Data Matrix Completion And Application Based On Spectral Regularization Algorithm

In the matrix completion problem, we will predict the unknown informationaccording to the information we have known about the matrix. The most important thing isto establish a suitable target model. According to the different models, different solutionsare put forward. Based on the traditional regularization model, spectral regularizationalgorithm is proposed. The algorithm works well. But due to its high computationalcomplexity, we combine Maximum-Margin Matrix Factorization and non-negative matrixfactorization and propose an improved regularization algorithm, and this methodeffectively reduces the computational complexity.Firstly, this paper studies the matrix completion based on non-negative matrixfactorization.The experiment of voice bandwidth expansion introduce the regularizationmodel in details and present the process of the model. And present algorithm based on thenon-negative matrix factorization and sigular value decomposition to spread the highfrequency of the voice signal. Experiments compared with the traditional the non-negativematrix factorization and sigular value decomposition, this method prove its feasibility.Secondly, this paper studies the matrix completion based on spectral regularizationmatrix. According to the regularization model state a spectral regularization algorithm, atthe same time state Hardimpute algorithm for the data of different condition, and then sortout a comprehensive broad spectrum regularization of different model and algorithm.Finally applied to the Netflix data sets, and got a satisfactory result. But the computationalcomplexity of this method is high, it need to be improved.Finally, this paper studies the matrix completion based on the improved spectralregularization algorithm. Due to the difficult calculation of spectral regularization algorith,we combine Maximum-Margin Matrix Factorization and spectral regularization algorithm,and put forward the improved spectral regularization algorithm. It solved the bottleneckproblem of computing, and got a better solution.