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Locally Linear Discriminant Analysis for Multimodally Distributed Classes for Face Recognition with a Single Model Image
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—We present a novel method of nonlinear discriminant analysis involving a set of locally linear transformations called “Locally Linear Discriminant Analysis (LLDA). ” The underlying idea is that global nonlinear data structures are locally linear and local structures can be linearly aligned. ..."
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Cited by 51 (3 self)
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Abstract—We present a novel method of nonlinear discriminant analysis involving a set of locally linear transformations called “Locally Linear Discriminant Analysis (LLDA). ” The underlying idea is that global nonlinear data structures are locally linear and local structures can be linearly aligned. Input vectors are projected into each local feature space by linear transformations found to yield locally linearly transformed classes that maximize the betweenclass covariance while minimizing the withinclass covariance. In face recognition, linear discriminant analysis (LDA) has been widely adopted owing to its efficiency, but it does not capture nonlinear manifolds of faces which exhibit pose variations. Conventional nonlinear classification methods based on kernels such as generalized discriminant analysis (GDA) and support vector machine (SVM) have been developed to overcome the shortcomings of the linear method, but they have the drawback of high computational cost of classification and overfitting. Our method is for multiclass nonlinear discrimination and it is computationally highly efficient as compared to GDA. The method does not suffer from overfitting by virtue of the linear base structure of the solution. A novel gradientbased learning algorithm is proposed for finding the optimal set of local linear bases. The optimization does not exhibit a localmaxima problem. The transformation functions facilitate robust face recognition in a lowdimensional subspace, under pose variations, using a single model image. The classification results are given for both synthetic and real face data. Index Terms—Linear discriminant analysis, generalized discriminant analysis, support vector machine, dimensionality reduction, face recognition, feature extraction, pose invariance, subspace representation. æ 1
Mutual Information in Learning Feature Transformations
 In Proceedings of the 17th International Conference on Machine Learning
, 2000
"... We present feature transformations useful for exploratory data analysis or for pattern recognition. Transformations are learned from example data sets by maximizing the mutual information between transformed data and their class labels. We make use of Renyi's quadratic entropy, and we extend th ..."
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Cited by 50 (8 self)
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We present feature transformations useful for exploratory data analysis or for pattern recognition. Transformations are learned from example data sets by maximizing the mutual information between transformed data and their class labels. We make use of Renyi's quadratic entropy, and we extend the work of Principe et al. to mutual information between continuous multidimensional variables and discretevalued class labels. 1.
Linear Feature Extractors Based on Mutual Information
 In Proceedings of the 13th International Conference on Pattern Recognition
, 1996
"... This paper presents and evaluates two linear feature extractors based on mutual information. These feature extractors consider general dependencies between features and class labels, as opposed to well known linear methods such as PCA which does not consider class labels and LDA, which uses only sim ..."
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Cited by 23 (2 self)
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This paper presents and evaluates two linear feature extractors based on mutual information. These feature extractors consider general dependencies between features and class labels, as opposed to well known linear methods such as PCA which does not consider class labels and LDA, which uses only simple low order dependencies. As evidenced by several simulations on high dimensional data sets, the proposed techniques provide superior feature extraction and better dimensionality reduction while having similar computational requirements. 1. Introduction The capabilities of a classifier are ultimately limited by the quality of the features in each input vector. In particular, when the measurement space is highdimensional but the number of samples is limited, one is faced with the "curse of dimensionality" problem during training [3]. Feature extraction is often used to alleviate this problem. Although linear feature extractors are ultimately less flexible than the more general nonlinear ...
Discriminant Component Analysis For Face Recognition
 In ICPR
, 2000
"... We propose using a feature extraction scheme, Discriminant Component Analysis, for face recognition. This scheme decomposes a signal into orthogonal bases such that for each base there is an eigenvalue representing the discriminatory power of projection in that direction. The bases and eigenvalues a ..."
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Cited by 20 (0 self)
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We propose using a feature extraction scheme, Discriminant Component Analysis, for face recognition. This scheme decomposes a signal into orthogonal bases such that for each base there is an eigenvalue representing the discriminatory power of projection in that direction. The bases and eigenvalues are obtained by iteratively applying Fisher's Linear Discriminant Analysis (LDA). We illustrate the motivation of this scheme and show how it can be used to construct new distance metrics for the purpose of enhanced classification. Finally, good performance for face recognition on a dataset of 738 gallery images and 115 probe images is obtained using new distance metrics. 1 Introduction It is important that for different applications, we use different representations for the same signal [1]. For example, PCA (Principal Component Analysis) or wavelet decompositions is commonly used for efficient signal reconstruction by treating all samples as belonging to one class. On the other hand, signa...
Nonparametric Weighted Feature Extraction for Classification
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2004
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Linear discriminant analysis in document classification
 In IEEE ICDM Workshop on Text Mining
, 2001
"... Document representation using the bagofwords approach may require bringing the dimensionality of the representation down in order to be able to make effective use of various statistical classification methods. Latent Semantic Indexing (LSI) is one such method that is based on eigendecomposition of ..."
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Cited by 17 (0 self)
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Document representation using the bagofwords approach may require bringing the dimensionality of the representation down in order to be able to make effective use of various statistical classification methods. Latent Semantic Indexing (LSI) is one such method that is based on eigendecomposition of the covariance of the documentterm matrix. Another often used approach is to select a small number of most important features out of the whole set according to some relevant criterion. This paper points out that LSI ignores discrimination while concentrating on representation. Furthermore, selection methods fail to produce a feature set that jointly optimizes class discrimination. As a remedy, we suggest supervised linear discriminative transforms, and report good classification results applying these to the Reuters21578 database. 1
High Dimensional Feature Reduction Via Projection Pursuit
, 1995
"...  iiTable of Contents ABSTRACT.................................................................................................................................... v 1. INTRODUCTION..................................................................................................................... 1 ..."
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Cited by 15 (3 self)
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 iiTable of Contents ABSTRACT.................................................................................................................................... v 1. INTRODUCTION..................................................................................................................... 1 1.1 Background.............................................................................................................. 1
ScaleInvariant Image Recognition Based On Higher Order Autocorrelation Features
 Pattern Recognition
, 1996
"... We propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes. The system employs higher order autocorrelation features of scale space data which permit linear classification. An optimal linear classification method is pr ..."
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Cited by 12 (1 self)
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We propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes. The system employs higher order autocorrelation features of scale space data which permit linear classification. An optimal linear classification method is presented, which is able to cope with a large number of classes represented by many, as well as very few samples. In the course of the analysis of our system, we examine which numerical methods for feature transformation and classification show sufficient stability to fulfill these demands. The implementation has been extensively tested. We present the results of our own application and several classification benchmarks. Image recognition Face recognition Scale invariancy Scale space Higher order autocorrelation Optimal linear classification 1. INTRODUCTION The task of visual recognition which was defined by Marr (1) with the question: "What objects are where in the environment?" is still ...
Nonlinear Feature Transforms Using Maximum Mutual Information
 In Proc. IJCNN
, 2001
"... Finding the right features is an essential part of a pattern recognition system. This can be accomplished either by selection or by a transform from a larger number of "raw" features. In this work we learn nonlinear dimension reducing discriminative transforms that are implemented as neur ..."
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Cited by 10 (4 self)
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Finding the right features is an essential part of a pattern recognition system. This can be accomplished either by selection or by a transform from a larger number of "raw" features. In this work we learn nonlinear dimension reducing discriminative transforms that are implemented as neural networks, either as radial basis function networks or as multilayer perceptrons. As the criterion, we use the joint mutual information (MI) between the class labels of training data and transformed features. Our measure of MI makes use of Renyi entropy as formulated by Principe et al. Resulting lowdimensional features enable a classifier to operate with less computational resources and memory without compromising the accuracy.
Classification of high dimensional data
, 1998
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