Neighbourhood sensitive preserving embedding for pattern classification

Recently, a large family of supervised or unsupervised manifold learning algorithms that stem from statistical or geometrical theory has been designed to solve the problem of pattern classification. In this study, consider the fact that the data are usually sampled from a low-dimensional manifold space which resides in a high-dimensional Euclidean space, the authors propose a novel two-graph-based supervised linear classification algorithm called neighbourhood sensitive preserving embedding (NSPE). Different from local linear embedding (LLE) (or neighbourhood preserving embedding (NPE)) which preserves the local neighbourhood structure with one graph, NSPE can discover both the intrinsic and discriminant structure of the data manifold by constructing two graphs, that is, the within-class graph and the between-class graph. Thus, the data are mapped into a subspace where the nearby points with the same label are close to each other, whereas the nearby points with different labels are far apart. As a classification method, besides being defined on training samples, NSPE is also defined on testing samples. Experiments carried on the real-world face databases demonstrate that the results of all two-graph-based spectral methods are comparable and better than that of one-graph-based methods.