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Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.


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Journal Article
TL;DR: The main result shows that under a mild condition which holds in many applications involving high-dimensional data, NLDA is equivalent to OLDA, which confirms the effectiveness of the regularization in ROLDA.
Abstract: Dimensionality reduction is an important pre-processing step in many applications. Linear discriminant analysis (LDA) is a classical statistical approach for supervised dimensionality reduction. It aims to maximize the ratio of the between-class distance to the within-class distance, thus maximizing the class discrimination. It has been used widely in many applications. However, the classical LDA formulation requires the nonsingularity of the scatter matrices involved. For undersampled problems, where the data dimensionality is much larger than the sample size, all scatter matrices are singular and classical LDA fails. Many extensions, including null space LDA (NLDA) and orthogonal LDA (OLDA), have been proposed in the past to overcome this problem. NLDA aims to maximize the between-class distance in the null space of the within-class scatter matrix, while OLDA computes a set of orthogonal discriminant vectors via the simultaneous diagonalization of the scatter matrices. They have been applied successfully in various applications. In this paper, we present a computational and theoretical analysis of NLDA and OLDA. Our main result shows that under a mild condition which holds in many applications involving high-dimensional data, NLDA is equivalent to OLDA. We have performed extensive experiments on various types of data and results are consistent with our theoretical analysis. We further apply the regularization to OLDA. The algorithm is called regularized OLDA (or ROLDA for short). An efficient algorithm is presented to estimate the regularization value in ROLDA. A comparative study on classification shows that ROLDA is very competitive with OLDA. This confirms the effectiveness of the regularization in ROLDA.

166 citations

Journal ArticleDOI
TL;DR: Wang et al. as discussed by the authors combined two different methodological approaches to discriminative feature selection in a unified framework, namely, linear discriminant analysis and locality preserving projection, to select class-discriminative and noise-resistant features.
Abstract: The high feature-dimension and low sample-size problem is one of the major challenges in the study of computer-aided Alzheimer's disease (AD) diagnosis. To circumvent this problem, feature selection and subspace learning have been playing core roles in the literature. Generally, feature selection methods are preferable in clinical applications due to their ease for interpretation, but subspace learning methods can usually achieve more promising results. In this paper, we combine two different methodological approaches to discriminative feature selection in a unified framework. Specifically, we utilize two subspace learning methods, namely, linear discriminant analysis and locality preserving projection, which have proven their effectiveness in a variety of fields, to select class-discriminative and noise-resistant features. Unlike previous methods in neuroimaging studies that mostly focused on a binary classification, the proposed feature selection method is further applicable for multiclass classification in AD diagnosis. Extensive experiments on the Alzheimer's disease neuroimaging initiative dataset showed the effectiveness of the proposed method over other state-of-the-art methods.

166 citations

Journal ArticleDOI
TL;DR: A new minimum recognition error formulation and a generalized probabilistic descent (GPD) algorithm are analyzed and used to accomplish discriminative training of a conventional dynamic-programming-based speech recognizer.
Abstract: A new minimum recognition error formulation and a generalized probabilistic descent (GPD) algorithm are analyzed and used to accomplish discriminative training of a conventional dynamic-programming-based speech recognizer. The objective of discriminative training here is to directly minimize the recognition error rate. To achieve this, a formulation that allows controlled approximation of the exact error rate and renders optimization possible is used. The GPD method is implemented in a dynamic-time-warping (DTW)-based system. A linear discriminant function on the DTW distortion sequence is used to replace the conventional average DTW path distance. A series of speaker-independent recognition experiments using the highly confusible English E-set as the vocabulary showed a recognition rate of 84.4% compared to approximately 60% for traditional template training via clustering. The experimental results verified that the algorithm converges to a solution that achieves minimum error rate. >

165 citations

Journal ArticleDOI
01 Oct 1999
TL;DR: A method to evaluate the performance of a variety of data-preprocessing techniques for the problem of odour classification using an array of gas sensors, also referred to as an electronic nose.
Abstract: The performance of a pattern recognition system is dependent on, among other things, an appropriate data-preprocessing technique, In this paper, we describe a method to evaluate the performance of a variety of these techniques for the problem of odour classification using an array of gas sensors, also referred to as an electronic nose. Four experimental odour databases with different complexities are used to score the data-preprocessing techniques. The performance measure used is the cross-validation estimate of the classification rate of a K nearest neighbor voting rule operating on Fisher's linear discriminant projection subspace.

165 citations

Journal ArticleDOI
TL;DR: Diversity measures indicated that Boosting succeeds in inducing diversity even for stable classifiers whereas Bagging does not, confirming in a quantitative way the intuitive explanation behind the success of Boosting for linear classifiers for increasing training sizes, and the poor performance of Bagging.

165 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20242
2023756
20221,711
2021678
2020815