Research And Application Of Dimension Reduction Method Based On Non-negative Matrix Factorization

In the era of big data,data is presented with the characteristics of high dimensionality,mixed knowledge system and large amount of data,which brings great challenges to data-based research.Dimension reduction is to extract knowledge from high-dimensional data,form organization,and discover intrinsic laws,thus reducing redundancy,enhancing characteristic value density,and improving subsequent calculation efficiency.Non-negative matrix factorization(NMF),as a non-linear and non-negative constraint matrix factorization dimensionality reduction method,is widely used in face recognition,blind source separation,time sequence segmentation and other fields due to its advantages such as interpretability,simple computation and large-scale data processing.However,there are still problems such as easy to be interfered by noise and ignoring high-dimensional sparse characteristics.In view of the existing problems of NMF algorithm,this topic will put forward corresponding solutions.The work of this paper is summarized as follows:(1)Aiming at the imbalance between the stability and sparsity of non-negative matrix factorization,a local regularized non-negative matrix factorization based on elastic network is proposed.In order to improve the generalization ability of the algorithm,the regularization term of elastic network is used to balance the stability and sparsity.Local linear embedding algorithm is used to retain the local linear of high-dimensional structure and enhance local features.The effectiveness of the proposed algorithm is proved by the comparative experiments on real datasets.(2)To solve the problem of poor robustness of NMF algorithm to noise,a weighted sparse graph non-negative matrix factorization based on L21-norm is proposed.The L21-norm is used as the metric criterion to improve the robustness of the algorithm.The sparse weighted graph is used to preserve the high-dimensional structure to ensure the smooth sparsity of the high-dimensional space.The original data is decomposed into the product of two non-negative matrices and the sum of noise terms,which approximates the real model.The robustness and effectiveness of the proposed algorithm are verified by comparing several groups of experiments on the noise-adding datasets.(3)Considering that the non-negative matrix factorization algorithm is easily affected by noise and outliers,a robust non-negative matrix factorization algorithm based on sparse constraint graph is proposed.The sparse constraint graph regularization term of the proposed method uses multiple measures to enhance the high-dimensional reconstruction effect.Meanwhile,high-dimension sparse constraints are directly utilized in the nonlinear reconstruction process to make the high-dimensional structure more clear and intuitive.The L2p-norm is used as the metric criterion to construct the model,which not only controls the sparsity of the global low-dimensional subspace,but also reduces the influence of noise on the algorithm performance.Experiments on several databases show that the classification accuracy and clustering effect are improved,and the effectiveness of the proposed algorithm is verified.