Analyzing And Application Of Dimensionality Reduction Based On Manifold Learning

With the rapid development of the data acquisition technology, the number of thehigh-dimensional data is increasing in the pattern recognition filed. There is much redundantinformation in the high-dimensional data and this not only will increase the complexity ofcomputation, but also will degrade the performance of the classifier. Further more，thesehigh-dimensional data will cause the famous problem so called “the curse of dimensionality”.Dimensionality reduction as an effective technique to overcome the curse of dimensionalityhas been attracting much attention. The recent researches have indicated that thesehigh-dimensional data perhaps is embedded in a non-linear high-dimensional space. Thispresents many challenges to the methods, which based on the global linear Euclideanstructure. The methods based on manifold learning, as a new dimensionality reductiontechnology, could explore the essential structure of the data and preserve the main geometricstructure of the data. And they have been successfully applied to face recognition and datavisualization. However there are many limits in these technologies such as out-of-sampleproblems、overfitting problem and the recognition rate is unsatisfactory. In order to furtherenhance the recognition ability of manifold learning, two novel supervised dimensionalityreduction methods, which are based on the manifold learning, are presented in this paper.1. In this paper, a novel supervised dimensionality reduction method, namelynonparametric locally linear discriminant embedding (NLLDE), is proposed by adding thecriterion of weighted nonparametric maximum margin criterion (WNMMC) into the objectivefunction of LLE to further improve the recognition ability of LLE. Finally the proposedmodel is verified by the face recognition experiment.2. A novel supervised algorithm named local similarity and diversity preservingdiscriminant projection (LSDDP) is presented in this paper. LSDDP defines two weightedadjacency graphs, namely similarity graph and diversity graph, and the weights of thesimilarity graph and the diversity graph were adjusted according to the label information andthe local information of the data. Finally the proposed model is verified by the face andhandwriting digits recognition experiment.