Semi-Supervised Learning by

Under consideration for publication in Knowledge and Information

Systems

Semi-Supervised Learning by Disagreement

Zhi-Hua Zhou and Ming Li

National Key Laboratory for Novel Software Technology

Nanjing University,Nanjing210093,China

Abstract.In many real-world tasks there are abundant unlabeled examples but the number of labeled training examples is limited,because labeling the examples requires human e?orts and expertise.So,semi-supervised learning which tries to exploit unla-beled examples to improve learning performance has become a hot topic.Disagreement-based semi-supervised learning is an interesting paradigm,where multiple learners are trained for the task and the disagreements among the learners are exploited during the semi-supervised learning process.This survey article provides an introduction to research advances in this paradigm.

Keywords:Machine Learning;Data Mining;Semi-Supervised Learning;Disagreement-Based Semi-Supervised Learning

1.Introduction

In traditional supervised learning,hypotheses are learned from a large number of training examples.Each training example has a label which indicates the desired output of the event described by the example.In classi?cation,the label indicates the category into which the corresponding example falls into;in regression,the label is a real-valued output such as temperature,height,price,etc.

Advances in data collection and storage technology enable the easy accu-mulation of a large amount of training instances without labels in many real-world applications.Assigning labels to those unlabeled examples is expensive because the labeling process requires human e?orts and expertise.For example, in computer-aided medical diagnosis,a large number of X-ray images can be obtained from routine examination,yet it is di?cult to ask physicians to mark

Received October16,2008

Revised March16,2009

Accepted April03,2009

2Z.-H.Zhou and M.Li all focuses in all images.If we use traditional supervised learning techniques to build a diagnosis system,then only a small portion of training data,on which the focuses have been marked,are useful.Due to the limited amount of labeled training examples,it may be di?cult to get a strong diagnosis system.Then,a question arises:Can we leverage the abundant unlabeled training examples with a few labeled training examples to generate a strong hypothesis?Roughly speak-ing,there are three major techniques for this purpose[82],i.e.,semi-supervised learning,transductive learning and active learning.

Semi-supervised learning[21,92]deals with methods for automatically ex-ploiting unlabeled data in addition to labeled data to improve learning per-formance,where no human intervention is assumed.Transductive learning is a cousin of semi-supervised learning,which also tries to exploit unlabeled data au-tomatically.The main di?erence between them lies in the di?erent assumptions on the test data.Transductive learning takes a“close-world”assumption,i.e., the test data set is known in advance and the goal of learning is to optimize the generalization ability on this test data set,while the unlabeled examples are exactly the test examples.Semi-supervised learning takes an“open-world”assumption,i.e.,the test data set is not known and the unlabeled examples are not necessary test examples.In fact,the idea of transductive learning originated from statistical learning theory[69].Vapnik[69]believed that one often wants to make predictions on test examples at hand instead of on all potential examples, while inductive learning that seeks the best hypothesis over the whole distri-bution is a problem more di?cult than what is actually needed;we should not try to solve a problem by solving a more di?cult intermediate problem,and so, transductive learning is more appropriate than inductive learning.Up to now there is still a debate in the machine learning community on this learning phi-losophy.Nevertheless,it is well recognized that transductive learning provides an important insight into the exploitation of unlabeled data.

Active learning deals with methods that assume that the learner has some control over the input space.In exploiting unlabeled data,it requires an oracle, such as a human expert,from which the ground-truth labels of instances can be queried.The goal of active learning is to minimize the number of queries for building a strong learner.Here,the key is to select those unlabeled examples where the labeling will convey the most helpful information to the learner.There are two major schemes,i.e.,uncertainty sampling and committee-based sampling. Approaches of the former train a single learner and then query the unlabeled example on which the learner is least con?dent[45];approaches of the latter generate multiple learners and then query the unlabeled example on which the learners disagree to the most[1,63].

In this survey article,we will introduce an interesting and important semi-supervised learning paradigm,i.e.,disagreement-based semi-supervised learning. This line of research started from Blum&Mitchell’s seminal paper on co-training [13]1.Di?erent relevant approaches have been developed with di?erent names, and recently the name disagreement-based semi-supervised learning was coined [83]to re?ect the fact that they are actually in the same family,and the key for the learning process to proceed is to maintain a large disagreement between base learners.Although transductive learning or active learning may be involved in some place,we will not talk more on them.In the following we will start by a 1This seminal paper won the“ten years best paper award”at ICML’08.

Semi-Supervised Learning by Disagreement3 brief introduction to semi-supervised learning,and then we will go to the main theme to introduce representative disagreement-based semi-supervised learning approaches,theoretical foundations,and some applications to real-world tasks.

2.Semi-Supervised Learning

In semi-supervised learning,a labeled training data set L={(x1,y1),(x2,y2),...,

(x|L|,y|L|)}and an unlabeled training data set U={x 1,x 2,...,x

|U|}are pre-

sented to the learning algorithm to construct a function f:X→Y for predicting the labels of unseen instances,where X and Y are respectively the input space and output space,x i,x j∈X(i=1,2,...,|L|,j=1,2,...,|U|)are d-dimensional feature vectors drawn from X,and y i∈Y is the label of x i;usually|L| |U|.

It is well-known that semi-supervised learning originated from[64].In fact, some straightforward use of unlabeled examples appeared even earlier[40,50, 52,53,57].Due to the di?culties in incorporating unlabeled data directly into conventional supervised learning methods(e.g.,BP neural networks)and the lack of a clear understanding of the value of unlabeled data in the learning process, the study of semi-supervised learning attracted attention only after the middle of1990s.As the demand for automatic exploitation of unlabeled data increases and the value of unlabeled data was disclosed by some early analyses[54,78], semi-supervised learning has become a hot topic.

Most early studies did not provide insight or explanation to the reason why unlabeled data can be bene?https://www.doczj.com/doc/5f816874.html,ler and Uyar[54]provided possibly the ?rst explanation to the usefulness of unlabeled data from the perspective of data distribution estimation.They assumed that the data came from a Gaussian mixture model with L mixture components,i.e.,

f(x|θ)=

L

l=1

αl f(x|θl),(1)

whereαl is the mixture coe?cient satisfying L

l=1

αl=1,whileθ={θl}are

the model parameters.In this case,label c i can be considered a random variable C whose distribution P(c i|x i,m i)is determined by the mixture component m i and the feature vector x i.The optimal classi?cation rule for this model is the MAP(maximum a posterior)criterion,that is,

h(x)=arg max

k

j

P(c i=k|m i=j,x i)P(m i=j|x i),(2)

where

P(m i=j|x i)=

αj f(x i|θj)

L

l=1

αl f(x i|θl)

.(3)

Thus,the objective of learning is accomplished by estimating the terms P(c i=k|m i=j,x i)and P(m i=j|x i)from the training data.It can be found that only the estimate of the?rst probability involves the class label.So,unla-beled examples can be used to improve the estimate of the second probability,and hence improve the performance of the learned https://www.doczj.com/doc/5f816874.html,ter,Zhang and Oles

4Z.-H.Zhou and M.Li [78]analyzed the value of unlabeled data for parametric models.They suggested that if a parametric model can be decomposed as P(x,y|θ)=P(y|x,θ)P(x|θ), the use of unlabeled examples can help to reach a better estimate of the model parameters.

