Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.

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Locality Preserving Projections

We have witnessed great interest and a wealth of promise in content-based image retrieval as an emerging technology. While the last decade laid foundation to such promise, it also paved the way for a large number of new techniques and systems, got many new people involved, and triggered stronger association of weakly related fields. In this article, we survey almost 300 key theoretical and empirical contributions in the current decade related to image retrieval and automatic image annotation, and in the process discuss the spawning of related subfields. We also discuss significant challenges involved in the adaptation of existing image retrieval techniques to build systems that can be useful in the real world. In retrospect of what has been achieved so far, we also conjecture what the future may hold for image retrieval research.

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Image retrieval: Ideas, influences, and trends of the new age

We propose an appearance-based face recognition method called the Laplacianface approach. By using locality preserving projections (LPP), the face images are mapped into a face subspace for analysis. Different from principal component analysis (PCA) and linear discriminant analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition.

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Face recognition using Laplacianfaces

A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions

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Graph Embedding and Extensions: A General Framework for Dimensionality Reduction

The fuzzy c-means (FCM) algorithm is one of the most frequently used clustering algorithms. The weighting exponent m is a parameter that greatly influences the performance of the FCM. But there has been no theoretical basis for selecting the proper weighting exponent in the literature. In this paper, we develop a new theoretical approach to selecting the weighting exponent in the FCM. Based on this approach, we reveal the relation between the stability of the fixed points of the FCM and the data set itself. This relation provides the theoretical basis for selecting the weighting exponent in the FCM. The numerical experiments verify the effectiveness of our theoretical conclusion.

Analysis of the weighting exponent in the FCM

Dimensionality reduction is an essential data preprocessing technique for large-scale and streaming data classification tasks. It can be used to improve both the efficiency and the effectiveness of classifiers. Traditional dimensionality reduction approaches fall into two categories: feature extraction and feature selection. Techniques in the feature extraction category are typically more effective than those in feature selection category. However, they may break down when processing large-scale data sets or data streams due to their high computational complexities. Similarly, the solutions provided by the feature selection approaches are mostly solved by greedy strategies and, hence, are not ensured to be optimal according to optimized criteria. In this paper, we give an overview of the popularly used feature extraction and selection algorithms under a unified framework. Moreover, we propose two novel dimensionality reduction algorithms based on the orthogonal centroid algorithm (OC). The first is an incremental OC (IOC) algorithm for feature extraction. The second algorithm is an orthogonal centroid feature selection (OCFS) method which can provide optimal solutions according to the OC criterion. Both are designed under the same optimization criterion. Experiments on Reuters Corpus Volume-1 data set and some public large-scale text data sets indicate that the two algorithms are favorable in terms of their effectiveness and efficiency when compared with other state-of-the-art algorithms.

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Effective and efficient dimensionality reduction for large-scale and streaming data preprocessing

Active appearance model (AAM), which makes ingenious use of both shape and texture constraints, is a powerful tool for face modeling, alignment and facial feature extraction under shape deformations and texture variations. However, as we show through our analysis and experiments, there exist admissible appearances that are not modeled by AAM and hence cannot be reached by AAM search; also the mapping from the texture subspace to the shape subspace is many-to-one and therefore a shape should be determined entirely by the texture in it. We propose a new appearance model, called direct appearance model (DAM), without combining from shape and texture as in AAM. The DAM model uses texture information directly in the prediction of the shape and in the estimation of position and appearance (hence the name DAM). In addition, DAM predicts the new face position and appearance based on principal components of texture difference vectors, instead of the raw vectors themselves as in AAM. These lead to the following advantages over AAM: (1) DAM subspaces include admissible appearances previously unseen in AAM, (2) convergence and accuracy are improved, and (3) memory requirement is cut down to a large extent. The advantages are substantiated by comparative experimental results.

Direct appearance models

Image clustering, an important technology for image processing, has been actively researched for a long period of time. Especially in recent years, with the explosive growth of the Web, image clustering has even been a critical technology to help users digest the large amount of online visual information. However, as far as we know, many previous works on image clustering only used either low-level visual features or surrounding texts, but rarely exploited these two kinds of information in the same framework. To tackle this problem, we proposed a novel method named consistent bipartite graph co-partitioning in this paper, which can cluster Web images based on the consistent fusion of the information contained in both low-level features and surrounding texts. In particular, we formulated it as a constrained multi-objective optimization problem, which can be efficiently solved by semi-definite programming (SDP). Experiments on a real-world Web image collection showed that our proposed method outperformed the methods only based on low-level features or surround texts.

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Web image clustering by consistent utilization of visual features and surrounding texts

Heterogeneous data co-clustering has attracted more and more attention in recent years due to its high impact on various applications. While the co-clustering algorithms for two types of heterogeneous data (denoted by pair-wise co-clustering), such as documents and terms, have been well studied in the literature, the work on more types of heterogeneous data (denoted by high-order co-clustering) is still very limited. As an attempt in this direction, in this paper, we worked on a specific case of high-order co-clustering in which there is a central type of objects that connects the other types so as to form a star structure of the inter-relationships. Actually, this case could be a very good abstract for many real-world applications, such as the co-clustering of categories, documents and terms in text mining. In our philosophy, we treated such kind of problems as the fusion of multiple pair-wise co-clustering sub-problems with the constraint of the star structure. Accordingly, we proposed the concept of consistent bipartite graph co-partitioning, and developed an algorithm based on semi-definite programming (SDP) for efficient computation of the clustering results. Experiments on toy problems and real data both verified the effectiveness of our proposed method.

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Qiansheng Cheng

Papers

Analysis of the weighting exponent in the FCM

Effective and efficient dimensionality reduction for large-scale and streaming data preprocessing

Direct appearance models

Web image clustering by consistent utilization of visual features and surrounding texts

Consistent bipartite graph co-partitioning for star-structured high-order heterogeneous data co-clustering