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114
Statistical pattern recognition: A review
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2000
"... The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques ..."
Abstract

Cited by 667 (22 self)
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The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have bean receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the wellknown methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 397 (6 self)
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Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximumlikelihood framework, based on a specific form of Gaussian latent variable model. This leads to a welldefined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its applicat...
An Eigenspace Update Algorithm for Image Analysis
, 1997
"... this paper However, the vision research community has largely overlooked makes the following contributions: parallel developments in signal processing and numerical linear algebra concerning efficient eigenspace updating algorithms. . We provide a comparison of some of the popular tech These new ..."
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Cited by 115 (3 self)
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this paper However, the vision research community has largely overlooked makes the following contributions: parallel developments in signal processing and numerical linear algebra concerning efficient eigenspace updating algorithms. . We provide a comparison of some of the popular tech These new developments are significant for two reasons: Adopt niques existing in the vision literature for SVD/KLT com ing them will make some of the current vision algorithms more putations and point out the problems associated with robust and efficient. More important is the fact that incremental those techniques
SMEM Algorithm for Mixture Models
 NEURAL COMPUTATION
, 1999
"... We present a split and merge EM (SMEM) algorithm to overcome the local maxima problem in parameter estimation of finite mixture models. In the case of mixture models, local maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely sepa ..."
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Cited by 99 (2 self)
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We present a split and merge EM (SMEM) algorithm to overcome the local maxima problem in parameter estimation of finite mixture models. In the case of mixture models, local maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations we repeatedly perform simultaneous split and merge operations using a new criterion for efficiently selecting the split and merge candidates. We apply the proposed algorithm to the training of Gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split and merge operations to improve the likelihood of both the training data and of heldout test data. We also show the practical usefulness of the proposed algorithm by applying it to image compression and pattern recognition problems.
Data Exploration Using SelfOrganizing Maps
 ACTA POLYTECHNICA SCANDINAVICA: MATHEMATICS, COMPUTING AND MANAGEMENT IN ENGINEERING SERIES NO. 82
, 1997
"... Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and timeconsuming. Interesting, novel relations between the data items may be hidden in the data. The selforganizing map (SOM) algorithm of Kohonen can be used to aid the ..."
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Cited by 97 (4 self)
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Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and timeconsuming. Interesting, novel relations between the data items may be hidden in the data. The selforganizing map (SOM) algorithm of Kohonen can be used to aid the exploration: the structures in the data sets can be illustrated on special map displays. In this work, the methodology of using SOMs for exploratory data analysis or data mining is reviewed and developed further. The properties of the maps are compared with the properties of related methods intended for visualizing highdimensional multivariate data sets. In a set of case studies the SOM algorithm is applied to analyzing electroencephalograms, to illustrating structures of the standard of living in the world, and to organizing fulltext document collections. Measures are proposed for evaluating the quality of different types of maps in representing a given data set, and for measuring the robu...
Discriminative common vectors for face recognition
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2005
"... In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the withinclass scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as t ..."
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Cited by 67 (7 self)
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In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the withinclass scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the “small sample size” problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher’s Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the withinclass scatter matrix of the samples in the training set while the other uses the subspace methods and the GramSchmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher’s Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.
Candid covariancefree incremental principal component analysis
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2003
"... Abstract—Appearancebased image analysis techniques require fast computation of principal components of highdimensional image vectors. We introduce a fast incremental principal component analysis (IPCA) algorithm, called candid covariancefree IPCA (CCIPCA), used to compute the principal components ..."
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Cited by 55 (9 self)
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Abstract—Appearancebased image analysis techniques require fast computation of principal components of highdimensional image vectors. We introduce a fast incremental principal component analysis (IPCA) algorithm, called candid covariancefree IPCA (CCIPCA), used to compute the principal components of a sequence of samples incrementally without estimating the covariance matrix (so covariancefree). The new method is motivated by the concept of statistical efficiency (the estimate has the smallest variance given the observed data). To do this, it keeps the scale of observations and computes the mean of observations incrementally, which is an efficient estimate for some wellknown distributions (e.g., Gaussian), although the highest possible efficiency is not guaranteed in our case because of unknown sample distribution. The method is for realtime applications and, thus, it does not allow iterations. It converges very fast for highdimensional image vectors. Some links between IPCA and the development of the cerebral cortex are also discussed. Index Terms—Principal component analysis, incremental principal component analysis, stochastic gradient ascent (SGA), generalized hebbian algorithm (GHA), orthogonal complement. æ 1
Discriminative Learning and Recognition of Image Set Classes Using Canonical Correlations
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—We address the problem of comparing sets of images for object recognition, where the sets may represent variations in an object’s appearance due to changing camera pose and lighting conditions. Canonical Correlations (also known as principal or canonical angles), which can be thought of as ..."
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Cited by 50 (10 self)
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Abstract—We address the problem of comparing sets of images for object recognition, where the sets may represent variations in an object’s appearance due to changing camera pose and lighting conditions. Canonical Correlations (also known as principal or canonical angles), which can be thought of as the angles between two ddimensional subspaces, have recently attracted attention for image set matching. Canonical correlations offer many benefits in accuracy, efficiency, and robustness compared to the two main classical methods: parametric distributionbased and nonparametric samplebased matching of sets. Here, this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations. Motivated by their proven effectiveness, a novel discriminative learning method over sets is proposed for set classification. Specifically, inspired by classical Linear Discriminant Analysis (LDA), we develop a linear discriminant function that maximizes the canonical correlations of withinclass sets and minimizes the canonical correlations of betweenclass sets. Image sets transformed by the discriminant function are then compared by the canonical correlations. Classical orthogonal subspace method (OSM) is also investigated for the similar purpose and compared with the proposed method. The proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views. The method is also applied to object category recognition using ETH80 database. The proposed method is shown to outperform the stateoftheart methods in terms of accuracy and efficiency. Index Terms—Object recognition, face recognition, image sets, canonical correlation, principal angles, canonical correlation analysis, linear discriminant analysis, orthogonal subspace method. Ç 1