There are two basic assumptions in semi-supervised learning,that is,the cluster assumption and the manifold assumption.The former assumes that data with similar inputs should have similar class labels;the latter assumes that data with similar inputs should have similar outputs.The cluster assumption concerns classi?cation,while the manifold assumption can also be applied to tasks other than classi?cation.In some sense,the manifold assumption is a generalization of the cluster assumption.These assumptions are closely related to the idea of low density separation,which has been taken by many semi-supervised learning algorithms.No matter which assumption is taken,the common underlying belief is that the unlabeled data provide some helpful information on the ground-truth data distribution.So,a key of semi-supervised learning is to exploit the distributional information disclosed by unlabeled examples.

Many semi-supervised learning algorithms have been developed.Roughly speaking,they can be categorized into four categories,i.e.,generative meth-ods[54,56,64],S3VMs(Semi-Supervised Support Vector Machines)[22,37,42,44], graph-based methods[7–9,80,93],and disagreement-based methods[13,16,36, 48,55,85,88,89,91].

In generative approaches,both labeled and unlabeled examples are assumed to be generated by the same parametric model.Thus,the model parameters directly link unlabeled examples and the learning objective.Methods in this category usually treat the labels of the unlabeled data as missing values of model parameters,and employ the EM(expectation-maximization)algorithm[29]to conduct maximum likelihood estimation of the model parameters.The methods di?er from each other by the generative models used to?t the data,for example, mixture of Gaussian[64],mixture of experts[54],Na¨?ve Bayes[56],etc.The generative methods are simple and easy to implement,and may achieve better performance than discriminative models when learning with a very small number of labeled examples.However,methods in this category su?er from a serious de?ciency.That is,when the model assumption is incorrect,?tting the model using a large number of unlabeled data will result in performance degradation [23,26].Thus,in order to make it e?ective in real-world applications,one needs to determine the correct generative model to use based on domain knowledge. There are also attempts of combining advantages of generative and discriminative approaches[4,33].

S3VMs try to use unlabeled data to adjust the decision boundary learned from the small number of labeled examples,such that it goes through the less dense region while keeping the labeled data being correctly classi?ed.Joachims [42]proposed TSVM(Transductive Support Vector Machine).This algorithm ?rstly initiates an SVM using labeled examples and assigns potential labels to unlabeled data.Then,it iteratively maximizes the margin over both labeled and unlabeled data with their potential labels by?ipping the labels of the unlabeled examples on di?erent sides of the decision boundary.An optimal solution is reached when the decision boundary not only classi?es the labeled data as accu-rate as possible but also avoids going through the high density region.Chapelle and Zien[22]derived a special graph kernel using the low density separation cri-terion,and employed gradient descent to solve the SVM optimization problem. The non-convexity of the loss function of TSVM leads to the fact that there are

Semi-Supervised Learning by Disagreement5 many local optima.Many studies tried to reduce the negative in?uence caused by the non-convexity.Typical methods include:employing a continuation approach, which begins by minimizing an easy convex objective function and sequentially deforms it to the non-convex loss function of TSVM[20];employing a determin-istic annealing approach,which decomposes the original optimization problem into a series of convex optimization problems,from easy to hard,and solves them sequentially[65,66];employing the convex-concave procedure(CCCP)[77] to directly optimize the non-convex loss function[25],etc.

The?rst graph-based semi-supervised learning method is possibly[11].Blum and Chawla[11]constructed a graph whose nodes are the training examples (both labeled and unlabeled)and the edges between nodes re?ect certain re-lation,such as similarity,between the corresponding examples.Based on the graph,the semi-supervised learning problem can be addressed by seeking the minimum cut of the graph such that nodes in each connected component have the same https://www.doczj.com/doc/5f816874.html,ter,Blum et al.[12]disturbed the graph with some random-ness and produced a“soft”minimum cut using majority voting.Note that the predictive function in[11]and[12]is discrete,i.e.,the prediction on unlabeled ex-amples should be one of the possible labels.Zhu et al.[93]extended the discrete prediction function to continuous case.They modelled the distribution of the prediction function over the graph with Gaussian random?elds and analytically showed that the prediction function with the lowest energy should have the har-monic property.They designed a label propagation strategy over the graph using such a harmonic property.Zhou et al.[80]de?ned a quadratic loss of the predic-tion function over both the labeled and unlabeled data,and used a normalized graph Laplacian as the regularizer.They provided an iterative label propagation method yielding the same solution of the regularized loss function.Belkin and Niyogi[7]assumed that the data are distributed on a Riemannian manifold,and used the discrete spectrum and its eigenfunction of a nearest neighbor graph to reform the learning problem to interpolate over the data points in Hillbert space. Then,Belkin et al.[8,9]further extended the idea of manifold learning in semi-supervised learning scenario,and proposed manifold regularization framework in Reproducing Kernel Hillbert Space(RKHS).This framework directly exploits the local smoothness assumption to regularize the loss function de?ned over the labeled training examples such that the learned prediction function is biased to give similar output to the examples in a local region.Sindhwani et al.[67] embedded the manifold regularization into a semi-supervised kernel de?ned over the overall input space.They modi?ed the original RKHS by changing the norm while keeping the same function space.This leads to a new RKHS,in which learning supervised kernel machines with only the labeled data is equivalent to a certain manifold regularization over both labeled and unlabeled data in original input space.

Most of the previous studies on graph-based semi-supervised learning usually focus on how to conduct semi-supervised learning over a given graph.It is note-worthy that how to construct a graph which re?ects the essential relationship between examples is a key that will seriously a?ect the learning performance. Although the graph construction might favor certain domain knowledge,some re-searchers have attempted to construct graphs of high quality using some domain-knowledge-independent properties.Carreira-Perpinan and Zemel[19]generated multiple minimum spanning trees based on perturbation to construct a robust graph.Wang and Zhang[70]used the idea of LLE[60]that instances can be reconstructed by their neighbors to obtain weights over the edges in the graph.

6Z.-H.Zhou and M.Li Zhang and Lee[79]selected a better RBF bandwidth to minimize the predic-tive error on labeled data using cross validation.Hein and Maier[39]attempted to remove noisy data and hence obtained a better graph.Note that,although graph-based semi-supervised learning approaches have been used in many ap-plications,they su?er seriously from poor scalability.This de?ciency has been noticed and some e?orts have been devoted to this topic[34,76,94].Recently, Goldberg et al.[35]proposed an online manifold regularization framework as well as e?cient solutions,which improves the applicability of manifold regularization to large-scale and real-time problems.

