Manifold Regularized Matrix Factorization With Constrains And Its Applications In Image Clustering

With the development of the Internet and the popularity of smart phones,we can obtain and access more and more image data.Image data has a striking feature that it is always in a high dimension.Greatly convenient at the same time,we are also faced with the problem that how to effectively analyze and deal with the mass data.Image clustering technology has been widely applied in the high dimensional image data,it clusters image data of high similarity into a cluster,while divides images with low similarity into different clusters.In recent years,the non-negative matrix factorization(NMF)technology has been proved to be an effective dimensionality reduction method,and has been widely used in computer vision,pattern recognition and information retrieval.NMF,however,is actually an unsupervised method,it can't use prior information of data to improve the accuracy of clustering.In this paper,based on the research of manifold learning,we present a semi-supervised non-negative matrix factorization method based on manifold regularization,which not only employs the geometry information of data but also appropriately uses the prior label information to enhance the accuracy of NMF.Specifically,we expect a manifold regularization term can preserve the local structure of the original data,meanwhile,in the low-dimensional space,data points with the same label will be clustered into the same cluster,while data points possessing different labels should be divided into different clusters.As a result,after the dimensionality reduction,the learned representations will have more discriminating power.We apply this method in image clustering,using two metrics to measure the performance.The experimental results manifest the effectiveness of our algorithm.