Constrained Nonnegative Matrix Factorization And Incremental Form Algorithm Study

In the era of massive data, how to effectively deal with large-scale data is a problem to be urgently solved of the science and engineer. Nonnegative Matrix Factorization(NMF) is an effective method for high-dimensional data processing, and from the beginning it has been an upward trend. NMF combines the nonnegative constraints, thus obtaining parts-based representation, and enhancing the interpretability of the decomposition results. NMF is simple and easy to implement and its factorization results have clear physical meaning. It has become an important research area in massive data reduction and analysis. Based on the in-depth study and analysis of the existing NMF algorithms, two kinds of improved NMF algorithms are proposed in this thesis: 1. A Euclidean Local Nonnegative Matrix Factorization(EU-LNMF). This method applies orthogonal constraints to the basis matrix to make every column of the basis matrix orthogonal to each other as much as possible. The orthogonal constraints ensure the sparseness and orthogonality of the factorization results, reduce the factorization error and improve the ability of local feature extraction. Meanwhile, in order to retain the more important part of the local information of the basis matrix, the coefficient matrix is also applied with constraints. In order to verify the effectiveness, the proposed method is applied to extract the eigenfaces. Experimental results show that the proposed method has better performance compared to similar methods. 2. A Euclidean Incremental Local Nonnegative Matrix Factorization(EU-ILNMF). When processing large-scale data online, traditional NMF method is not efficient. In order to solve this problem, the EU-LNMF is expanded to an incremental form to make it suitable for online data processing. The proposed method only processes the newly added columns of the data matrix, and only updates the corresponding column of the coefficient matrix to generate a new basis matrix. During the iterative progress, it is not necessary to store the entire data matrix, and only part of the coefficient matrix is updated, which greatly reduces the amount of calculation. Additionally, the proposed algorithm retains the orthogonal constraints of EU-LNMF, and has good local features. Experiments show that not only can this method effectively reduce the computation time but also retain more local features compared to other similar method.