The name disagreement-based semi-supervised learning was coined recently by Zhou[83],but this line of research started from Blum&Mitchell’s seminal work[13].In those approaches,multiple learners are trained for the same task and the disagreements among the learners are exploited during the learning process. Here,unlabeled data serve as a kind of“platform”for information exchange.If one learner is much more con?dent on a disagreed unlabeled example than other learner(s),then this learner will teach other(s)with this example;if all learners are comparably con?dent on a disagreed unlabeled example,then this example may be selected for query.Since methods in this category do not su?er from the model assumption violation,nor the non-convexity of the loss function,nor the poor scalability of the learning algorithms,disagreement-based semi-supervised learning has become an important learning paradigm.In the following sections, we will review studies of this paradigm in more detail.

3.Disagreement-Based Semi-Supervised Learning

A key of disagreement-based semi-supervised learning is to generate multiple learners,let them collaborate to exploit unlabeled examples,and maintain a large disagreement between the base learners.In this section,we roughly classify existing disagreement-based semi-supervised learning techniques into three cat-egories,that is,learning with multiple views,learning with single view multiple classi?ers,and learning with single view multiple regressors.

3.1.Learning with Multiple Views

In some applications,the data set has several disjoint subsets of attributes(each subset is called as a view).For example,the web page classi?cation task has two views,i.e.,the texts appearing on the web page itself and the anchor text attached to hyper-links pointing to this page[13].Naturally,we can generate multiple learners with these multiple views and then use the multiple learn-ers to start disagreement-based semi-supervised learning.Note that there were abundant research on multi-view learning,yet a lot of work was irrelevant to semi-supervised learning,and so they are not mentioned in this section.

The?rst algorithm of this paradigm is the co-training algorithm proposed by Blum and Mitchell[13].They assumed that the data has two su?cient and redundant views(i.e.,attribute sets),where each view is su?cient for training a strong learner and the views are conditionally independent to each other given the class label.

The co-training procedure,which is illustrated in Fig.1,is rather simple. In co-training,each learner is generated using the original labeled data.Then,

Semi-Supervised Learning by Disagreement7

Fig.1.An illustration of the co-training procedure

each learner will select and label some high-con?dent unlabeled examples for its peer https://www.doczj.com/doc/5f816874.html,ter,the learners will be re?ned using the newly labeled examples provided by its peer.With such a process,when two learners disagree on an unlabeled example,the learner which misclassi?es this example will be taught by its peer.The whole process will repeat until no learner changes or a pre-set number of learning rounds has been executed.Blum and Mitchell[13]analyzed the e?ectiveness of the co-training algorithm,and showed that co-training can e?ectively exploit unlabeled data to improve the generalization ability,given that the training data are described by su?cient and redundant views which are conditionally independent to each other given the class label.

Another famous multi-view semi-supervised learning algorithm,co-EM[55], combines multi-view learning with the probabilistic EM approach.This algo-rithm requires the base learners be capable of estimating class probabilities, and so na¨?ve Bayes classi?ers are generally used.Through casting linear classi-?ers into a probabilistic framework,Brefeld and Sche?er[15]replaced the na¨?ve Bayes classi?ers by support vector machines.The co-EM algorithm has also been applied to unsupervised clustering[10].

Brefeld et al.[14]tried to construct a hidden markov perceptron[3]in each of the two views,where the two hidden markov perceptrons were updated according to the heuristic that,if the two perceptrons disagree on an unlabled example then each perceptron is moved towards that of its peer view.Brefeld et al.[14]did not mention how to extend this method to more than two views,but it could be able to move the perceptrons towards their median peer view when they disagree, according to the essential of their heuristics.However,the convergence of the process has not been proved even for two-view case.Brefeld and Sche?er[16] extended SVM-2K[32],a supervised co-SVM that minimizes the training error as well as the disagreement between the two views,to semi-supervised learning and applied it to several tasks involving structured output variables such as multi-class classi?cation,label sequence learning and natural language parsing.

In real-world applications,when the data has two views,it is rarely that the two views are conditionally independent given the class label.Even a weak

8Z.-H.Zhou and M.Li conditional independence[2]is di?cult to be met in practice.In fact,the as-sumption of su?cient and redundant views,which are conditionally independent to each other given the class label,is so strong that when it holds,a single labeled training example is able to launch a successful semi-supervised learning[91].

Zhou et al.[91]e?ectively exploited the“compatibility”of the two views to turn some unlabeled examples into labeled ones.Speci?cally,given two su?-cient and redundant views v1and v2(in this case,an instance is represented by

x=(x(v1),x(v2))),a prediction function f v

i is learned from each view respec-

tively.Since the two views are su?cient,the learned prediction functions satisfy

f v

1(x(v1))=f v

2

(x(v2))=y,where y is the ground-truth label of x.Intuitively,

some projections in these two views should have strong correlation with the ground-truth.For either view,there should exist at least one projection which is correlated strongly with the ground-truth,since otherwise this view could not be su?cient.Since the two su?cient views are conditionally independent given the class label,the most strongly correlated pair of projections should be in accor-dance with the ground-truth.Thus,if such highly correlated projections of these two views can be identi?ed,they can help induce the labels of some unlabeled ex-amples.With those additional labeled examples,two learners can be generated, and then they can be improved using the standard co-training routine,i.e.,if the learners disagree on an unlabeled example,the learner which misclassi?es this example will be taught by its peer.To identify the correlated projections,Zhou et al.[91]employed kernel canonical component analysis(KCCA)[38]to?nd two sets of basis vectors in the feature space,one for each view,such that after projecting the two views onto the corresponding sets of basis vectors,the corre-lation between the projected views is maximized.Here the correlation strength (λ)of the projections are also given by KCCA.Instead of considering only the highest correlated projections,they used top m projections with the m-highest correlation strength.Finally,by linearly combining similarity in each projection, they computed con?denceρi of each unlabeled example x i as being with the same label as that of the single labeled positive example x0,as shown in Eq.4,

ρi=

m

j=1

λj sim i,j,(4)

where

sim i,j=exp

?d2

P j(x(v1)

i

),P j(x(v1)

)

+

exp

?d2

P j(x(v2)

i

),P j(x(v2)

)

(5)

and d(a,b)measures the Euclidian distance between a and b.

Thus,several unlabeled examples with the highest and lowest con?dence values can be picked out,respectively,and used as extra positive and negative examples.Based on this augmented labeled training set,standard co-training can be employed for semi-supervised learning.Again,intuitively,when the two learners disagree on an unlabeled example,the learner which misclassi?es this example will be taught by its peer.Such kind of method has been applied to content-based image retrieval[91]where there is only one example image in the ?rst round of query.

Semi-Supervised Learning by Disagreement9 3.2.Learning with Single View Multiple Classi?ers

In most real-world applications the data sets have only one attribute set rather than two.So the e?ectiveness and usefulness of the standard co-training is lim-ited.To take advantage of the interaction between learners when exploiting un-labeled data,methods that do not rely on the existence of two views have been developed.

A straightforward way to tackle this problem is to partition the attribute sets into two disjoint sets,and conduct standard co-training based on the manually generated views.Nigam and Ghani[55]empirically studied the performance of standard co-training algorithm in this case.The experimental results suggested that when the attribute set is su?ciently large,randomly splitting the attributes and then conducting standard co-training may lead to a good performance.How-ever,many applications are not described by a large number of attribute,and co-training on randomly partitioned views is not always e?ective.Thus,a better way is to design single-view methods that can exploit the interaction between multiple learners rather than tailoring the data sets for standard two-view co-training.

