Generalized discriminant analysis: a matrix exponential approach.

Area of Science:

• Machine Learning
• Data Science
• Pattern Recognition

Background:

• Linear Discriminant Analysis (LDA) is a standard technique for classification.
• High-dimensional data with small training sets presents the 'small-sample-size' or 'undersampled' problem, limiting LDA's direct application.

Purpose of the Study:

• To propose Exponential Discriminant Analysis (EDA) as a solution to the undersampled problem in high-dimensional data.
• To enhance classification accuracy by leveraging discriminant information often lost in existing LDA extensions.

Main Methods:

• EDA transforms data into a new space using distance diffusion mapping before applying LDA.
• This approach extracts discriminant information from the null space of the within-class scatter matrix.
• It also preserves discriminant information from the non-null space, unlike Null-Space LDA (NLDA).

Main Results:

• EDA demonstrates superior performance compared to several existing LDA extensions, including PCA+LDA, NLDA, and others.
• The distance diffusion mapping in EDA enlarges the margin between classes, improving classification.
• Experimental results on various datasets confirm the effectiveness of the proposed EDA method.

Conclusions:

• Exponential Discriminant Analysis (EDA) is an effective technique for discriminant analysis with small sample sizes in high-dimensional data.
• EDA offers advantages over existing methods by utilizing a broader range of discriminant information and enhancing class separation.