Incremental Nonnegative Matrix Factorization Based On L_2,1 Sparse Constraints

In this era of rapid expansion of information a.nd data,many data information can be regarded as a high-dimensiona.l matrix,so dimension reduction of matrix had become an important field of current research.According to practical needs,scholars have proposed many methods of dimension reduction of matrix,the most typical of which is non-negat,ive matrix factorization(NMF)proposed by Lee et al.In the process of factorization,non-negative constraints are in line with the objective reality of human beings.They are widely used in data mining,image processing and so on.It has aroused t,he positive affirmation of many scholars.This paper combines the non-negative matrix factorization with the incremental learning,and then adds the sparse constraint,proposes two a.lgorithms and studies their effectiveness.The specific research contents are as follows:Firstly,using the principle of approximation in incremental non-negative matrix factorization(INMF),the decomposition results of the previous step a.re involved in the subsequent operation,,which has a good application in image recognition.In or-der to improve the effectiveness of the incremental non-negative matrix factorization algorithm and the sparse degree of the decomposed data,the factorization part of the incremental data is measured by L2,1norm,and t,he L2,1 incremental learning algo-rithm for nonnegative matrix factorization under L2,1 sparse constraints(LINMFSC)is proposed.It makes the target function have faster convergence speed in the it-erative operation and bett,er sparse degree of the decomposed data.Two image databases are used to verify the advantages of this method.Secondly,we combine robust nonnegative matrix factorization with incremental learning when the sparse constraints of coefficient matrices a.re increased.To solve the problem that the operation scale of robust nonnegative matrix factorization increases with the increase of training samples,we propose an incremental robust nonnegative matrix factorization algorithm with L2,1 sparse constraints,and give its iterative solution process.In the part,of numerical experiment,the algorithm in this section is compared with the robust non-negat,ive matrix factorization algorithm and the sparse-constrained robust non-negative matrix factorization algorithm.Through numerical verification of two kinds of face databases,the algorithm is superior to the other two algorithms in terms of operation time and sparsity of decomposed data,and has better clustering accuracy.