Discriminant feature extraction by generalized difference subspace

This paper reveals the discriminant ability of the orthogonal projection of data onto a generalized difference subspace (GDS) both theoretically and experimentally. In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces. 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. gFDA can work stably even under few samples, bypassing the small sample size (SSS) problem of FDA. Next, we prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, we discuss two useful extensions of these methods, 1) nonlinear extension by kernel trick, 2) the combination of convolutional neural network (CNN) features. The equivalence and the effectiveness of the extensions have been verified through extensive experiments on the extended Yale B+, CMU face database, ALOI, ETH80, MNIST and CIFAR10, focusing on the SSS problem

Dimensionality reduction of clustered data sets

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets