5.3.2.2 Dependence on the parameters

Kernel PCA depends on the number of principal components q and the width of the Gaussian kernel $\sigma$. For the ring-line-square distribution, the quality measure and the fractional variance, explained by the principal subspace in feature space, increased with increasing q (table 5.1). A limit in the quality was reached at about 30 principal components. For 20 principal components, the covered variance also increased with the width $\sigma$. However, the quality was almost constant about the tested $\sigma$ values, with a slight peak at $\sigma$ = 0.5 (table 5.2). For the same parameters, the results for the vortex distribution were similar. Here, the optimum was at about $\sigma$ = 0.1. The reason for the difference is the smaller variance of the vortex distribution, which requires the optimal $\sigma$ to be smaller.

Table 5.1: Dependence of the quality Q and variance v--explained by q principal components--on the number of principal components q, for $\sigma$ = 0.3 and the ring-line-square distribution.

q	v	Q
10	51.5%	77.1%
20	76.3%	86.5%
30	88.5%	94.2%
40	94.5%	93.7%

Table 5.2: Dependence of the quality Q and the variance v--explained by 20 principal components--on the Gaussian width $\sigma$, for the ring-line-square distribution.

$\sigma$	v	Q
0.1	25.6%	85.6%
0.3	76.3%	86.5%
0.5	94.3%	87.7%
0.7	98.7%	82.2%