Online Nonnegative Matrix Factorization Algorithm And Its Application

Nonnegative matrix factorization is a tool for feature extraction.It can extract local feature matrices of high-dimensional data quickly.Although nonnegative matrix factorization has been applied to various fields,it can only process data in batches at single time,and it can not process data quickly when the data changes frequently.With the diversification and complexity of data,the data in real life has been changing dramatically from time to time.With the diversification and complexity of data,the data in real life has changed greatly from time to time.Obviously,non-negative matrix factorization is not suitable for processing this type of data,so it need an online feature extraction method.This paper lists the classical nonnegative matrix factorization and its recent improved algorithms,and proposes a new online nonnegative matrix factorization method.In this paper,the nonnegative matrix factorization algorithm will be introduced in detail.Firstly,this paper describes the research status of this subject at home and abroad in detail,and elaborates the background significance in detail.Secondly,In this paper,various improved batch-processing nonnegative matrix factorization algorithms are introduced,and the mathematical expressions,characteristics and purposes of each algorithm are described in detail.The disadvantages of batch-processing nonnegative matrix factorization are pointed out;thirdly,this paper points out the shortcomings of traditional nonnegative matrix factorization,and introduces various improved batch-processing non-negative matrix factorization algorithms in detail.The mathematical expressions,characteristics and purposes of each algorithm are in troduced in detail.Finally,aiming at the problem that non-negative matrix factorization in batch processing is not suitable for real-time updating of data streams,incremental nonnegative matrix factorization is proposed.Various online nonnegative matrix factorization algorithms are listed,and the process of converting the algorithm from batch processing to online form is introduced in detail.The main research content of this paper is to propose an online learning nonnegative matrix factorization.In the model of nonsmooth nonnegative matrix factorization algorithm,incremental learning is introduced,and its iteration update formula is deduced by using selective forgett ing method.Online learning nonnegative matrix factorization algorithm can process data online.Because the algorithm only needs to process the new data for each iteration update,it can extract a new base matrix,which greatly reduces the computational complexity of iteration update.The algorithm can get the matrix with high sparseness.In the experimental part,first prove the convergence and stability of the algorithm;then,compare the sparseness of the base matrix with other three online forms of NMF using two face data sets and one random data set.The experimental results show that the base matrix extracted by online learning nonnegative matrix factorization algorithm has the highest sparsity.Finally,we use EEG data sets to classify the left and right brain signals of four online processing forms of NMF algorithm.The experimental results show that the classification accuracy of online learning nonnegative matrix factorization algorithm is the best,but the time is not dominant.