Figure 6

Weighted values vs. Euclidean distance. For each plot, the black trend line is drawn based on ordering the values for each vector (weighted values and Euclidean distance values); this gives a general fitting of each curve. The portion of the rainbow spectrum (ROYGB) shading for the lines are drawn by the same criterion, however, each line is calculated based on a set of increasing epsilon smoothing values. For example, epsilon values are increased from the 1% quantile to the 50% quantile of the squared Euclidean distance distribution, where each set of 10% values are plotted with a separate color in the rainbow spectrum, staring at red and ending at blue. This method of line shading illustrates how the transformed Euclidean distances are adjusted across a dynamic range of epsilon values for each method. (a) Gaussian radial basis function kernel values vs. Euclidean distances. (b) Entries in the matrix of the weighted graph Laplacian, L from Ng et al., vs. Euclidean distance. (c) Entries in the matrix of the weighted graph Laplacian, K from Lafon vs. Euclidean distance.