Linear and quadratic discriminant analysis are considered in the small sample high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassificat...

The Internet of Things (IoT) generates lots of high-dimensional sensor intelligent data. The processing of high-dimensional data (e.g., data visualization and data classification) is very difficult, so it requires excellent subspace learning algorithms to learn a latent subspace to preserve the intrinsic structure of the high-dimensional data, and abandon the least useful information in the sub...

This report describes our experience in implementing a non-parametric (distribution free) discriminant analysis module for use in a wide range of pattern recognition problems. Issues discussed include performance results on both real and simulated data sets, comparisons to other methods, and the computational environment. In some cases, this module performs betther than other existing methods. ...

When it becomes necessary to reduce the complexity of a classifier, dimensionality reduction can be an effective way to address classifier complexity. Linear Discriminant Analysis (LDA) is one approach to dimensionality reduction that makes use of a linear transformation matrix. The widely used Fisher’s LDA is “sub-optimal” when the sample class covariance matrices are unequal, meaning that ano...

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten and Tibshirani, 2011, Cai and Liu, 2011, Mai et al., 2012 and Fan et al., 2012). In this paper, we develop high-dimensional sparse semiparametric discriminant analysis (SSDA) that generalizes the normal-theory discr...

Linear Discriminant Analysis (LDA) is a popular data-analytic tool for studying the class relationship between data points. A major disadvantage of LDA is that it fails to discover the local geometrical structure of the data manifold. In this paper, we introduce a novel linear algorithm for discriminant analysis, called Locality Sensitive Discriminant Analysis (LSDA). When there is no sufficien...

Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection and keyframe extraction cannot provide consistent instance-label pairs, while LDA requires labels on instance level for training. Thus it cannot be directly ap...

Barycenter The mean of the observations from a given category (also called center of gravity, center of mass, mean vector, or centroid) Confidence interval An interval encompassing a given proportion (e.g., 95%) of an estimate of a parameter (e.g., a mean) Discriminant analysis A technique whose goal is to assign observations to some predetermined categories Discriminant factor scores A linear ...

Kernel methods for data analysis are frequently considered to be restricted to positive definite kernels. In practice, however, indefinite kernels arise e.g. from problem-specific kernel construction or optimized similarity measures. We, therefore, present formal extensions of some kernel discriminant analysis methods which can be used with indefinite kernels. In particular these are the multi-...

Some empirical localized discriminant analysis methods for classifying images are introduced. They use spatial correlation of images in order to improve classification reducing the ‘pseudo-nuisance’ present in pixel-wise discriminant analysis. The result is obtained through an empirical (data driven) and local (pixelwise) choice of the prior class probabilities. Local empirical discriminant ana...