ ] Indicator function 指示函数[ ] Individual learner 个体学习器[ ] Induction 归纳[ ] Inductive bias 归纳偏好[ ] Inductive learning 归纳学习[ ] Inductive Logic Programming／ILP 归纳逻辑程序设计[ ] Information entropy 信息熵[ ] Information gain 信息增益[ ] Input layer 输入层[ ] Insensitive loss 不敏感损失[ ] Inter-cluster similarity 簇间相似度[ ] International Conference for Machine Learning/ICML 国际机器学习大会[ ] Intra-cluster similarity 簇内相似度[ ] Intrinsic value 固有值[ ] Isometric Mapping/Isomap 等度量映射[ ] Isotonic regression 等分回归[ ] Iterative Dichotomiser 迭代二分器Letter K[ ] Kernel method 核方法[ ] Kernel trick 核技巧[ ] Kernelized Linear Discriminant Analysis／KLDA 核线性判别分析[ ] K-fold cross validation k 折交叉验证／k 倍交叉验证[ ] K-Means Clustering K –均值聚类[ ] K-Nearest Neighbours Algorithm/KNN K近邻算法[ ] Knowledge base 知识库[ ] Knowledge Representation 知识表征Letter L[ ] Label space 标记空间[ ] Lagrange duality 拉格朗日对偶性[ ] Lagrange multiplier 拉格朗日乘子[ ] Laplace smoothing 拉普拉斯平滑[ ] Laplacian correction 拉普拉斯修正[ ] Latent Dirichlet Allocation 隐狄利克雷分布[ ] Latent semantic analysis 潜在语义分析[ ] Latent variable 隐变量[ ] Lazy learning 懒惰学习[ ] Learner 学习器[ ] Learning by analogy 类比学习[ ] Learning rate 学习率[ ] Learning Vector Quantization/LVQ 学习向量量化[ ] Least squares regression tree 最小二乘回归树[ ] Leave-One-Out/LOO 留一法[500 ] linear chain conditional random field 线性链条件随机场[ ] Linear Discriminant Analysis／LDA 线性判别分析[ ] Linear model 线性模型[ ] Linear Regression 线性回归[ ] Link function 联系函数[ ] Local Markov property 局部马尔可夫性[ ] Local minimum 局部最小[ ] Log likelihood 对数似然[ ] Log odds／logit 对数几率[ ] Logistic Regression Logistic 回归[ ] Log-likelihood 对数似然[ ] Log-linear regression 对数线性回归[ ] Long-Short Term Memory/LSTM 长短期记忆[ ] Loss function 损失函数Letter M[ ] Machine translation/MT 机器翻译[ ] Macron-P 宏查准率[ ] Macron-R 宏查全率[ ] Majority voting 绝对多数投票法[ ] Manifold assumption 流形假设[ ] Manifold learning 流形学习[ ] Margin theory 间隔理论[ ] Marginal distribution 边际分布[ ] Marginal independence 边际独立性[ ] Marginalization 边际化[ ] Markov Chain Monte Carlo/MCMC 马尔可夫链蒙特卡罗方法[ ] Markov Random Field 马尔可夫随机场[ ] Maximal clique 最大团[ ] Maximum Likelihood Estimation/MLE 极大似然估计／极大似然法[ ] Maximum margin 最大间隔[ ] Maximum weighted spanning tree 最大带权生成树[ ] Max-Pooling 最大池化[ ] Mean squared error 均方误差[ ] Meta-learner 元学习器[ ] Metric learning 度量学习[ ] Micro-P 微查准率[ ] Micro-R 微查全率[ ] Minimal Description Length/MDL 最小描述长度[ ] Minimax game 极小极大博弈[ ] Misclassification cost 误分类成本[ ] Mixture of experts 混合专家[ ] Momentum 动量[ ] Moral graph 道德图／端正图[ ] Multi-class classification 多分类[ ] Multi-document summarization 多文档摘要[ ] Multi-layer feedforward neural networks 多层前馈神经网络[ ] Multilayer Perceptron/MLP 多层感知器[ ] Multimodal learning 多模态学习[550 ] Multiple Dimensional Scaling 多维缩放[ ] Multiple linear regression 