Recursive universum linear discriminant analysis

Universum linear discriminant analysis was recently proposed to improve linear discriminant analysis by incorporating Universum information. However, it obtains each of the discriminant directions by just using samples from two classes, while other class samples are considered as Universum. This not only leads to the ignoring of some discriminant information, but also restricts its number of extracted features to at most 0.5k(k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5k(k-1)$$\end{document}, where k is the number of classes. To fully explore discriminant information from all classes, this paper studies a novel Universum linear discriminant analysis by considering a unified model that simultaneously uses all classes. Compared to the existing Universum linear discriminant analysis, all Universum information is fully utilized in the proposed model when obtaining each discriminant direction, where the Universum can be self-constructed as well can be given advanced of any types. The constrained concave-convex procedure can be used to solve the proposed method, which makes the algorithm convergent to a local minimum. By employing a recursive technique, arbitrary number of discriminant directions can be obtained. Experimental results on real-world benchmark datasets and image datasets illustrate the advantages of the proposed method.

Automated summary

This paper proposes a Universum linear discriminant analysis method to improve linear discriminant analysis. Compared to existing methods, this method fully utilizes Universum information to obtain discriminant directions and can obtain any number of discriminant directions.