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.

Classification tools in chemistry. Part 1: linear models. PLS-DA

Abstract: The common steps to calibrate and validate classification models based on partial least squares discriminant analysis are discussed in the present tutorial. All issues to be evaluated during model training and validation are introduced and explained using a chemical dataset, composed of toxic and non-toxic sediment samples. The analysis was carried out with MATLAB routines, which are available in the ESI of this tutorial, together with the dataset and a detailed list of all MATLAB instructions used for the analysis.

Efficient and robust feature extraction by maximum margin criterion

Abstract: In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal component analysis (PCA) and linear discriminant analysis (LDA) are the two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features, and LDA is not stable due to the small sample size problem . In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.

Face recognition using LDA-based algorithms

Abstract: Low-dimensional feature representation with enhanced discriminatory power is of paramount importance to face recognition (FR) systems. Most of traditional linear discriminant analysis (LDA)-based methods suffer from the disadvantage that their optimality criteria are not directly related to the classification ability of the obtained feature representation. Moreover, their classification accuracy is affected by the "small sample size" (SSS) problem which is often encountered in FR tasks. In this paper, we propose a new algorithm that deals with both of the shortcomings in an efficient and cost effective manner. The proposed method is compared, in terms of classification accuracy, to other commonly used FR methods on two face databases. Results indicate that the performance of the proposed method is overall superior to those of traditional FR approaches, such as the eigenfaces, fisherfaces, and D-LDA methods.

Discriminant Analysis by Gaussian Mixtures

Abstract: Fisher-Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered. Low dimensional views are an important by-product of LDA-our new techniques inherit this feature. We can control the within-class spread of the subclass centres relative to the between-class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA.

Maximum neighborhood margin discriminant projection for classification

Abstract: We develop a novel maximum neighborhood margin discriminant projection (MNMDP) technique for dimensionality reduction of high-dimensional data. It utilizes both the local information and class information to model the intraclass and interclass neighborhood scatters. By maximizing the margin between intraclass and interclass neighborhoods of all points, MNMDP cannot only detect the true intrinsic manifold structure of the data but also strengthen the pattern discrimination among different classes. To verify the classification performance of the proposed MNMDP, it is applied to the PolyU HRF and FKP databases, the AR face database, and the UCI Musk database, in comparison with the competing methods such as PCA and LDA. The experimental results demonstrate the effectiveness of our MNMDP in pattern classification.