Incremental And Randomized Nonnegative Matrix Factorizations With Variable Target Ranks

Nonnegative matrix factorization(NMF)is one of the indispensable dimensionality reduction techniques in high-dimensional data analysis.It has been widely used in document clustering,image processing,face recognition and other fields.However,NMF is computationally intensive and becomes infeasible for massive data in the era of big data.When the data or target rank increases or decreases in the NMF problem,how to quickly update the NMF solution is a very important topic.There have been a large number of researches on incremental nonnegative matrix factorization and nonnegative matrix factorization with increasing or decreasing target rank recently,but they have not considered the situation that the target rank will change at the same time as the samples are increased.In order to quickly figure out the appropriate target rank and its corresponding NMF under the condition of continuous increment,we firstly proposed the incremental nonnegative matrix factorization problem with increasing or decreasing target rank.For the problem of incremental nonnegative matrix factorization with increasing target rank,a three-stage algorithm is proposed.Moreover,in order to calculate the incremental nonnegative matrix factorization of high-dimensional large sample data with increasing target rank more quickly and efficiently,we use the randomized algorithms to further accelerate the relatively time-consuming stage of the three-stage algorithm.In addition,based on the existing nonnegative matrix factorization algorithm for increasing or decreasing target rank,we proposed a new nonnegative matrix factorization algorithm with decreasing target rank,which provides a suitable initial value by sacrificing less CPU time to further reduces iterations and more CPU time of NMF.According to our nonnegative matrix factorization algorithm with decreasing target rank,an incremental nonnegative matrix factorization algorithm with decreasing target rank is proposed.Combined with the randomized algorithm,we proposed an incremental nonnegative matrix factorization randomized algorithm with decreasing target rank.Finally,numerical experiments verify the rationality and effectiveness of the algorithm.