Goldman and Zhou[36]proposed a method that does not rely on two views. They employed di?erent learning algorithms to train the two classi?ers,respec-tively.It is required that each classi?er is able to partition the instance space into a number of equivalence classes.In order to identify which unlabeled ex-ample to label,and to decide how to make the prediction when two classi?ers disagree,ten-fold cross validations are executed such that the con?dences of the two classi?ers as well as the con?dences of the equivalence classes that contain the concerned instance can be https://www.doczj.com/doc/5f816874.html,ter,this idea was extended to in-volving more learning algorithms[81].Note that although[36]does not rely on the existence of two views,it requires special learning algorithms to construct classi?ers.This prevents its application to other kinds of learning algorithms.

Zhou and Li[88]proposed the tri-training method,which requires neither the existence of two views nor special learning algorithms,thus it can be applied to more real-world problems.In contrast to the previous studies[13,36,55],tri-training attempts to exploit unlabeled data using three classi?ers.Such a setting tackles the problem of determining how to e?ciently select most con?dently predicted unlabeled examples to label and produces?nal hypothesis.Note that the essential of tri-training is extensible for more than three classi?ers,which will be introduced later.The use of more classi?ers also provides a chance to employ ensemble learning techniques[84]to improve the performance of semi-supervise learning.

Generally,tri-training works in the following way.First,three classi?ers are initially trained from the original labeled data.Unlike[36],tri-training uses the same learning algorithm(e.g.,C4.5decision tree)to generate the three classi?ers. In order to make the three classi?ers diverse,the original labeled example set is bootstrap sampled[31]to produce three perturbed training sets,on each of which a classi?er is then generated.The generation of the initial classi?ers is similar to training an ensemble from the labeled example set using Bagging[17].Then, intuitively,in each tri-training round,if two classi?ers agree on the labeling of an unlabeled example while the third one disagrees,then these two classi?ers will teach the third classi?er on this example.Finally,three classi?ers are combined by majority voting.Note that the“majority teaches minority”strategy serves as an implicit con?dence measurement,which avoids the use of complicated time-

10Z.-H.Zhou and M.Li consuming approaches to explicitly measure the predictive con?dence,and hence the training process is e?cient.Such an implicit measurement,however,might not be as accurate as an explicit estimation,since sometimes“minority holds the truth”.Thus,some additional control is needed to reduce the negative in?uence of incorrectly labeled examples.Zhou and Li[88]analytically showed that the negative in?uence can be compensated if the amount of newly labeled examples is su?cient under certain conditions.

Inspired by[36],Zhou and Li[88]derived the criterion based on theoretical results of learning from noisy examples[5].In detail,if a sequenceσof m samples is drawn,where the sample size m satis?es Eq.6,

m≥

2

2(1?2η)2

ln(

2N

δ

),(6)

where is the hypothesis worst-case classi?cation error rate,η(<0.5)is an upper bound on the classi?cation noise rate,N is the number of hypotheses,and δis the con?dence,then a hypothesis H i that minimizes disagreement withσwill have the PAC property,i.e.,

Pr[d(H i,H?)≥ ]≤δ,(7) where d(,)is the sum over the probability of elements from the symmetric dif-ference between the two hypothesis sets H i and H?(the ground-truth).Let

c=2μln(2N

δ)whereμmakes Eq.6hold equality.After some reforming,Eq.6

becomes Eq.8.

u=c

=m(1?2η)2(8)

For each classi?er,in order to keep improving the performance in the training process,the u value of the current round should be greater than that in its previous round.Let L t and L t?1denote the newly labeled data set of a classi?er in the t-th round and(t?1)-th round,respectively.Then the training sets for this classi?er in the t-th round and(t?1)-th round are L∪L t of the size of |L∪L t|and L∪L t?1of the size of|L∪L t?1|,respectively.Letˇe t andˇe t?1 denote the upper bound of the classi?cation error rate of the hypothesis derived from the combination of the other two classi?ers in the t-th round and(t?1)-th round,respectively.By comparing Eq.8in the subsequent rounds,the condition that a classi?er’s performance can be improved through the re?nement in the t-th round is shown as

0<

ˇe t

ˇe t?1

<

|L t?1|

|L t|

<1.(9)

Such a condition is used as the stopping criterion for tri-training algorithm. If none of the three classi?ers satis?es the condition shown in Eq.9in the t-th round,tri-training stops and outputs the learned classi?ers.Note that Eq.9 sometimes could not be satis?ed,due to the fact that|L t|may be far bigger than |L t?1|instead ofˇe t being higher thanˇe t?1.When this happens,in order not to stop training before the error rate of the classi?er becomes low,L t are randomly subsampled to size s according to Eq.10to make Eq.9hold again,

s=

ˇe t?1|L t?1|

ˇe t

?1

,(10)

Semi-Supervised Learning by Disagreement11 Table1.Pseudo-code describing the tri-training algorithm[88]

tri-training(L,U,Learn)

Input:L:Original labeled example set

U:Unlabeled example set

Learn:Learning algorithm

for i∈{1..3}do

S i←BootstrapSample(L)

h i←Learn(S i)

e i ←.5;l

i

←0

end of for

repeat until none of h i(i∈{1..3})changes for i∈{1..3}do

L i←?;update i←F ALSE

e i←MeasureError(h j&h k)(j,k=i)

if(e i

i )%otherwise Eq.9is violated

then for every x∈U do

if h j(x)=h k(x)(j,k=i)

then L i←L i∪{(x,h j(x))}

end of for

if(l

i

=0)%h i has not been updated before

then l

i ←

e i

e

i

?e i

+1

%refer Eq.11

if(l

i

<|L i|)%otherwise Eq.9is violated

then if(e i|L i|

i l

i

)%otherwise Eq.9is violated

then update i←T RUE

else if l

i >e i

e

i

?e i

%refer Eq.11

then L i←Subsample(L i,

e

i

l

i

e i

?1

)

%refer Eq.10

update i←T RUE

end of for

for i∈{1..3}do

if update i=T RUE

then h i←Learn(L∪L i);e

i ←e i;l

i

←|L i|

end of for end of repeat

Output:h(x)←arg max

y∈label

i:h i(x)=y

1

where L t?1should satisfy Eq.11such that the size of L t after subsampling,i.e. s,is still bigger than|L t?1|.

|L t?1|>

ˇe t

ˇe?ˇe

(11)

The pseudo-code of tri-training algorithm is shown in Table1.The function MeasureError(h j&h k)estimates the classi?cation error rate of the hypothe-sis derived from the combination of h j and h k.The function Subsample(L t,s) randomly removes|L t|?s examples from L t where s is computed according to Eq.10.

