Nonlinear dimensionality reduction for face recognition

Principal component analysis (PCA) has long been a dominating linear technique for dimensionality reduction. Many nonlinear methods and neural networks have been proposed to extend PCA for complex nonlinear data. They include kernel PCA, local linear embedding, isomap, self-organising map (SOM), and visualization induced SOM (ViSOM), a variant of SOM for a faithful and metric-preserving mapping. In this paper, we investigate these nonlinear manifold methods for face recognition, and compare their performances with linear PCA. Results from the experiments on real-world face databases show that although nonlinear methods have greater capability than PCA, the differences in classification rate of most nonlinear methods and PCA are insignificant. However, ViSOM has produced marked improvement over PCA and other nonlinear methods. A nonlinearity measure is used to quantify the degree of nonlinearity of a data set in the reduced subspace. It can be used to indicate the effectiveness of nonlinear or linear dimensionality reduction.