Image Classification Based On Graph Spectral Theory And Non-negative Matrix Factorization

With the development of science and technology, there appear a large number of digital images in our real life, how to deal with these digital images is a very important subject. And as an important aspect of the digital image processing, the image classification is also get more and more attention.The main processes of image classification include getting the basic information, extracting the feature of image, learning and training the sample, and finally giving the classification and discrimination. In the process of image classification,the image features extraction and the optimal classifier selecting affect the image classification results directly. This thesis will combine graph theory and nonnegative matrices theory,and use several common classifiers for different images classification. The main research contents and results are as follows:First of all, an algorithm of image classification is proposed, which is based on graph Laplace matrix and nonnegative matrices factorization of image classification method. The classification method is mainly depend on the graph Laplace matrix can representing the basic structure of image information. First,extracted the feature points from different images,and use these feature points to construct the graph Laplace matrix, then get the image characteristics vector from the matrix constructed respectively singular value decomposition and non-negative matrix factorization. At last, put the characteristics vector into RBF (Radial Basis Function) neural network classifier to classify images. Simulated images and real images of the results of multiple groups based on the graph of Laplace matrix and nonnegative matrices factorization is better than image classification method based on graph with Laplace matrix and singular value decomposition method.Secondly,the adjacency matrix of graph based on the increasing weighting function combined with the method of non-negative matrix factorization is applied to the image classification.. First, the character points can be distilled from different images. Then, these points will be used to construct the adjacency matrix of the increasing weighting function, and the eigenvector of the image can be obtained by the non-negative matrix factorization of the adjacency matrix. Finally, the eigenvector will be put into PNN(Probabilistic Neural Network)classifier to accomplish the image classification. Several groups of experiment are presented between simulating images and real images. The results show that the method presented in this paper is feasible and accurate.Finally,proposed a image classification method based on graph Laplace matrix of gaussian kernel and non-negative matrix factorization.The feature points of image based on the structure of gaussian kernel function diagram of the matrix, and respectively use nonnegative matrices,local nonnegative matrices and sparse nonnegative matrices factorization to the matrix,and put the decomposed eigenvector of PNN classifier into the image classification.Compare the different algorithm evaluate through multiple sets of simulated images and real images of experimental results.