Study On Improved Discriminant Non-negative Matrix Factorization

The processing of massive data is the key technology urgently to be solved by scientific researches at present. How to reduce the high-dimensional data to the low-dimensional data and make the potential structure of data become clear is the hot and difficult spot of the research. Non-negative matrix factorization(NMF) is a kind of matrix factorization method under non-negative constraints and can greatly reduce the dimension of expression data. Also, the factorization characteristics of NMF conform to the intuitive experience of human perception, and the factorization results of NMF have strong interpretability. In addition, NMF has such advantages as simplicity and easy implementation. For the characteristics above, NMF has been widely used in fields of dimension reduction, feature extraction, pattern recognition, etc. On the basis of deep analysis and research on the existing NMF methods, this thesis presents the following two kinds of improved NMF methods.1. A Weighted Discriminant Non-negative Matrix Factorization(WDNMF) method. In order to overcome the problem of low recognition accuracy due to the local information losing caused by continuous occlusion of large area in a target object, this thesis firstly constructs a weight matrix according to the occluded region in a target object, and then employs this matrix to extend the generalized Kullback-Leibler divergence(GKLD) to a weighted GKLD(WGKLD) objective function in order to weaken or even neglect the impact of occluded region on feature extraction, and rather give emphasis on the data of occlusion-free regions. Meanwhile, in order to obtain more localized features, the sparseness constraints term on the basis matrix is added in the objective function that includes WGKLD and discriminant constraints items on the coefficient matrix. Finally, the update rules of basis and coefficient matrixes are derived by using the simple and effective multiplicative update algorithm. Experimental results in face recognition demonstrate that the WDNMF method is robust to the continuous occlusion of large area relative to other methods, and can extract the salient feature information in facial images more effectively and accurately. Accordingly, the classification accuracy is improved well.2. A Blocked Discriminant Non-negative Matrix Factorization(BDNMF) method. In order to use the class information more effectively and reduce the interference between different localized features in feature extraction, so as to extract the facial localized features more accurately and improve the robustness and adaptability of method for occlusion consequently, the following steps are conducted. Firstly, an optimized between-class scatter constraints term is proposed by constructing a weight matrix of between-class dissimilarity degree for the greater use of the class information, and then the blocked discriminant NMF(BDNMF) method is developed by introducing the optimized between-class scatter constraints term in the basic discriminant NMF(DNMF) model and also combining the block preprocessing. Secondly, the BDNMF method is utilized to extract the basis spaces of several facial non-overlapping sub-blocks in order to reduce the interference between different localized features in feature extraction. Finally, the information of each sub-block is fully used according to the feature fusion rules, and the nearest neighbor classifier is adopted for face recognition. Experimental results show that compared with other methods, this method has strong robustness for continuous occlusion of large area, and can further improve the localization representation characteristics of features, and accordingly, the classification performance is improved significantly.