Research On Robust Non-negative Matrix Factorization Algorithm

With the development of sensing technology and computer hardware technology,there are various ways for humans to obtain different types of data,and more and more raw data are available.We have entered the era of big data.It is important to extract hidden,low-dimensional information that reflects the essential characteristics of data from massive,highdimensional,and unrelated data.This can help humans to optimize business processes and operational efficiency,improve products and services,and also can provide better insight and decision support,promote innovation and development.Therefore,the research of dimensionality reduction algorithm has become a key point in the era of big data,and also a research hotspot in recent years.As a kind of dimensionality reduction technique with good explanatory,non-negative matrix factorization(NMF)is widely used in many research fields,such as biomedical engineering,signal processing,pattern recognition,data mining,computer vision,and so on.Based on the idea of NMF,in this paper we propose two NMF models to explore the essential characteristics of data.The two models are as follows:Firstly,a manifold regularized non-negative matrix factorization based on clean data(MRNMF/CD)algorithm is proposed.In order to enhance the robustness of the algorithm,the low-rank constraint,manifold regularization and non-negative matrix factorization techniques are seamlessly integrated in one model to make the algorithm perform better.In the first,we process and purify the noise data to obtain clean data with low-rank constraint algorism,and obtain the global structure of the data,thus making the algorithm more robust.In the meantime,we integrate the manifold regularization into the objective function to obtain the geometric structure information.So,we finally get the low-dimensional essential information of the data.The five algorisms are compared on three data sets to show that MRNMF/CD has a good effect on improving the robustness and clustering performance.The convergence of MRNMF/CD is demonstrated through theory and experiments by the proposed iterative algorithm.Secondly,we propose robust structural concept factorization(RSCF)algorithm.Concept factorization(CF)algorithm,as an important extension of non-negative matrix factorization algorithm,has achieved good results in image processing and clustering.However,the existing CF algorithm still has some problems.Firstly,CF is an unsupervised discrimination method,which has no supervised label information.Secondly,CF algorithm is based on the Frobenius norm to define the objective function,which makes it more sensitive to noise and outliers.In addition,how CF makes use of sparsity and locality of samples.Improvements are made in the RSCF algorithm.In the RSCF algorithm,the 2,pL norm is first used to standardize the objective function,making it relatively robust to noise.Then,the label information of the sample is used by defining the diagonal structure of the block.Finally,the above two processes are consociated into a one framework,and the corresponding objective expression is designed.In addition,we propose an iterative algorithm to solve the objective function and verify its convergence.The six algorisms are compared on three data sets to show that RSCF has better performance than existing algorithms.