Non-negative Matrix Factorization And Its Application In Image Classification And Clustering

Matrix factorization,which can extract useful information from high-dimensional data and obtain low-dimensional representation of raw data,is one of the most useful tools in the fields of scientific computing,data mining and computer vision.Non-negative matrix factorization(NMF)approximately decomposes a non-negative data matrix into a product of two(or three)non-negative factor matrices.Due to the combination of non-negative constraints,decomposition results of NMF with interpretability and easy implementation have been widely concerned.This thesis focuses on NMF based image classification and clustering algorithms,embedding orthogonality constraints,incremental learning and manifold learning into NMF models,and proposes two novel NMF algorithms to achieve better classification and clustering performance.The main contributions are:(1)Present an incremental learning model based on subspace dimensionality reduction,called orthogonal incremental non-negative matrix factorization(OINMF).OINMF applies orthogonal constraints to the base matrix and uses the results of gradient on Stiefel manifold to derive the iterative formula,which can solve the re-decomposition problem of NMF with the increase of data.By using the orthogonality constraint,the new algorithm can improve the sparsity of factor matrix and obtain stronger local expression ability.The performance of OINMF algorithm is evaluated through classification experiments on open image datasets of different scales,and the indexes such as orthogonality,sparsity,time efficiency and recognition rate are selected to make a comparison between OINMF algorithm and other eight representative algorithms.The experimental results show that OINMF achieves better sparsity and orthogonality while maintaining incremental learning time efficiency and higher recognition rate.(2)Propose a constrained dual graph regularized orthogonal non-negative matrix tri-factorization(CDONMTF)algorithm.The new method improves the clustering performance obviously by employing hard constraints to retain the priori label information of samples,establishing two nearest neighbor graphs to encode the geometric structure of data manifold and feature manifold and combining with bi-orthogonal constraints as well.Furthermore,CDONMTF's iterative optimization scheme is derived,and the convergence of the optimization strategy is proved theoretically.In addition,image clustering experiments on seven different types and scales of public image datasets show that the clustering performance of CDONMTF algorithm is better than that of 8 existing algorithms on the indexes of clustering accuracy,normalized mutual information and purity.