Locality sensitive discriminant analysis

TLDR

Linear Discriminant Analysis is widely used for class separation but cannot capture local manifold geometry, which is especially important when training samples are limited. This work proposes Locality Sensitive Discriminant Analysis, a new linear method that incorporates local structure into discriminant analysis. LSDA projects data into a subspace where nearby points of the same class are close and nearby points of different classes are far, maximizing local class margins. Experiments on standard face databases demonstrate that LSDA outperforms traditional LDA-based recognition.

Abstract

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 sufficient training samples, local structure is generally more important than global structure for discriminant analysis. By discovering the local manifold structure, LSDA finds a projection which maximizes the margin between data points from different classes at each local area. Specifically, the data points are mapped into a subspace in which the nearby points with the same label are close to each other while the nearby points with different labels are far apart. Experiments carried out on several standard face databases show a clear improvement over the results of LDA-based recognition.