Feature Extraction Based On Manifold Learning

With the rapid development of science and technology, the number of variables for the measurement of patterns is becoming more and more. So, how to efficiently represent the patterns in the low-dimensional space is one of the key problems to be solved. Among the most methods, subspace analysis methods have become an active research area for feature extraction and pattern representation. In this dissertation, the recognition methods based on manifold learning techniques and the most expressive subspace is studied in detail. The main contribution and work are as follows:1. Two-dimensional Local Similarity and Diversity Preserving Projection (2DLSDPP) is proposed. 2DLSDPP defines two adjacency graphs, namely similarity graph and diversity graph, over the training data to model the spatial similarity and diversity of data, respectively. Similarity scatter and diversity scatter are calculated from the two graphs. Based on this content, a concise feature extraction criterion is then raised by minimizing the ratio of the similarity scatter to diversity scatter.2. Two-dimensional supervised local similarity and diversity preserving projection (2DSLSDPP) is developed. 2DSLSDPP also defines two adjacency graphs, similarity graph and diversity graph, to model data, but different from 2DLSDPP, 2DSLSDPP employs the class label of data in constructing the similarity graph. Thus, 2DSLSDPP can well preserve the similarity between the same class patterns.3. Two-dimensional discriminating projection based on local similarity and diversity (2DDLSDP) is proposed. 2DDLSDP employs similarity graph and diversity graph to model the similarity and diversity of data, respectively. The similarity graph gives the large weight for the same class adjacency data, and small weight for different class adjacency data. Similarity and diversity scatters are calculated from the two adjacency graphs. A concise feature extraction criterion is then raised via minimizing the ratio of the similarity scatter to diversity scatter.