多元线性回归[ ] Multi-response Linear Regression ／MLR 多响应线性回归[ ] Mutual information 互信息Letter N[ ] Naive bayes 朴素贝叶斯[ ] Naive Bayes Classifier 朴素贝叶斯分类器[ ] Named entity recognition 命名实体识别[ ] Nash equilibrium 纳什均衡[ ] Natural language generation/NLG 自然语言生成[ ] Natural language processing 自然语言处理[ ] Negative class 负类[ ] Negative correlation 负相关法[ ] Negative Log Likelihood 负对数似然[ ] Neighbourhood Component Analysis/NCA 近邻成分分析[ ] Neural Machine Translation 神经机器翻译[ ] Neural Turing Machine 神经图灵机[ ] Newton method 牛顿法[ ] NIPS 国际神经信息处理系统会议[ ] No Free Lunch Theorem／NFL 没有免费的午餐定理[ ] Noise-contrastive estimation 噪音对比估计[ ] Nominal attribute 列名属性[ ] Non-convex optimization 非凸优化[ ] Nonlinear model 非线性模型[ ] Non-metric distance 非度量距离[ ] Non-negative matrix factorization 非负矩阵分解[ ] Non-ordinal attribute 无序属性[ ] Non-Saturating Game 非饱和博弈[ ] Norm 范数[ ] Normalization 归一化[ ] Nuclear norm 核范数[ ] Numerical attribute 数值属性Letter O[ ] Objective function 目标函数[ ] Oblique decision tree 斜决策树[ ] Occam’s razor 奥卡姆剃刀[ ] Odds 几率[ ] Off-Policy 离策略[ ] One shot learning 一次性学习[ ] One-Dependent Estimator／ODE 独依赖估计[ ] On-Policy 在策略[ ] Ordinal attribute 有序属性[ ] Out-of-bag estimate 包外估计[ ] Output layer 输出层[ ] Output smearing 输出调制法[ ] Overfitting 过拟合／过配[600 ] Oversampling 过采样Letter P[ ] Paired t-test 成对t 检验[ ] Pairwise 成对型[ ] Pairwise Markov property 成对马尔可夫性[ ] Parameter 参数[ ] Parameter estimation 参数估计[ ] Parameter tuning 调参[ ] Parse tree 解析树[ ] Particle Swarm Optimization/PSO 粒子群优化算法[ ] Part-of-speech tagging 词性标注[ ] Perceptron 感知机[ ] Performance measure 性能度量[ ] Plug and Play Generative Network 即插即用生成网络[ ] Plurality voting 相对多数投票法[ ] Polarity detection 极性检测[ ] Polynomial kernel function 多项式核函数[ ] Pooling 池化[ ] Positive class 正类[ ] Positive definite matrix 正定矩阵[ ] Post-hoc test 后续检验[ ] Post-pruning 后剪枝[ ] potential function 势函数[ ] Precision 查准率／准确率[ ] Prepruning 预剪枝[ ] Principal component analysis/PCA 主成分分析[ ] Principle of multiple explanations 多释原则[ ] Prior 先验[ ] Probability Graphical Model 概率图模型[ ] Proximal Gradient Descent/PGD 近端梯度下降[ ] Pruning 剪枝[ ] Pseudo-label 伪标记[ ] Letter Q[ ] Quantized Neural Network 量子化神经网络[ ] Quantum computer 量子计算机[ ] Quantum Computing 量子计算[ ] Quasi Newton method 拟牛顿法Letter R[ ] Radial Basis Function／RBF 径向基函数[ ] Random Forest Algorithm 随机森林算法[ ] Random walk 随机漫步[ ] Recall 查全率／召回率[ ] Receiver Operating Characteristic/ROC 受试者工作特征[ ] Rectified Linear Unit/ReLU 线性修正单元[650 ] Recurrent Neural Network 循环神经网络[ ] Recursive neural network 递归神经网络[ ] Reference model 参考模型[ ] Regression 回归[ ] Regularization 正则化[ ] Reinforcement learning/RL 强化学习[ ] Representation learning 表征学习[ ] Representer theorem 表示定理[ ] reproducing kernel Hilbert space/RKHS 