Non-negative Matrix Factorization And Its Application In Face Recognition

Nonnegative matrix factorization (Non-negative Matrix Factorization, NMF) is a kind of matrix decomposition method which to deal with a large-scale and high-dimensional data. The results of the decomposition is not negative, the extracted features are based on the part, localization and pure additive description. These and other unique advantages make NMF different from other methods. As a kind of new method of feature extraction, since Lee and Seung proposed have already widely used in the field of face recognition.In face feature extraction, people always want to get a matrix decomposition method with the result more sparseness, local characteristics obvious, smaller data redundancy and a faster speed. Therefore, a large number of studies and experiments have been conducted and proposed a lot of improved algorithms. These algorithms results in more suitable decomposition for us, but there are also have some shortcomings. For example, local features is not obvious enough, the sparseness of the weighted matrix is not strong, slow convergence speed and so on. These all make nonnegative matrix decomposition in the application of face recognition is not very perfect.For solving the NMF algorithm extract the local features not obvious enough, in this paper we propose a base matrix sparseness reinforced algorithm. Through combine the sparse constraint with the classic NMF Objective function and using the gradient desce-nt method obtain the iterative formula. This algorithm resulted in the distance between the basis matrixes bigger, thus local characteristics is more outstanding.In face feature extraction, the sparseness of H can reduce the redundancy between the data, improve the recognition efficiency, and increase the information of the original image. Therefore, similar to the algorithm of enhance basis matrix sparseness method, this paper give an algorithm for learning more sparseness information of the weighted matrix, and given the iterative formula. The algorithm improves the sparseness degree of the weighted matrix, which makes the distance between the basis matrixes bigger, the number of zero increased, recognition efficiency improved and the information of the original image increased. For solving the speed of NMF is slow, in this paper we propose A Decorrelation-based nonnegative matrix factorization algorithm for face recognition. Because of the correlation between the adjacent rows (column) of a face image matrix is very strong. So by reducing the correlation between them, reduced the dimensions of the matrix at the same time, and improve the speed of algorithm. This algorithm not only improves identification efficiency greatly, but also recognition rate has improved a little.Experiment have done on the ORL face database for these three algorithms, form the experiment we can see the algorithm is effective.