Figure 1

Parameter optimization plot for image example. Regression coefficients for image ordering determined by different epsilon values for kernel PCA and the spectral method from Ng et al. Epsilon values were increased to 300,000 to assess image ordering accuracy (data not shown), but truncated for the plot to better visualize the global maxima. The dashed black horizontal line indicates a rho statistic value of 1, though neither method reaches this threshold. Large fluctuations in the rho statistic are observed for both methods at minimal values of epsilon. For kernel PCA a non-optimal solution is determined in the variable region, while for the spectral method from Ng et al., a maximum is determined in this region. The variability in the rho values at these minimal values can be associated with the optimal convergence of remote and local distances in the weight matrices (Figure 6) of kernel PCA and the spectral method from Ng et al (L). Small values of the epsilon parameter provide minimal convergence of the L matrix distribution tails (very small distances and very large distance), which is optimal for the spectral method from Ng et al for this example. For kernel PCA, larger values of the epsilon parameter provide convergence of large distances and greater convergence of small distances in the Gaussian radial basis function kernel matrix, which is determined to be optimal for this example.