In machine learning, linear discriminant analysis (LDA) is a popular dimension reduction method. In this paper, we first provide a new perspective of LDA from an information theory perspective. From this new perspective, we propose a new formulation of LDA, which uses the pairwise averaged class covariance instead of the globally averaged class covariance used in standard LDA. This pairwise (av...

In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum `1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a `1-minimizati...

The classiication rules of linear discriminant analysis are deened by the true mean vectors and the common covariance matrix of the populations from which the data come. As these true parameters are in general unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. These sample statistics are howe...

We propose a new method of discriminant analysis, called High Dimensional Discriminant Analysis (HHDA). Our approach is based on the assumption that high dimensional data live in different subspaces with low dimensionality. Thus, HDDA reduces the dimension for each class independently and regularizes class conditional covariance matrices in order to adapt the Gaussian framework to high dimensio...

The applications that are related to classification problem are wide-ranging. In fact, differentiating between patients with strong prospects for recovery and those highly at risk, between good credit risks and poor ones, or between promising new firms and those likely to fail, are among the most known of these applications. To solve such classification problem, several approaches have been app...

We show that Gabor lter representations of facial images give quantitatively indistinguishable results for classi cation of facial expressions as local PCA representations, in contrast to other recent work. We then show that a linear discriminant analysis performed on the Gabor lter representation automatically locates the important regions corresponding to the facial actions involved in portra...

We present the analysis performed over eleven speakers (five women and 6 men) in order to obtain the most important parameters as far as speaker identity is concerned. Parameters that have been studied are F0, six formants, five bandwidths and four source parameters. Feature selection is based on linear discriminant analysis. Results show that the most relevant parameter is F0, followed by form...

The authors consider a robust linear discriminant function based on high breakdown location and covariance matrix estimators. They derive influence functions for the estimators of the parameters of the discriminant function and for the associated classification error. The most B-robust estimator is determined within the class of multivariate S-estimators. This estimator, which minimizes the max...

Linear discriminant analysis with binary response is considered when the predictor is a functional random variableX = {Xt, t ∈ [0, T ]}, T ∈ R. Motivated by a food industry problem, we develop a methodology to anticipate the prediction by determining the smallest T ∗, T ∗ ≤ T , such that X∗ = {Xt, t ∈ [0, T ∗]} and X give similar predictions. The adaptive prediction concerns the observation of ...

This article considers the problem of educational placement. Several discriminant techniques are applied to a data set from a survey project of science ability. A profile vector for each student consists of five science-educational indictors. The students are intended to be placed into three reference groups: advanced, regular, and remedial. Various discriminant techniques, including Fisher’s d...