Research On Nonnegative Matrix Factorization Algorithm Based On Orthogonal Factor

Nonnegative matrix factorization focuses on methods and strategies for factoring a given non-negative matrix into products of two nonnegative matrixs.Nonnegative matrix factorization has advantages of simple form,good interpretability and less storage space,so it has great potential and research value in the field of data science.In this paper,the process of non-negative matrix factor-ization is described geometrically and the key concepts of nonnegative matrix decomposition are defined as orthogonal factor and scaling factor.Analysis shows that the orthogonal factor based matrix factorization algorithm can be effectively used to solve the nonnegative decomposition of these matrices for some nonnegative matrices satisfying certain conditions.Compared with tra-ditional projection non-negative decomposition methods,the new method obtains a non-negative decomposition by searching suitable orthogonal factors,which greatly reduces the computational complexity of each iteration.We also analyze how the initial value of the orthogonal factor affect the performance of the algorithm and provide a strategy of choosing the best initial value.Finally,we evaluate the performance of the new algorithm by numerical experiments.Experiments show that the new algorithm has better performance in terms of computing speed and accuracy.