Visualizations of Kernel Principal Components Analysis

Grayscale visualizations of the kernel space for toy 2D examples trained using KPCA

This code can aid in visualizing the kernel space for 2D data trained using Kernel Principal Components Analysis.

You can: (1) choose among 5 types of kernels (you can also add more), (2) input your own kernel parameters, and (3) choose among 5 toy 2D data sets to play with. The sample data sets include: (1) a face, (2) a spiral, (3) three clusters, (4), two moons, and (5) concentric circles. The output Figure 1 contains plots of: (1) raw data, (2) normalized data, (3) sorted eigenvalues, (4) 3D kernel projection of training and test data. Figure 2 contains grayscale visualizations of the top 9 (or less) eigenvalues from KPCA. You can rotate the plots in Fig. 2 so you can see the actual kernel surface. It is hoped that the user will gain insights to the effect of kernels and their parameters for KPCA on simple 2D data.

Reference: Scholkopf, Smola, Muller (1998). Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, 10, 1299–1319.