As mentioned before,the essential of tri-training is extensible for much more

12Z.-H.Zhou and M.Li classi?ers.Li and Zhou[48]proposed the Co-Forest algorithm,which extended tri-training to the collaboration of many classi?ers in training process.By using an ensemble of classi?ers,several immediate bene?ts can be achieved.First,for each classi?er h i,its concomitant ensemble H i,i.e.,ensemble of all the other classi?es,is used to label several unlabeled examples for this classi?er.As an ensemble of classi?ers usually achieves a better generalization than a single clas-si?er[73,84],the labeling of unlabeled data becomes more reliable,and thus, classi?er re?nement using these high quality newly labeled data can lead to bet-ter performances.Second,without employing sophisticated and time-consuming methods to estimate the predictive con?dence,the use of multiple classi?ers enables an e?cient estimation of the predictive con?dence.Such an explicit es-timate can be further exploited to guide the use of the corresponding unlabeled example in the training stage.

Although the advantages of using multiple classi?ers seems promising,a straightforward extension su?ers from a problem,that is,the“majority teaches minority”process hurts the generalization ability of an ensemble of classi?ers.It is known that the diversity of the learners is a key of a good ensemble[84].Dur-ing the“majority teaches minority”process,the behaviors of the learners will become more and more similar,and thus the diversity of the learners decreases rapidly.

To address this problem,Li and Zhou[48]proposed to inject certain ran-domness into the semi-supervised learning process.They employed two strate-gies.First,randomness is injected into the classi?er learning process,such that any two classi?ers in the ensemble can be diverse even when their training data are similar.For implementation convenience,they used Random Forest[18]to construct the ensemble.Second,randomness is injected into the unlabeled data selection process.Instead of directly selecting the highly con?dent unlabeled ex-amples,some candidate examples for labeling are randomly subsampled from the original unlabeled training set to meet a condition similar as Eq.9,and highly con?dent examples in the candidate pool are then selected and labeled.Thus, the learners will encounter di?erent training sets in each round.Such a strategy is helpful not only for the diversity,but also for reducing the chance of being trapped into local minima,just like a similar strategy adopted in[13].

3.3.Learning With Single View Multiple Regressors

Previous studies on semi-supervised learning mainly focus on classi?cation tasks. Although regression is almost as important as classi?cation,semi-supervised re-gression has rarely been studied.One reason is that for real valued labels the cluster assumption is not applicable.Although methods based on manifold as-sumption can be extended to regression,as pointed out by[92],these methods are essentially transductive instead of really semi-supervised since they assume that the unlabeled examples are exactly test examples.

Zhou and Li[87]?rst proposed a disagreement-based semi-supervised regres-sion approach Coreg,which employs two k NN regressors[27]to conduct the data labeling as well as the predictive con?dence estimation.The use of k NN regressors as base learners enables e?cient re?nement of a regressor based on the newly labeled data from its peer regressor since this lazy learning approach does not hold a separate training phase when updating the current regressor.

Semi-Supervised Learning by Disagreement13 Moreover,k NN regressor can be easily coupled with the predictive con?dence estimation method.

In order to choose appropriate unlabeled examples for labeling in semi-supervised regression,the labeling con?dence should be estimated such that the most con?dently labeled example can be identi?ed.In classi?cation this is rela-tively straightforward because when making classi?cations,many classi?ers(e.g.

a Na¨?ve Bayes classi?er)can also provide an estimated probability(or an ap-proximation)for the classi?cation.Therefore,the predictive con?dence can be estimated through consulting the probabilities of the unlabeled examples being labeled to di?erent classes.Unfortunately,in regression there is no such estimated probability that can be used directly.This is because in contrast to classi?cation where the number of labels to be predicted is?nite,the possible predictions in re-gression are in?nite.Therefore,Zhou and Li[87]proposed a predictive con?dence estimation criterion for disagreement-based semi-supervised learning method.

Intuitively,the most con?dently labeled example of a regressor should de-crease most the error of the regressor on the labeled example set,if the the most con?dently labeled example is utilized.In other words,the most con?dently la-beled example should be the one which makes the regressor most consistent with the labeled example set.Thus,the mean squared error(MSE)of the regressor on the labeled example set can be evaluated?rst.Then,the MSE of the regres-sor utilizing the information provided by a newly labeled example(x u,?y u)can be evaluated on the labeled example set,where the real-valued label?y u of the unlabeled instance x u is generated by the regressor.Let?u denote the result of subtracting the latter MSE from the former MSE.Note that the number of?u to be estimated equals to the number of unlabeled examples.Finally,(x u,?y u) associated with the biggest positive?u can be regarded as the most con?dently labeled example.

To avoid repeatedly measuring the MSE of the k NN regressor on the whole labeled training set in each iteration,approximation is employed to compute the MSE based on only the k-nearest labeled examples of an unlabeled instance. Let?u denote the set of its k-nearest labeled examples of x u,then the most con?dently labeled example?x is identi?ed through maximizing the value of?x

u in Eq.12,

?x

u =

x i∈?u

(y i?h(x i))2?(y i?h (x i))2

,(12)

where h denotes the original regressor while h denotes the re?ned regressor which has utilized the information provided by(x u,?y u),?y u=h(x u).

Another important aspect in Coreg is the diversity between two regressors. Note that the labeling of an unlabeled example is obtained by averaging the real-valued labels of its k-nearest neighbors in the labeled training set.As only a few examples are labeled at early stage,the labeling of unlabeled data can be noisy. Zhou and Li[87,89]showed that using diverse regressors can help to reduce the negative in?uence of the noisy newly labeled data.Since k NN regressor is used as the base learner,a natural way to make the k NN regressors di?erent is to en-able them to identify di?erent vicinities,which can be achieved by manipulating the parameter settings of the k NN regressors.In[87],Minkowsky distances of di?erent orders were used to generate two diverse k NN regressors.This strategy was extended to a more general case,i.e.,achieving diversity by using di?er-ent distance metrics and/or di?erent number of neighbors identi?ed for a given

14Z.-H.Zhou and M.Li Table2.Pseudo-code describing the Coreg algorithm[89]

Algorithm:Coreg

Input:labeled example set L,unlabeled example set U,

maximum number of learning iterations T,

number of nearest neighbors k1,k2

distance metrics D1,D2

Process:

L1←L;L2←L

Create pool U of size s by randomly picking examples from U

h1←kNN(L1,k1,D1);h2←kNN(L2,k2,D2)

Repeat for T rounds:

for j∈{1,2}do

for each x u∈U do

?u←Neighbors(x u,L j,k j,D j)

?y u←h j(x u)

h

j

←kNN(L j∪{(x u,?y u)},k j,D j)

?x

u ←

x i∈?u

(y i?h j(x i))2?

y i?h

j

(x i)

2

end of for

if there exists an?x

u >0

then?x j←arg max

x u∈U ?x

u

;?y j←h j(?x j)

πj←{(?x j,?y j)};U ←U ??x j

elseπj←?

end of for

L1←L1∪π2;L2←L2∪π1

if neither of L1and L2changes then exit

else

h1←kNN(L1,k1,D1);h2←kNN(L2,k2,D2)

Replenish U to size s by randomly picking examples from U

end of Repeat

Output:regressor h?(x)←1(h1(x)+h2(x))

example[89].Additionally,such a setting also brings another bene?t,that is, since it is usually di?cult to decide the appropriate parameter settings for k NN regressor for a speci?c task,combining the regressors with di?erent parameter settings can obtain somewhat complementary e?ect.

The pseudo code of Coreg is shown in Table2,where kNN(L j,k j,D j)is a function that returns a k NN regressor on the labeled training set L j,whose k value is k j and distance metric is D j.The learning process stops when the max-imum number of learning iterations,i.e.T,is reached,or there is no unlabeled example which is capable of reducing the MSE of any of the regressors on the labeled example set.A pool of unlabeled examples smaller than U is used,as what was used in[13].Note that in each iteration the unlabeled example chosen by h1won’t be chosen by h2,which is an extra mechanism for encouraging the diversity of the regressors.Thus,even when h1and h2are similar,the examples they labeled for each other will still be di?erent.

It is evident that the method introduced in this section is closely related to those introduced in Section3.2.The key is to generate multiple diverse learners and then try to exploit their disagreements on unlabeled data to implement the

Semi-Supervised Learning by Disagreement15 performance boost.Actually,“learning with multiple views”(Section3.1)is a special case which uses multiple views to help generate multiple diverse learners.

3.4.The Combination with Active Learning

In disagreement-based semi-supervised learning approaches,the unlabeled ex-amples that are labeled for a learner are examples on which most other learners agree but the concerned learner disagrees.If all learners disagree on the labeling of an unlabeled example,this example is simply neglected.However,it is highly probable that such an example is not able to be learned well by the learning sys-tem itself.As mentioned in Section1,active learning is another major technique of learning with labeled and unlabeled data.It actively selects some informative unlabeled examples and queries their labels from an oracle independent to the learning system.It is evident that the unlabeled example on which all learners disagree is a good candidate to query.

Zhou et al.[85,86]proposed a disagreement-based active semi-supervised learning method Ssair for content-based image retrieval.After obtaining a small number of labeled images from relevance feedback,they constructed two learners using the labeled images.Each learner attempts to assign a rank to all images in the imagebase.The smaller the rank,the higher the chance that the concerned image is relevant to the user query.The two most con?dent irrelevant images of each learner are passed to the other learner as negative examples.Such a pro-cess is repeated and the two learners are re?ned.In previous relevance feedback methods,the user randomly picks some images from the retrieval result to give feedback.Zhou et al.[85,86]thought that letting the user to give feedback on images that have been learned well is not helpful to improve the performance. So,instead of passively waiting user feedback,they actively prepared a pool of images for user to give feedback.The pool contains images on which the two learners are with contradict predictions but similar con?dences,and images on which the two learners are both with low con?dences.Thus,in each round of relevance feedback,both semi-supervised learning and active learning are ex-ecuted to exploit the images existing in imagebase to the most.It is evident that although the combination of the disagreement-based semi-supervised learn-ing and active learning is simple,it provides a good support to the interesting active semi-supervised relevance feedback scheme which is useful in information retrieval tasks.

4.Theoretical Foundations for Disagreement-Based

Semi-Supervised Learning

Early theoretical analyses of the disagreement-based semi-supervised learning approaches mainly focus on the case where there exists two views.

Blum and Mitchell[13]analyzed the e?ectiveness of co-training.Let X1and X2denote the two su?cient and redundant views of the input space X,and hence an instance can be represented by x=(x1,x2)∈X1×X2.Assume that f=(f1,f2)∈C1×C2is a target function de?ned over X and C1,C2are concept classes de?ned over X1,X2respectively,and then f(x)=f1(x1)= f2(x2)=y should be held due to the su?ciency of the two views,where y is the ground-truth label of x.Therefore,they de?ned compatibility between target

16Z.-H.Zhou and M.Li

Fig.2.The bipartite graph for instance distribution.Plot based on a similar?gure in[13]. function f=(f1,f2)and the unknown data distribution D,based on which co-training is analyzed.Here,f=(f1,f2)is compatible with D means that D assigns probability zero to any instance(x1,x2)such that f1(x1)=f2(x2).

If the“compatibility”is satis?ed,as[13]pointed out,even if the concept classes C1and C2are large and complex(i.e.,in high VC-dimension),the set of target concepts that is compatible with D could be smaller and simpler.There-fore,unlabeled data can be used to verify which are the compatible target con-cepts,and hence lead to the reduction of the number of labeled data needed in learning.They illustrated this idea by an bipartite graph shown in Fig.2.In this graph,vertices in left hand side and right hand side denote the instances in X1 and X2,respectively.For any pair of vertices on each side of the graph,there exists an edge on between if and only if the corresponding instance(x1,x2)can be drawn with non-zero probability under the distribution D.The solid edges denote the instances observed in the?nite training set.Obviously,under this rep-resentation,the concepts that are compatible with D correspond to the graph partitions without any cross-edges.The instances in the same connected compo-nent share the same label,and only a labeled example is required to determine the labeling of this component.The value of unlabeled data is their assistance for identifying the connected components of the graph,and in fact identifying the distribution D.

Based on this bi-partite representation,Blum and Mitchell[13]analytically showed that“If C2is learnable in the PAC model with classi?cation noise,and if the conditional independence assumption is satis?ed,then(C1,C2)is learn-able in Co-training model from unlabeled data only,given an initial weak-useful predictor h(x1)”.This is a very strong conclusion which implies that if the two views are conditionally independent,the predictive accuracy of an initial weak learner can be boosted to arbitrarily high with unlabeled data using co-training.

Later,Dasgupta et al.[28]analyzed the generalization bound for standard co-training.Let S be a set of i.i.d samples.For any statementΦ[s],let S(Φ) be a subset of S that satis?esΦ.For two statementsΦandΨ,the empirical estimate?P(Φ|Ψ)=|S(Φ∧Ψ)|/|S(Ψ)|.They assumed that the data is drawn from some distribution over triples x1,y,x2 with x1∈X1and x2∈X2,and

Semi-Supervised Learning by Disagreement17 P(x1|y,x2)=P(x1|y)and P(x2|y,x1)=P(x2|y);in other words,the data has two views that are independent given the class label.Assume that there are k di?erent classes,and if a learner h fails to classify x into the k classes,then h(x)=⊥.Let|h|denote a complex measurement of h,and h1and h2denote the learner constructed in X1and X2,respectively.Then,they showed that with probability at least1?δover the choice of S,for all pairs of learners h1and h2such thatγi(h1,h2,δ/2)>0and b i(h1,h2,δ/2)≤(k?1)/k,the following inequity holds,

error(h1)≤

?P(h

1

=⊥)? (|h1|,δ/2)

max

j

b j(h1,h2,δ/2)

+

k?1

k

?P(h

1

=⊥)+ (|h1|,δ/2)

(13)

where

(k,δ)=

k ln2+ln2/δ

2|S|

(14)

b i(h1,h2,δ)=

1

γi(h1,h2,δ)

?P(h

1

=i|h2=i,h1=⊥)+ i(h1,h2,δ)

(15)

i(h1,h2,δ)=

(ln2)(|h1|+|h2|)+ln(2k/δ)

2|S(h2=i,h1=⊥)|

(16)

γi(h1,h2,δ)=?P(h1=i|h2=i,h1=⊥)??P(h1=i|h2=i,h1=⊥)

?2 i(h1,h2,δ)(17) The result of Dasgupta et al.[28]shows that when there are two su?cient and redundant views which are conditionally independent given the class label, the generalization error of co-training is upper-bounded by the disagreement between the two classi?ers.This suggests that a better learning performance can be obtained if the disagreement can be exploited in a better way.

