A novel supervised dimensionality reduction algorithm: Graph-based Fisher analysis

In this paper, a novel supervised dimensionality reduction (DR) algorithm called graph- based Fisher analysis (GbFA) is proposed. More specifically, we redefine the intrinsic and penalty graph and trade off the importance degrees of the same-class points to the intrinsic graph and the importance degrees of the not-same-class points to the penalty graph by a strictly monotone decreasing function; then the novel feature extraction criterion based on the intrinsic and penalty graph is applied. For the non-linearly separable problems, we study the kernel extensions of GbFA with respect to positive definite kernels and indefinite kernels, respectively. In addition, experiments are provided for analyzing and illustrating our results.

► A novel feature extraction criterion based on the Spectral Graph Theory is proposed.
► GbFA algorithm derivation for the small sample size cases is specified.
► We extended the kernel GbFA model for the linear non-separated problem.