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Equivalence of Several Twostage Methods for Linear Discriminant Analysis ∗
"... component analysis, generalized singular value decomposition, QR decomposition, text classification Linear discriminant analysis (LDA) has been used for decades to extract features that preserve class separability. It is classically defined as an optimization problem involving covariance matrices th ..."
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equivalence to the singlestage LDA/GSVD method, provided either principal component analysis or latent semantic indexing is used in the first stage over a certain range of intermediate dimensions. We also present a computationally simpler choice for the first stage, and conclude with a discussion
Abstract Equivalence of Several Twostage Methods for Linear Discriminant Analysis ∗
"... Linear discriminant analysis (LDA) has been used for decades to extract features that preserve class separability. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be ..."
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have taken a twostage approach in which the first stage reduces the dimension of the data enough so that it can be followed by classical LDA. In this paper, we justify the twostage approach by establishing its equivalence to the singlestage LDA/GSVD method, provided either principal component
Equivalence of Several Twostage Methods for Linear Discriminant Analysis ∗
"... Linear discriminant analysis (LDA) has been used for decades to extract features that preserve class separability. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be ..."
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have taken a twostage approach in which the first stage reduces the dimension of the data enough so that it can be followed by classical LDA. In this paper, we justify the twostage approach by establishing its equivalence to the singlestage LDA/GSVD method, provided either principal component
ModelBased Clustering, Discriminant Analysis, and Density Estimation
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
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Cited by 557 (28 self)
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Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However
Fisher Discriminant Analysis With Kernels
, 1999
"... A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision f ..."
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Cited by 493 (18 self)
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A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision
Automatic Word Sense Discrimination
 Journal of Computational Linguistics
, 1998
"... This paper presents contextgroup discrimination, a disambiguation algorithm based on clustering. Senses are interpreted as groups (or clusters) of similar contexts of the ambiguous word. Words, contexts, and senses are represented in Word Space, a highdimensional, realvalued space in which closen ..."
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Cited by 530 (1 self)
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This paper presents contextgroup discrimination, a disambiguation algorithm based on clustering. Senses are interpreted as groups (or clusters) of similar contexts of the ambiguous word. Words, contexts, and senses are represented in Word Space, a highdimensional, realvalued space in which
Exploiting Generative Models in Discriminative Classifiers
 In Advances in Neural Information Processing Systems 11
, 1998
"... Generative probability models such as hidden Markov models provide a principled way of treating missing information and dealing with variable length sequences. On the other hand, discriminative methods such as support vector machines enable us to construct flexible decision boundaries and often resu ..."
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Cited by 538 (11 self)
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result in classification performance superior to that of the model based approaches. An ideal classifier should combine these two complementary approaches. In this paper, we develop a natural way of achieving this combination by deriving kernel functions for use in discriminative methods such as support
Using Discriminant Eigenfeatures for Image Retrieval
, 1996
"... This paper describes the automatic selection of features from an image training set using the theories of multidimensional linear discriminant analysis and the associated optimal linear projection. We demonstrate the effectiveness of these Most Discriminating Features for viewbased class retrieval ..."
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Cited by 504 (15 self)
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This paper describes the automatic selection of features from an image training set using the theories of multidimensional linear discriminant analysis and the associated optimal linear projection. We demonstrate the effectiveness of these Most Discriminating Features for viewbased class
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Linear pattern matching algorithms
 IN PROCEEDINGS OF THE 14TH ANNUAL IEEE SYMPOSIUM ON SWITCHING AND AUTOMATA THEORY. IEEE
, 1972
"... In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but suboptimal algorithms. In this paper, we introduce an interesting data structure called a bitree. A linear ti ..."
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Cited by 549 (0 self)
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time algorithm for obtaining a compacted version of a bitree associated with a given string is presented. With this construction as the basic tool, we indicate how to solve several pattern matching problems, including some from [4], in linear time.
Results 1  10
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