5. Kernel PCA for pattern association

This chapter presents an alternative to the pattern association based on a mixture of local PCA. This mixture is replaced by a single PCA in an infinite-dimensional feature space, into which the data are (virtually) mapped. The principal components in this feature space can be extracted using kernel PCA, which operates only on the data points within the original space (section 2.4). In the original space, a potential field is constructed based on these principal components. To associate an output with an input, a point, whose input portion is given, relaxes along a constraint subspace, whose offset from zero is the input. Herein, relaxation is a gradient descent in the potential field. Potential fields were computed for two-dimensional synthetic data, and the pattern-association method was applied to a synthetic distribution and to the kinematic arm model from section 4.5. On the pattern association, kernel PCA is compared to the mixture of local PCA.

- 5.1 Motivation
- 5.2 Pattern association algorithm

- 5.3 Experiments

- 5.4 Discussion

2005-03-22