Matrix Factorization And Its Application Research On Image Classification And Clustering

With the rapid development of image information technology and image acquisitions, past decades have witnessed an exponential explosion of image information, which is filled with our daily lives. Consequently, the problems of image classification and image clustering have exhibited wide application value and research prospects. Nevertheless, the mass image information always appear with large number, high dimensionality and nonlinear structure, which make it difficult to deal with these image data efficiently.After years of research, scholars find that the nature of high dimensional data displays low dimensionality. To extract the intrinsic patterns and internal relationships within image data, the high dimensional data need to be projected into lower dimensional subspace, thus studying the hidden semantic information and seeking for more efficient and compact representation. Fortunately, matrix factorization is an effective way to reduce dimension, since it enables us to get the projective basis and subspace representation.In this thesis, we incorporated manifold learning, nonnegative matrix factorization and sparse coding theory, proposed Graph Regularized Nonnegative Matrix Factorization with Sparse Coding (GRNMF_SC) algorithm for image classification and clustering. GRNMF_SC aims to preserve the intrinsic geometrical structure and ensure the sparseness of encoding matrix, then obtains optimal lower dimensional representation. Furthermore, motivated by the research process of scholars, we proposed the concept ""Desired Matrix Factorization" for the first time, and designed another innovative matrix factorization, named Sparse concept Discriminant Matrix Factorization (SDMF), which satisfies all the requirements desirable for matrix factorization. Definitely, SDMF is a very flexible matrix factorization scheme, the fisher-like criterion in SDMF enables learned basis to capture discriminant information across feature spaces. Moreover, the fisher-like criterion even tries to extract discrimiant information when category information is missing, thus enabling SDMF to be implemented in both supervised (S-SDMF) and unsupervised (U-SDMF) versions for image classification and clustering, respectively. Compared with GRNMF_SC, SDMF also gets improvements with respect to recognition, clustering performance and even instantaneity of algorithm.