Note that in the analyses in[13]and[28],it was assumed that there exist two su?cient and redundant views that are conditionally independent given the class label.Since such a strong requirement is not often satis?ed,analyses under more realistic assumptions are desired.Balcan et al.[6]pointed out that if a PAC learner can be obtained on each view,the conditional independence assumption or even weak independent assumption[2]is unnecessary;a weaker assumption of“expansion”of the underlying data distribution is su?cient for iterative co-training to succeed.They consider that the learning algorithm used in each view is con?dent about being positive and is able to learn from positive examples only, and the“expansion”is de?ned as follows:Let X+denote the positive region and D+denote the distribution over X+.For S1?X1and S2?X2,let S i be the event that an instance(x1,x2)has x i∈S i(i=1,2).Let P(S1∧S2)denote the probability on examples for being con?dent on both views,and P(S1⊕S2) denote the probability on examples for being con?dent on only one view.Let

18Z.-H.Zhou and M.Li

H i ∩X +i ={h ∩X +i :h ∈H i },where H i (i =1,2)is hypothesis class.If Eq.18holds for any S 1?X 1and S 2?X 2,then D +is -expanding;if Eq.18holds for any S 1?H 1∩X 1and S 2?H 2∩X 2,then D +is -expanding with respect to hypothesis class H 1×H 2.

P (S 1⊕S 2)≥ min P (S 1∧S 2),P (ˉS 1∧ˉS 2) (18)

If some data distribution satis?es the expansion assumption,with a small con?dence set S j of the hypothesis of view j (j =1,2),the iterative co-training can succeed to achieve a classi?er whose error rate is smaller than with a large probability.

All the previous theoretical studies investigated the standard two-view co-training.Theoretical foundation of other disagreement-based semi-supervised learning approaches,in particular,those work on a single view,has not been established,although the e?ectiveness of those approaches have been empirically veri?ed.Wang and Zhou [71]presented a theoretical study for those approaches.Let H denote the hypothesis space and D is the data distribution generated by the ground-truth hypothesis h ?∈H .Let d (h i ,h ?)denote the di?erence between the two classi?er h i and h ?,which can be measured by Pr x ∈D [h i (x )=h ?(x )].Let h i 1and h i 2denote the classi?ers in i -th round of the iterative co-training process.Then,their main result is summarized in Theorem 1shown as follows.Theorem 1Given the initial labeled data set L which is clean,and assuming that the size of L is su?cient to learn two classi?ers h 01and h 02whose upper bound of the generalization error is a 0<0.5and b 0<0.5with high probability

(more than 1?δ)in the PAC model,respectively,i.e.l ≥max[1a 0ln |H|

δ,1b 0ln |H|δ].Then h 01selects u number of unlabeled instances from U to label and puts them

into σ2which contains all the examples in L ,and then h 12is trained from σ2by minimizing the empirical risk.If lb 0≤e M √M !?M ,then

Pr[d (h 12,h ?)≥b 1]≤δ.(19)

where M =ua 0and b 1=max[

lb 0+ua 0?ud (h 01,h 12)l ,0].Such a theorem suggests that the key for the disagreement-based approaches to succeed is the large di?erence between the learners,which explains the reason why the disagreement-based approaches still work well even when there are no two views.Note that in contrast to all previous studies which assumed that data is drawn from some distribution over triples x 1,y,x 2 (that is,the data has two views),the above theorem does not assume that data is drawn from distribution over two views.Actually,from Theorem 1we can know that the existence of two views is a su?cient condition instead of necessary condition for disagreement-based approaches.This is because when there are two su?cient and redundant views,the learners trained from the two views respectively are of course diverse,and so the disagreement-based learning process can succeed.When there are no two views,it is also possible to get two diverse learners,and thus disagreement-based approaches are also able to succeed.It is worth mentioning that all previous studies,either theoretical or algorithmic,tried to maximize the consensus among the learners;in other words,they always tried to minimize the error for labeled examples and maximize the agreement for

Semi-Supervised Learning by Disagreement19 unlabeled examples,but never revealed that keeping a large disagreement among the learners is a necessary condition for co-training to proceed.

Moreover,Wang and Zhou[71]analyzed the reason why the performance of the disagreement-based approaches could not be improved further after a number of training rounds.Such a problem is frequently encountered in many practical applications of the disagreement-based approaches but could not be explained by previous theoretical results.Based on Theorem1,Wang and Zhou[71]showed that as the learning process continues,the learners will become more and more similar,and therefore,the required diversity could not be met and the learners could not improve each other further.Based on this recognition,a preliminary method for roughly estimating the appropriate iteration to terminate the learning process was proposed.

Section3.4introduced that the combination of disagreement-based semi-supervised learning with active learning can lead to good performance.Recently, Wang and Zhou[72]analyzed this situation and got the result in Theorem2. Theorem2For data distribution Dα-expanding with respect to hypothesis class H1×H2,let andδdenote the?nal desired accuracy and con?dence parameters.

If s= logα8

log1

C ,m0=1

L

(4V log(1

L

)+2log(8(s+1)

δ

))and m i=16

α

(4V log(16

α

)+

2log(8(s+1)

δ))(i=1,2,···,),a classi?er will be generated with error rate no

more than with probability1?δ,according to a similar approach in[85].

Here,V=max[V C(H1),V C(H2)]where V C(H)denotes the VC-dimension

of the hypothesis class H,constant C=α/4+1/α

1+1/αand constant L=min[α

16

,1

16L1L2

].

This theorem suggests that under assumption ofα-expansion on the hypothe-sis class H1×H2,the sample complexity can be exponentially reduced by combin-ing disagreement-based semi-supervised learning with active learning in contrast to pure disagreement-based semi-supervised learning.This is the?rst theoreti-cal analysis on the combination of semi-supervised learning with active learning, which also contains the?rst analysis on multi-view active learning.

Both Theorem1and Theorem2provide theoretical explanations to the ef-fectiveness of general disagreement-based semi-supervised learning approaches whose e?ectiveness has been empirically veri?ed in practice.Although some strong assumptions are still required in the analyses,the results serve as an important step towards the establishment of the whole theoretical foundation for the disagreement-based learning framework.However,note that all the cur-rent theoretical analyses are on the use of two learners,while theoretical analysis on disagreement-based semi-supervised learning with more than two learners re-mains an open problem.

