Multi-Class Linear Feature Extraction by Nonlinear PCA

The traditional way to find a linear solution to the feature extraction problem is based on the maximization of the class-between scatter over the class-within scatter (Fisher mapping). For the multi-class problem this is, however, sub-optimal due to class conjunctions, even for the simple situation of normal distributed classes with identical covariance matrices. We propose a novel, equally fast method, based on nonlinear PCA. Although still sub-optimal, it may avoid the class conjunction. The proposed method is experimentally compared with Fisher mapping and with a neural network based approach to nonlinear PCA. It appears to outperform both methods, the first one even in a dramatic way.