Research Of Nonlinear Manifold Learning Algorithms Based On Spectral Graph Theory

With the rapid development of science and technology，people have more and morechannels to access to data，but the data dimension has risen sharply as well. How to reducethe dimension of these data and extract useful information becomes the focus of attentionin the field of pattern recognition and machine learning. This dissertation focuses on thedimensionality reduction algorithms, especially the nonlinear manifold learning algorithmsbased on spectral graph theory. We analyze several existing classical algorithms andimprove its inadequacies, and then two efficient feature extraction algorithms have beenproposed. The main contribution and innovative points of the dissertation are summarizedas follows:1) The background and development of the manifold learning algorithms both athome and abroad are introduced in this paper. Then several classical algorithms have beensummarized, and we also analyze the advantage and disadvantage of them.2) In Local Neighborhood Embedding(LNE) algorithm, the traditional neighborhoodsample selection methods will result in the generation of pseudo-nearest samples. Inaddition, LNE algorithm is a nonlinear manifold learning method with out-of-sampleproblem. It also ignores the class information and the extracted feature includes a lot ofredundant information. To solve these problems, Uncorrelated Discriminant LocalNeighborhood Embedding(UDLNE) algorithm is proposed. Firstly, LNE algorithm islinearized, then with the consideration of class information in target function, samplescome from same class and different classes are well separated, and by adding anuncorrelated restriction, redundant information can be greatly reduced. This method is alinear supervised algorithm, can effectively extract feature with high recognition rate.3) Tangent Space Discriminant Analysis(TSDA)is a linear supervised algorithm, itpreserves the locality geometric structures of the intra-class and simultaneously maximizethe difference of the inter-class, which greatly enhances the discrimination of the algorithm.However, TSDA algorithm is just a linear method, can not extract the nonlinear feature,and due to the existing of small sample size problem and the damage to the distance metric structure of the samples, the performance of the algorithm is further weakened. To addressthese problems, kernel orthogonal discriminant local tangent space alignment algorithm(KODLTSA) is proposed, it can discover the nonlinear information, and remains thedistance metric structure of the data with orthogonal constraints, it demonstrates goodclassification results.