Study On Structure Constraint And Discriminant Information In The Application Of Non-negative Matrix Factorization

Feature extraction techniques aim to project data from high-dimensional space into alow-dimensional space to find compact representations of data. Among them, Non-negativematrix factorization (NMF) is an effective method for dealing with the large-scalehigh-dimensional data. Compared with other methods, NMF can learn a part-basedrepresentation due to the non-negativity constraints on basis matrix and coefficient matrix areimposed in it. Therefore, NMF has been widely applied in pattern recognition, imageprocessing, etc.In image recognition field, an ideal local feature representation should not onlycontribute to reduce the redundancy of the data, but also better interprets the concept of "parts-based representation of data". Therefore, a large number of improved NMF algorithmshave been developed for image recognition by introducing additional constraints to theoriginal NMF. Although improved NMF algorithms have been successfully applied to manyreal-world applications, they still suffer from the following limitations. Firstly, the baseslearned by previous NMF variants are not always sparse enough. Then, the original NMF andits sparse extensions are unsupervised. Finally, they may fail to discover the intrinsicgeometrical structure of the data space.To address these problems, a new non-negative matrix factorization method calledStructure constraint discriminative non-negative matrix factorization (SCDNMF) is proposedto improve the performance of NMF algorithm for recognition and classification tasks. In ourproposed algorithm, a pixel dispersion penalty (PDP) constraint is employed to preservespatial locality structured information of the basis obtained by NMF. At the same time, inorder to improve the classification performance, intra-class graph and inter-class graph arealso constructed to exploit discriminative information as well as geometric structure of thehigh-dimensional data. Therefore, the low-dimensional features obtained by our algorithm arestructured sparse and discriminative. Moreover, an iterative updating optimization scheme isalso developed to solve the objective function of the proposed SCDNMF. The proposedmethod is applied to the problem of image recognition using the well-known ORL, Yale andCOIL20databases. The experimental results demonstrate that the performance of ourproposed SCDNMF outperforms the state-of-the-art methods.