Research On Nonnegative Matrix Factorization Algorithm Based On Neurodynamics And Its Application In Medical Images Clustering

In the era of big data,in the face of complex high-dimensional data,it is of great practical significance to find low-dimensional representation of data through dimensionality reduction technology.Especially in the field of medical research,the initial dimension of the image is usually very high,and finding a suitable lowdimensional representation can effectively reduce the difficulty of subsequent image processing.As a popular dimension reduction algorithm,non-negative matrix factorization is a very effective method and means.The non-negative matrix factorization problem belongs to the optimization category,and the selection of the optimization method will directly affect the dimensionality reduction performance of the algorithm.As a parallel computing approach,neurodynamic optimization approach has significant advantages in solving many complex optimization problems.It is a promising research direction to use neurodynamic optimization approach to solve nonnegative matrix factorization problems.This paper mainly applies the neurodynamic theory to the research of non-negative matrix factorization algorithm,and specifically carries out the following aspects:1.The problem of solving the non-negative matrix factorization is transformed into a constrained global optimization problem,and a variant-scaling factor collaborative neurodynamic optimization approach is proposed.The approach utilizes multiple sets of variant-scaling factor type recurrent neural networks to perform localized search in the feasible domain space,so as to quickly obtain potential candidate solutions.Then,through the improved particle swarm algorithm based on wavelet mutation,the exploration space of the solution is continuously expanded,and the efficient search for the global optimal solution is realized.Through mathematical derivation,it is theoretically analyzed and proved that the algorithm converges to the global optimal solution with probability 1.The research results show that the proposed neurodynamic optimization approach can effectively solve the non-negative matrix factorization problem,and has better global search ability and solution accuracy.2.To further enhance the performance of the non-negative matrix factorization model,a graph-regularized non-negative low-rank matrix factorization model is constructed.The model is based on the standard non-negative matrix factorization model and introduces low-rank constraints,sparsity constraints,Tikhonov regularization constraints,and graph regularization constraints.A specific solution is given for the proposed model.Firstly,the low-rank structure of the matrix is extracted based on the bilateral random projection algorithm,and then the model is optimized and solved by the neurodynamic approach,and finally the factorization sub-matrix is obtained.The research results show that the proposed algorithm model can not only achieve fast convergence,but also has good feature extraction ability.3.A clustering method based on graph-regularized non-negative low-rank matrix factorization is proposed,and it is applied to the clustering of medical images.The method first uses the graph-regularized non-negative low-rank matrix factorization algorithm to reduce the dimension of the image data,and then performs cluster analysis on the low-dimensional data based on the K-means algorithm.Experiments on clustering analysis are performed on three public image datasets,and the results show that the proposed method has the best clustering performance among all the compared methods.