再生核希尔伯特空间[ ] Re-sampling 重采样法[ ] Rescaling 再缩放[ ] Residual Mapping 残差映射[ ] Residual Network 残差网络[ ] Restricted Boltzmann Machine/RBM 受限玻尔兹曼机[ ] Restricted Isometry Property/RIP 限定等距性[ ] Re-weighting 重赋权法[ ] Robustness 稳健性/鲁棒性[ ] Root node 根结点[ ] Rule Engine 规则引擎[ ] Rule learning 规则学习Letter S[ ] Saddle point 鞍点[ ] Sample space 样本空间[ ] Sampling 采样[ ] Score function 评分函数[ ] Self-Driving 自动驾驶[ ] Self-Organizing Map／SOM 自组织映射[ ] Semi-naive Bayes classifiers 半朴素贝叶斯分类器[ ] Semi-Supervised Learning 半监督学习[ ] semi-Supervised Support Vector Machine 半监督支持向量机[ ] Sentiment analysis 情感分析[ ] Separating hyperplane 分离超平面[ ] Sigmoid function Sigmoid 函数[ ] Similarity measure 相似度度量[ ] Simulated annealing 模拟退火[ ] Simultaneous localization and mapping 同步定位与地图构建[ ] Singular Value Decomposition 奇异值分解[ ] Slack variables 松弛变量[ ] Smoothing 平滑[ ] Soft margin 软间隔[ ] Soft margin maximization 软间隔最大化[ ] Soft voting 软投票[ ] Sparse representation 稀疏表征[ ] Sparsity 稀疏性[ ] Specialization 特化[ ] Spectral Clustering 谱聚类[ ] Speech Recognition 语音识别[ ] Splitting variable 切分变量[700 ] Squashing function 挤压函数[ ] Stability-plasticity dilemma 可塑性-稳定性困境[ ] Statistical learning 统计学习[ ] Status feature function 状态特征函[ ] Stochastic gradient descent 随机梯度下降[ ] Stratified sampling 分层采样[ ] Structural risk 结构风险[ ] Structural risk minimization/SRM 结构风险最小化[ ] Subspace 子空间[ ] Supervised learning 监督学习／有导师学习[ ] support vector expansion 支持向量展式[ ] Support Vector Machine/SVM 支持向量机[ ] Surrogat loss 替代损失[ ] Surrogate function 替代函数[ ] Symbolic learning 符号学习[ ] Symbolism 符号主义[ ] Synset 同义词集Letter T[ ] T-Distribution Stochastic Neighbour Embedding/t-SNE T –分布随机近邻嵌入[ ] Tensor 张量[ ] Tensor Processing Units/TPU 张量处理单元[ ] The least square method 最小二乘法[ ] Threshold 阈值[ ] Threshold logic unit 阈值逻辑单元[ ] Threshold-moving 阈值移动[ ] Time Step 时间步骤[ ] Tokenization 标记化[ ] Training error 训练误差[ ] Training instance 训练示例／训练例[ ] Transductive learning 直推学习[ ] Transfer learning 迁移学习[ ] Treebank 树库[ ] Tria-by-error 试错法[ ] True negative 真负类[ ] True positive 真正类[ ] True Positive Rate/TPR 真正例率[ ] Turing Machine 图灵机[ ] Twice-learning 二次学习Letter U[ ] Underfitting 欠拟合／欠配[ ] Undersampling 欠采样[ ] Understandability 可理解性[ ] Unequal cost 非均等代价[ ] Unit-step function 单位阶跃函数[ ] Univariate decision tree 单变量决策树[ ] Unsupervised learning 无监督学习／无导师学习[ ] Unsupervised layer-wise training 无监督逐层训练[ ] Upsampling 上采样Letter V[ ] Vanishing Gradient Problem 梯度消失问题[ ] Variational inference 变分推断[ ] VC Theory VC维理论[ ] Version space 版本空间[ ] Viterbi algorithm 维特比算法[760 ] Von Neumann architecture 冯· 诺伊曼架构Letter W[ ] Wasserstein GAN/WGAN Wasserstein生成对抗网络[ ] Weak learner 弱学习器[ ] Weight 权重[ ] Weight sharing 权共享[ ] Weighted voting 