Non-negative Matrix Factorization Algorithm And Its Application

Non-negative matrix factorization algorithm is an effective method for feature extraction and low-dimensional representation.The decomposition process and the decomposition result are interpretable.It can be solved quickly by multiplicative iterative rules.Therefore,it has a wide range of applications in feature extraction,classification,and clustering tasks.Different from the global features extracted by algorithms such as PCA and LDA,the NMF algorithm extracts local features,which can be interpreted as the original data is a pure additive combination of all local features.This decomposition characteristic is more in line with the cognitive way of human vision.With the deepening of the research on NMF algorithm,experts and scholars reasonably apply the NMF algorithm to different scenarios by analyzing the underlying data structure in specific scenarios.The NMF algorithm has three important improvements:The first is to add additional constraints or penalties to the objective function in order to improve performance in classification and clustering tasks,such as sparseness constraints,orthogonality constraints,graph regularization constraints,etc.The second is to rewrite the decomposition form,such as expanding the single-layer matrix decomposition to a multi-layer matrix decomposition,which can obtain richer hierarchical structure features.The third is to combine the non-negative constraints with other algorithms,which is an effective way to improve the performance of the algorithm.This paper studies non-negative matrix factorization algorithms in feature extraction and low-dimensional representation.Two effective NMF algorithms are proposed to improve the performance of image classification and clustering tasks.The main work of this article is as follows:?1?A graph regularization sparse discriminant non-negative matrix factorization algorithm was proposed.The label information is introduced to extend the unsupervised NMF algorithm into a supervised NMF algorithm in order to improve the discriminative performance of the algorithm;Combining graph regularization constraints and maximum margin criteria to extract effective local features;Combining sparsity constraints for effective feature selection.Different constraint terms play different roles,and the constraint terms can complement each other.A proper combination of different constraint terms can get better results in specific problems.?2?A self-paced learning based graph regularization non-smooth non-negative matrix factorization algorithm was proposed.Replacing the objective function represented by Euclidean distance with the objective function with L_2,1 norm to improve the robustness to noise data;Introducing a smoothing factor matrix to improve the sparseness of the two sub-matrixes after decomposition;Self-paced learning is used as a special dropout method to reduce the interaction between the base features and obtain a more stable decomposition result.This paper gives the basic model and the optimization method of the algorithms,and performs image classification and clustering experiments on ORL,AR,COIL20 datasets and noise-added datasets.Experiments show that the two improved NMF algorithms proposed in this paper are effective in feature extraction and low-dimensional representation.