Research On Deep Orthogonal Nonnegative Matrix Factorization And Its Clustering

Non-negative Matrix Factorization is composed of the idea that “the perception of the whole is perceived by the parts that make up the whole”.It decomposes the original matrix into a base matrix and a coefficient matrix by means of non-negative constraints.The original matrix can be regarded as the weighted sum of all column vectors in the base matrix.No negative value appears in the decomposition result,which has interpretability and clear physical meaning.Non-negative Matrix Factorization is a matrix decomposition method that deals with high-dimensional data.It projects high-dimensional samples into low-dimensional subspaces,and obtains the features of the samples from the subspace.The extracted features are based on part ial pure additive descriptions,and it occupies less storage space in the computer,has a wide range of applications in image processing,speech signal processing,text clustering and other fields.For complex data,the single-layer network formed by Non-negative Matrix Factorization cannot describe the deeper features of the data.In order to learn the hidden layer characteristics of complex data,it is necessary to use a deep network structure to extract features in layers.The deep network constructed by Non-negative Matrix Factorization not only can extract features in layers,but also can maintain the physical meaning that “the whole is composed of parts”.Therefore,the proposal of Deep Non-negative Matrix Factorization has important practical significance.At present,the research on deep nonnegative matrix is entering a new stage.In this paper,the Deep Orthogonal Non-negative Matrix Factorization is deeply studied.The main innovative work:1.A Deep Orthogonal Non-negative Matrix Factorization model is proposed in this paper.Orthogonal Nonnegative Matrix Factorization is an effective unsupervised learning method,because it is equivalent to a K-means algorithm which is easy to cluster analysis.The structure of single layer is hard to obtain the deep features of data.Based on the Deep Non-negative Matrix Factorization,a new algorithm model is proposed,which is a Deep Orthogonal Non-negative Matrix Factorization.Experiments on clustering performance on CMU-PIE,JAFFE and YALE datasets show that: Compared with Non-Negative Matrix Factorization,Semi-Nonnegative Matrix Factorization,Graph Regularization Non-negative Matrix Factorization,Deep Semi-Nonnegative Matrix Factorization and Orthogonal Nonnegative Matrix Factorization,Deep Orthogonal Non-Negative Matrix Factorization has better clustering perform ance,and can extract deep features of complex data.2.The hierarchical alternating least square method is proposed to optimize the deep model.The traditional Orthogonal Non-negative Matrix Factorization imposes strict orthogonal constraints,which decompose the data matrix into a base matrix and a coefficient matrix.The resulting coefficient matrix can not be guaranteed to be orthogonal.However,in practice,whether a sample belongs to a class has a ce rtain degree of membership.Therefore,this paper adopts an Approximate Orthogonal Non-negative Matrix Factorization with controllable orthogonality.The Approximate Orthogonal Nonnegative Matrix Factorization is efficient,and it can also ensure that the coefficient matrix after decomposition is approximately orthogonal,which provides good conditions for further research,and initializes and updates the iteration by the iterative algorithm of Approximate Orthogonal Non-negative Matrix Factorization,thus building a deep network structure.Experiments on clustering performance on CMU-PIE,JAFFE and YALE datasets show that: Compared with Nonnegative Matrix Factorization,Semi-nonnegative Matrix Factorization and Graph Regularization Non-negative Matrix Factorization,the Approximate Orthogonal Nonnegative Matrix Factorization has better clustering performance.