加权投票法[ ] Within-class scatter matrix 类内散度矩阵[ ] Word embedding 词嵌入[ ] Word sense disambiguation 词义消歧Letter Z[ ] Zero-data learning 零数据学习[ ] Zero-shot learning 零次学习第三部分A[ ] approximations近似值[ ] arbitrary随意的[ ] affine仿射的[ ] arbitrary任意的[ ] amino acid氨基酸[ ] amenable经得起检验的[ ] axiom公理，原则[ ] abstract提取[ ] architecture架构，体系结构；建造业[ ] absolute绝对的[ ] arsenal军火库[ ] assignment分配[ ] algebra线性代数[ ] asymptotically无症状的[ ] appropriate恰当的B[ ] bias偏差[ ] brevity简短，简洁；短暂[800 ] broader广泛[ ] briefly简短的[ ] batch批量C[ ] convergence 收敛，集中到一点[ ] convex凸的[ ] contours轮廓[ ] constraint约束[ ] constant常理[ ] commercial商务的[ ] complementarity补充[ ] coordinate ascent同等级上升[ ] clipping剪下物；剪报；修剪[ ] component分量；部件[ ] continuous连续的[ ] covariance协方差[ ] canonical正规的，正则的[ ] concave非凸的[ ] corresponds相符合；相当；通信[ ] corollary推论[ ] concrete具体的事物，实在的东西[ ] cross validation交叉验证[ ] correlation相互关系[ ] convention约定[ ] cluster一簇[ ] centroids 质心，形心[ ] converge收敛[ ] computationally计算(机)的[ ] calculus计算D[ ] derive获得，取得[ ] dual二元的[ ] duality二元性；二象性；对偶性[ ] derivation求导；得到；起源[ ] denote预示，表示，是…的标志；意味着，[逻]指称[ ] divergence 散度；发散性[ ] dimension尺度，规格；维数[ ] dot小圆点[ ] distortion变形[ ] density概率密度函数[ ] discrete离散的[ ] discriminative有识别能力的[ ] diagonal对角[ ] dispersion分散，散开[ ] determinant决定因素[849 ] disjoint不相交的E[ ] encounter遇到[ ] ellipses椭圆[ ] equality等式[ ] extra额外的[ ] empirical经验；观察[ ] ennmerate例举，计数[ ] exceed超过，越出[ ] expectation期望[ ] efficient生效的[ ] endow赋予[ ] explicitly清楚的[ ] exponential family指数家族[ ] equivalently等价的F[ ] feasible可行的[ ] forary初次尝试[ ] finite有限的，限定的[ ] forgo摒弃，放弃[ ] fliter过滤[ ] frequentist最常发生的[ ] forward search前向式搜索[ ] formalize使定形G[ ] generalized归纳的[ ] generalization概括，归纳；普遍化；判断（根据不足）[ ] guarantee保证；抵押品[ ] generate形成，产生[ ] geometric margins几何边界[ ] gap裂口[ ] generative生产的；有生产力的H[ ] heuristic启发式的；启发法；启发程序[ ] hone怀恋；磨[ ] hyperplane超平面L[ ] initial最初的[ ] implement执行[ ] intuitive凭直觉获知的[ ] incremental增加的[900 ] intercept截距[ ] intuitious直觉[ ] instantiation例子[ ] indicator指示物，指示器[ ] interative重复的，迭代的[ ] integral积分[ ] identical相等的；完全相同的[ ] indicate表示，指出[ ] invariance不变性，恒定性[ ] impose把…强加于[ ] intermediate中间的[ ] interpretation解释，翻译J[ ] joint distribution联合概率L[ ] lieu替代[ ] logarithmic对数的，用对数表示的[ ] latent潜在的[ ] Leave-one-out cross validation留一法交叉验证M[ ] magnitude巨大[ ] mapping绘图，制图；映射[ ] matrix矩阵[ ] mutual相互的，共同的[ ] monotonically单调的[ ] minor较小的，次要的[ ] multinomial多项的[ ] multi-class classification二分类问题N[ ] nasty讨厌的[ ] notation标志，注释[ ] naïve朴素的O[ ] obtain得到[ ] oscillate摆动[ ] optimization problem最优化问题[ ] objective function目标函数[ ] optimal最理想的[ ] orthogonal(矢量，矩阵等)正交的[ ] orientation方向[ ] ordinary普通的[ ] occasionally偶然的P[ ] partial derivative偏导数[ ] property性质[ ] proportional成比例的[ ] primal原始的，最初的[ ] permit允许[ ] pseudocode伪代码[ ] permissible可允许的[ ] polynomial多项式[ ] preliminary预备[ ] precision精度[ ] perturbation 不安，扰乱[ ] poist假定，设想[ ] positive semi-definite半正定的[ ] parentheses圆括号[ ] posterior probability后验概率[ ] plementarity补充[ ] pictorially图像的[ ] parameterize确定…的参数[ ] poisson distribution柏松分布[ ] pertinent相关的Q[ ] quadratic二次的[ ] quantity量，数量；分量[ ] query疑问的R[ ] regularization使系统化；调整[ ] reoptimize重新优化[ ] restrict限制；限定；约束[ ] reminiscent回忆往事的；提醒的；使人联想…的（of）[ ] remark注意[ ] random variable随机变量[ ] respect考虑[ ] respectively各自的；分别的[ ] redundant过多的；冗余的S[ ] susceptible敏感的[ ] stochastic可能的；随机的[ ] symmetric对称的[ ] sophisticated复杂的[ ] spurious假的；伪造的[ ] subtract减去；减法器[ ] simultaneously同时发生地；同步地[ ] suffice满足[ ] scarce稀有的，难得的[ ] split分解，分离[ ] subset子集[ ] statistic统计量[ ] successive iteratious连续的迭代[ ] scale标度[ ] sort of有几分的[ ] squares平方T[ ] trajectory轨迹[ ] temporarily暂时的[ ] terminology专用名词[ ] tolerance容忍；公差[ ] thumb翻阅[ ] threshold阈，临界[ ] theorem定理[ ] tangent正弦U[ ] unit-length vector单位向量V[ ] valid有效的，正确的[ ] variance方差[ ] variable变量；变元[ ] vocabulary词汇[ ] valued经估价的；宝贵的[ ] W [1038 ] wrapper包装。

A-Level数学词汇⼤全，三天就能背完！线性代数篇①algebraic cofactor代数余⼦式array数组canonical form标准型characteristic polynomial特征多项式characteristic root特征根coefficient matrix系数矩阵column列column rank列秩component分量determinant⾏列式diagonal element对⾓元素diagonal matrix对⾓矩阵dimension维数diagonalisable matrix可对⾓化矩阵eigenvalue特征值eigenvector特征向量fundamental solution基本解geometric multiplicity⼏何重数homogeneous equation齐次⽅程identity matrix单位矩阵infinite dimensional⽆穷维的inverse matrix逆矩阵least squares problem最⼩⼆乘问题linear combination线性组合②linear dependence线性相关linear equation线性⽅程linear independence线性⽆关linear transformation线性变换main diagonal主对⾓线matrix矩阵multidimensional多维nonsingular matrix⾮奇异矩阵normal equation法⽅程normal form标准型normal matrix正规矩阵orthogonal matrix正交矩阵principal minor主⼦式rank秩rectangular matrix长⽅阵row⾏row rank⾏秩row (column) vector⾏（列）向量③scalar标量singular matrix奇异矩阵singular matrix奇异矩阵square matrix⽅阵symmetric matrix对称矩阵trace迹transposed matrix转置矩阵unit vector单位向量vector向量zero element零元素zero vector零向量基础数学篇①axiom公理theorem定理calculation计算operation运算prove证明hypothesis, hypotheses(pl.)假设proposition命题arithmetic算术plus(prep.), add(v.), addition(n.)加augend, summand被加数addend加数sum和minus(prep.), subtract(v.), subtraction(n.) 减minuend被减数subtrahend减数②remainder差times(prep.), multiply(v.), multiplication(n.)乘multiplicand, faciend被乘数multiplicator乘数product积divided by(prep.), divide(v.), division(n.)