A second order polynomial based subspace projection method for dimensionality reduction

A novel feature extraction method that utilizes nonlinear mapping from the original data space to the feature space is presented in this paper. For most practical systems, the meaningful features of a pattern class lie in a low dimensional nonlinear constraint region (manifold) within the high dimensional data space. A learning algorithm to model this nonlinear region and to project patterns to this feature space is developed. Least squares estimation approach that utilizes interdependency between points in training patterns is used to form the nonlinear region. A feature space encompassing multiple pattern classes can be trained by modeling a separate constraint region for each pattern class and obtaining a mean constraint region by averaging all the individual regions. Unlike most other nonlinear techniques, the proposed method provides an easy intuitive way to place new points onto a nonlinear region in the feature space. Classification accuracy is further improved by introducing the concepts of modularity and discriminant analysis into the proposed method.