Two-dimensional supervised local similarity and diversity projection

This paper presents a novel manifold learning method, namely two-dimensional supervised local similarity and diversity projection (2DSLSDP), for feature extraction. The proposed method defines two weighted adjacency graphs, namely similarity graph and diversity graph. The affinity matrix of similarity graph is determined by the spatial relationship between vertices of this graph, while affinity matrix of diversity graph is determined by the diversity information of vertices of its graph. Using these two graphs, the proposed method constructs local similarity scatter and diversity scatter, respectively. A concise feature extraction criterion is then raised via minimizing the ratio of the local similarity scatter to local diversity scatter. Thus, 2DSLSDP can well preserve not only the adjacency similarity structure, but also the diversity of data points, which is important for the classification. Experiments on the AR and UMIST databases show the effectiveness of the proposed method.