5.Applications to Real-World Tasks

Disagreement-based semi-supervised learning paradigm has been successfully ap-plied to many real-world tasks,particularly in natural language processing.In fact,in the middle of1990s,it was accepted that constructing prediction models based on the di?erent attribute sets of the problem may help to achieve a better result.Yarowsky[75]constructed a word sense classi?er using the local context of the word and a classi?er based on the senses of other occurrences of that word

20Z.-H.Zhou and M.Li in the same document for word sense disambiguation.Rilo?and Jones[59]con-sidered both the noun phrase itself and the linguistic context in which the noun phrase appears for classifying noun phrase for geographic locations.Collins and Singer[24]utilized both the spelling of the entity and the context in which the entity appears for named entity classi?cation.

Pierce and Cardie[58]applied standard co-training to conduct named entity identi?cation.They treated the current word and k immediate words before it as the?rst view,and similarly,the current word and k immediate words after it as the second view.Based on these two views,standard co-training were directly applied with some necessary adaptations to multi-class classi?cation.By utilizing unlabeled data with co-training,the identi?cation error rate reduced by36%compared to the identi?cation using only the labeled data.Sarkar[62] decomposed statistical parser into two sequentially related probabilistic models. The?rst model,which is called tagging probability model,is responsible to select the most likely trees for each word by examining the local context,while the second model,which is called parsing probability model,is responsible for attaching the selected trees together to provide a consistent bracketing of the sentences.In the learning process,these two models employ a disagreement-based approach to exploit the unlabeled examples,where each model uses its most con?dent information about the prediction to help the other model to reduce the uncertainty in statistical parsing,and hence achieves a better performance in terms of both precision and https://www.doczj.com/doc/5f816874.html,ter,Steedman et al.[68]solved this problem from a di?erent perspective.Unlike[62],they used the two di?erent statistical parsers for co-training.In the training process,each parser assigns scores to unlabeled sentences that have been parsed by itself,using a scoring function to indicate the con?dence of the parse results.Then,the parser passes the parsed sentences with the top scores to the other parser.They empirically showed that such a method could also improve the performance of statistical parsing.Hwa et al.[41]combined disagreement-based semi-supervised learning with active learning in statistical parsing,where each learner teaches the other learner with its most con?dently parsed sentences,while its peer learner queries the parse result for its least con?dently parsed sentences from the user and feeds them to this learner.By applying such a method,the number of manually labeling can be greatly reduced.

In addition to natural language processing,disagreement-based semi-supervised learning paradigm has been applied to content-based image retrieval.Given a query image,a CBIR system is required to return the images in the imagebase that are relevant to the query image.Due to the semantic gap between the high-level image semantics and the low-level image features,relevance feedback[61] is usually employed to bridge the gap.Since it is usually infeasible for the user to provide many rounds of feedback,the number of images with the relevance judgement is insu?cient to achieve a good performance.Thus,unlabeled images in the imagebase can be further exploited to improve the performance of CBIR based on semi-supervised learning,while CBIR itself becomes a good applica-tion of learning with labeled and unlabeled data[82].In fact,semi-supervised learning in CBIR scenario has been studied in[30,74].

Zhou et al.[85,86]?rst applied a disagreement-based semi-supervised learn-ing method to exploit unlabeled images in the imagebase of a CBIR system.The method actually combines semi-supervised learning with active learning(see Sec-tion3.4for details).This research also leads to a new user interface design in CBIR.As shown in Fig.3,the region above the dark line displays the retrieved

知识管理和信息管理之间的联系和区别_[全文]

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完善知识管理理论构建知识共享系统 王玉晶 【摘　要】知识共享是知识管理的一个重要组成部分。本文从知识管理的概念入手,指出了知识共享在知识管理中的重要性和特殊地位,分析了企业中进行知识共享存在的障碍与不利因素,从建立知识共享技术支撑体系、构建知识共享组织结构、营造知识共享文化、完善知识共享激励机制等方面深入探讨了如何提高企业知识共享程度,加强企业竞争力。 【关键词】知识管理　知识共享　体系 Abstract:Kno wledge sharing is an important component of the kno wledge management.This paper obtained from the kno wledge management concept,has pointed out the importance and the special status of knowledge sharing in the knowledge manage ment,and analyzed the barrier and th e disadvantage factor of knowledge sharing in the enterprise.This article pointed out that the knowledge sharing should be established technical support system,built knowledge sharing structure,created a kno wledge sharing culture,and improved knowledge sharing incentive mechanism. Key words:kno wledge sharing　knowledge management　system 当今社会,企业竞争力已不局限于仅仅依赖其规模、信息和技术,而更注重其创新和应变能力。知识管理就是在知识经济大背景下,以当代信息技术为依托,着力于知识的开发和利用、积累和创新,帮助人们共享信息,进而对扩大了的知识资本进行有效运营,最终通过集体智慧提高企业创新和应变能力的一种全新的信息管理理论与方法。而创新本身,无论是技术创新还是管理创新,其实质就是一种新知识的创造,它要求企业内部各个部门之间以及各员工之间,企业内部与外部之间进行广泛的知识交流与共享。所以知识共享一直是知识管理的一个重要组成部分。它是发挥知识的效用,实现知识价值的必由之路,是实现知识共享的前提,是走向知识共享世界的先导。理解知识共享的内涵,分析企业知识共享存在的障碍与不利因素并提出解决的方案,对完善组织中的知识共享机制具有重要意义。 1　知识共享的含义 关于知识共享的概念,由于标准、角度的不同,学者对知识共享的界定也有所不同。知识共享是指个体知识、组织知识通过各种交流手段为组织中其他成员所共享。同时,通过知识创新,实现组织的知识增值。对知识共享的认识应从知识共享的对象———知识 内容,知识共享的手段———知识网络、会议及团队学习,知识共享的主体———个人、团队及组织这三个层面考虑。其中,人是知识共享的主体,文化是知识共享的背景,信息技术是知识共享的重要工具。 2　知识共享障碍因素分析 2.1　技术应用障碍 知识管理作为一种全新的管理模式,如果缺乏应有的技术支撑,将难以发挥其应有的效力,最终失之于形式,流于空泛。许多企业物质技术基础薄弱,缺少有效的计算机网络和通信系统,很多员工不知道到哪里去寻找所需要的知识。存在于员工头脑中的隐性知识难以明确的被他人观察、了解,也无法用言语表达或者只能用言语进行部分表达。因此,薄弱的技术基础不能够帮助人们跨越时间、空间和知识的数量及质量的限制,从而不能为有效地实现知识共享提供强有力的技术支持。 2.2　组织结构缺陷 传统的组织结构管理层次多,信息传递速度缓慢,信息衰退或信息失真现象非常严重,员工之间没有超越命令以外的直接接触和交流,无法实现面对面的互动式交流,无法突破岗位对个人的约束。多层管理结构森严,越级的知识传递几乎不可能实现;员工之间 27 RESEARCH ES I N LIBRARY SCIENCE　 DOI:10.15941/https://www.doczj.com/doc/5f816874.html, ki.issn1001-0424.2008.05.027