除dividend被除数divisor除数quotient商equals, is equal to, is equivalent to等于is greater than⼤于is lesser than⼩于is equal or greater than⼤于等于is equal or lesser than⼩于等于③operator运算符digit数字number数natural number⾃然数integer整数decimal⼩数decimal point⼩数点fraction分数numerator分⼦denominator分母ratio⽐positive正negative负null, zero, nought, nil零④decimal system⼗进制binary system⼆进制hexadecimal system⼗六进制weight, significance权carry进位truncation截尾round四舍五⼊round down下舍⼊round up上舍⼊significant digit有效数字insignificant digit⽆效数字⑤algebra代数formula, formulae(pl.)公式monomial单项式polynomial, multinomial多项式coefficient系数unknown, x-factor, y-factor, z-factor未知数equation等式，⽅程式simple equation⼀次⽅程quadratic equation⼆次⽅程cubic equation三次⽅程quartic equation四次⽅程inequation不等式⑥factorial阶乘logarithm对数exponent指数，幂power乘⽅square⼆次⽅，平⽅square⼆次⽅，平⽅cube三次⽅，⽴⽅the power of four, the fourth power四次⽅the power of n, the nth powern次⽅evolution, extraction开⽅square root⼆次⽅根，平⽅根cube root三次⽅根，⽴⽅根the root of four, the fourth root四次⽅根the root of n, the nth rootn次⽅根⑦aggregate集合element元素void空集subset⼦集intersection交集union并集complement补集mapping映射function函数domain, field of definition定义域range值域constant常量variable变量⑧monotonicity单调性parity奇偶性periodicity周期性image图象series数列，级数calculus微积分differential微分derivative导数limit极限infinite(a.) infinity(n.)⽆穷⼤infinitesimal⽆穷⼩integral积分definite integral定积分indefinite integral不定积分rational number有理数irrational number理数real number实数imaginary number虚数complex number复数matrix矩阵determinant⾏列式geometry⼏何⑨point点line线plane⾯solid体segment线段radial射线parallel平⾏intersect相交angle⾓degree⾓度radian弧度acute angle锐⾓right angle直⾓obtuse angle钝⾓straight angle平⾓perigon周⾓base底side边height⾼triangle三⾓形acute triangle锐⾓三⾓形right triangle直⾓三⾓形leg直⾓边hypotenuse斜边Pythagorean theorem勾股定理obtuse triangle钝⾓三⾓形scalene triangle不等边三⾓形isosceles triangle等腰三⾓形equilateral triangle等边三⾓形quadrilateral四边形⑩parallelogram平⾏四边形rectangle矩形length长width宽rhomb, rhombus, rhombi(pl.), diamond菱形square正⽅形trapezoid梯形trapezoid梯形right trapezoid直⾓梯形isosceles trapezoid等腰梯形pentagon五边形hexagon六边形heptagon七边形octagon⼋边形enneagon九边形decagon⼗边形hendecagon⼗⼀边形dodecagon⼗⼆边形polygon多边形equilateral polygon正多边形circle圆centre(BrE), center(AmE)圆⼼radius半径diameter直径pi圆周率arc弧semicircle半圆sector扇形ring环ellipse椭圆circumference圆周perimeter周长area⾯积locus, loca(pl.)轨迹similar相似similar相似congruent全等tetrahedron四⾯体pentahedron五⾯体hexahedron六⾯体parallelepiped平⾏六⾯体cube⽴⽅体heptahedron七⾯体octahedron⼋⾯体enneahedron九⾯体decahedron⼗⾯体hendecahedron⼗⼀⾯体dodecahedron⼗⼆⾯体icosahedron⼆⼗⾯体polyhedron多⾯体pyramid棱锥prism棱柱frustum of a prism棱台rotation旋转axis轴cone圆锥cylinder圆柱frustum of a cone圆台sphere球hemisphere半球undersurface底⾯surface area表⾯积volume体积space空间coordinates坐标系x-axis, y-axis, z-axis坐标轴x-coordinate横坐标y-coordinate纵坐标origin原点hyperbola双曲线parabola抛物线trigonometry三⾓sine正弦cosine余弦tangent正切cotangent余切secant正割cosecant余割arc sine反正弦arc cosine反余弦arc tangent反正切arc cotangent反余切arc secant反正割arc