Topic
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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TL;DR: However, for a task with very high dimensional data such as images, the traditional LDA algorithm encounters several difficulties, and before LDA can be used to reduce dimensionality, another procedure has to be first applied for dimensionality reduction.
1,579 citations
TL;DR: In this article, several methods of estimating error rates in discriminant analysis are evaluated by sampling methods, and two methods in most common use are found to be significantly poorer than some new methods that are proposed.
Abstract: Several methods of estimating error rates in Discriminant Analysis are evaluated by sampling methods. Multivariate normal samples are generated on a computer which have various true probabilities of misclassification for different combinations of sample sizes and different numbers of parameters. The two methods in most common use are found to be significantly poorer than some new methods that are proposed.
1,513 citations
TL;DR: It is proved that the most expressive vectors derived in the null space of the within-class scatter matrix using principal component analysis (PCA) are equal to the optimal discriminant vectorsderived in the original space using LDA.
1,447 citations
TL;DR: This study presents necessity and usefulness of multivariate statistical techniques for evaluation and interpretation of large complex data sets with a view to get better information about the water quality and design of monitoring network for effective management of water resources.
1,429 citations
TL;DR: This paper assesses performance of regularized radial basis function neural networks (Reg-RBFNN), standard support vector machines (SVMs), kernel Fisher discriminant (KFD) analysis, and regularized AdaBoost (reg-AB) in the context of hyperspectral image classification.
Abstract: This paper presents the framework of kernel-based methods in the context of hyperspectral image classification, illustrating from a general viewpoint the main characteristics of different kernel-based approaches and analyzing their properties in the hyperspectral domain. In particular, we assess performance of regularized radial basis function neural networks (Reg-RBFNN), standard support vector machines (SVMs), kernel Fisher discriminant (KFD) analysis, and regularized AdaBoost (Reg-AB). The novelty of this work consists in: 1) introducing Reg-RBFNN and Reg-AB for hyperspectral image classification; 2) comparing kernel-based methods by taking into account the peculiarities of hyperspectral images; and 3) clarifying their theoretical relationships. To these purposes, we focus on the accuracy of methods when working in noisy environments, high input dimension, and limited training sets. In addition, some other important issues are discussed, such as the sparsity of the solutions, the computational burden, and the capability of the methods to provide outputs that can be directly interpreted as probabilities.
1,428 citations