The Application Research Of Nonnegative Matrix Factorization For Unsupervised Image Clustering

With the development of the Internet and the multimedia technology,we are in the age of“big data”and lots of unlabeled high dimension data are produced.How to handle and cluster these high dimension data to extract the useful information is a challenging problem.In the problem of clustering the high dimension data the matrix factorization method is effective.For the pictures,because of theirs nonnegativity,the nonnegative matrix factorization(NMF)is extremely appropriate to handle and cluster these picture data.In this paper we present three improved algorithms based the NMF algorithm for the image clustering problem.First,the gathering condition of each picture may be different which can cause the quality of each picture is imparity.The pre-treatment is used before the factorization to improve pictures'quality.The pre-treatment is consist of two parts.The first stage is grayscale normalization to eliminate the influence of the different condition.The second stage is the wavelet analysis which can extract the low-sequence subpicture.After the pre-treatment,the hypergraph is established to save the connections between the multiple data while the simple graph just can keep the connections between two samples.The hypergraph Laplace matrix can save this trait of hypergraph.Basing above,the nonnegative matrix factorization with hypergraph based on pre-treatments(PHGNMF)is presented.Second,the nearest neighbor graph is constructed after the grayscale normalization.Basing the assumption that two samples which are close in the original space may be in the same cluster,we can have tough partitions from the nearest neighbor graph.The credible partitions from the tough partitions are chosen to form a new regularization to guide the factorization.So,we propose the nonnegative matrix factorization with the nearest neighbor after per-treatments(PNNMF).Third,the structure information of original data has important impacts on the clustering results.A new regularization is proposed to save the global structure.The graph regularization is used to keep the local structure.Combining these two regularizations can reduce the loss of the original structure information.The calculation of global structure is the cosine measure which can avoid the disadvantage of Euclidean distance.The constrains that l₂ norm equals one is added in the model to simplify the calculation of cosine measure.Then we present the nonnegative matrix factorization under structure constrains(SNMF).Above three algorithms are solved by the iterative methods and the corresponding experiment results show the effectiveness.