cosecant反余割phase相位period周期amplitude振幅incentre(BrE), incenter(AmE)内⼼excentre(BrE), excenter(AmE)外⼼escentre(BrE), escenter(AmE)旁⼼orthocentre(BrE), orthocenter(AmE)垂⼼barycentre(BrE), barycenter(AmE)重⼼inscribed circle内切圆circumcircle外切圆statistics统计average平均数weighted average加权平均数variance⽅差root-mean-square deviation, standard deviation标准差propotion⽐例percent百分⽐percentage百分点percentile百分位数permutation排列combination组合probability概率，或然率distribution分布normal distribution正态分布abnormal distribution⾮正态分布graph图表bar graph条形统计图histogram柱形统计图broken line graph折线统计图curve diagram曲线统计图pie diagram扇形统计图微积分微积分①analytic expression解析表达式analytic geometry解析⼏何antiderivative原函数asymptote渐进average value平均值boundary边界boundary integral边界积分bounded有界的calculus微积分chain rule链式法则change of variable变量替换closed set闭集complement补集complete完全的conditionally convergent条件收敛continuity连续性continuous everywhere处处连续②continuously differentiable连续可微convergence收敛convolution卷积covering覆盖critical point临界点cross product向量积cross section截⾯decay衰变definite integral定积分derivative导数differentiable everywhere处处可微differentiation微分divergence发散dot product点积double integral⼆重积分③elementary function初等函数empty set空集even function偶函数first derivative⼀阶导数Fourier series傅⾥叶级数Fourier transform傅⾥叶变换function series函数级数fundamental theorem基本定理generalised integral⼴义积分gradient梯度higher order derivative⾼阶导数identity function恒等函数implicit differentiation隐式求导implicit function隐函数④improper integral反常积分increment增量indefinite integral不定积分infinitesimal⽆穷⼩infinity⽆穷⼤inflection point拐点integrable可积的integral, integration积分integral sign积分号integrand被积函数integration by parts分部积分法integration by substitution换元积分法integration constant积分常数intermediate value theorem介值定理intersection交集⑤inverse mapping逆映射isolated point孤⽴点least value最⼩值limit极限L’Hospital’s rule洛必达法则Maclaurin series麦克劳林级数maximal value极⼤值mean value theorem中值定理minimum极⼩monotone function单调函数multiple integral多重积分multivariable function多元函数multivariate多变量natural exponential function⾃然指数函数natural logarithm⾃然对数neighbourhood邻域numerable可数的open set开集open set开集⑥ordinal number序数parameter参数parametric equation参数⽅程partial derivatives偏导数partial differential偏微分partial fraction部分分式power series幂级数product rule乘积法则proper subset真⼦集properly include真包含quantity量quotient rule商法则rate of change变化率remainder term余项second derivative⼆阶导数sequence序列set theory集合论⑦singular point奇异点smooth function光滑函数solid of revolution旋转体space curve空间曲线sub下标subset⼦集super上标surface integral⾯积分surface of revolution旋转曲⾯Taylor’s expansion泰勒展开式Taylor’s series泰勒级数total differential全微分triple integral三重积分unbounded function⽆界函数unbounded set⽆界集uncountable set不可数集uniformly bounded⼀致有界uniformly continuous⼀致连续uniformly convergent⼀致收敛union并集upper (lower) limit上（下）极限variation变差。