Generalized Discriminant Analysis Using a Kernel Approach

TLDR

The underlying theory is close to support vector machines, as GDA maps input vectors into a high‑dimensional feature space. The authors introduce generalized discriminant analysis (GDA) as a kernel‑based method for nonlinear discriminant analysis. GDA transforms data into a high‑dimensional space via a kernel, then solves an eigenvalue problem to extend linear discriminant analysis, allowing various kernels to capture diverse nonlinearities. Classification experiments on simulated and real seed data demonstrate that GDA accurately classifies samples and reveals the decision function shape across different kernels.

Abstract

We present a new method that we call generalized discriminant analysis (GDA) to deal with nonlinear discriminant analysis using kernel function operator. The underlying theory is close to the support vector machines (SVM) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space. In the transformed space, linear properties make it easy to extend and generalize the classical linear discriminant analysis (LDA) to nonlinear discriminant analysis. The formulation is expressed as an eigenvalue problem resolution. Using a different kernel, one can cover a wide class of nonlinearities. For both simulated data and alternate kernels, we give classification results, as well as the shape of the decision function. The results are confirmed using real data to perform seed classification.