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Discriminant Analysis Based on Projection Onto Generalized Difference Subspace by Fukui, Kazuhiro; Sogi, Naoya; Kobayashi, Takumi; Xue, Jing-Hao; Maki, Atsuto is a scholarly article available to read on EtoBox.

What is Discriminant Analysis Based on Projection Onto Generalized Difference Subspace about?

This paper discusses a new type of discriminant analysis based on the orthogonal projection of data onto a generalized difference subspace (GDS). In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace based classifiers. Interestingly, GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To avoid the difficulty, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. Our simplified Fisher criterion is derived from a heuristic yet practically plausible principle: the direction of the sample mean vector of a class is in most cases almost equal to that of the first principal component vector of the class, under the condition that the principal component vectors are calculated by applying the principal component analysis (PCA) without data centering. gFDA can work stably even under few samples, bypassing the

Author

Fukui, Kazuhiro; Sogi, Naoya; Kobayashi, Takumi; Xue, Jing-Hao; Maki, Atsuto

Published

2019

Language

EN