Research On Clustering Algorithms Based On Non-negative Matrix Factorization

Non-negative matrix factorization(NMF)is a novel dimension reduction paradigm in recent years,which has the ability to help people discover and extract critical core features and information from complex data samples with high dimension.NMF can be used in various applications such as pattern recognition,multimedia data analysis,signal processing,and computer vision and so on.On the feature analysis of image,due to the pure additive properties brought by non-negativity,NMF is able to extract the local features of images,so as to construct an abstraction that entireties are constituted by local components,which is very accord with human intuitive visual perception.With the progress of the nonnegative matrix factorization research,not only all kinds of acceleration and decomposition optimized algorithms have been proposed,but a growing number of derivative factorization paradigms based on NMF model have also attracted the attentions of many researchers.Because the potential cluster representations of NMF,researchers has discover the relationship between it and traditional spectral clustering or K-means clustering.After that,many clustering algorithms based on NMF are presented.These new paradigms of factorization and algorithms not only extended the range of application of NMF,but also improve its performance on unsupervised clustering.The first work of this paper is that presenting an accelerated factorized fuzzy cluster algorithm by using a non-monotone accelerated proximal gradient method(nmAPG),based on the framework of Factorized fuzzy c-means(F-FCM).In the meantime,we also present an efficient greedy algorithm to solve the proximal mapping problem of the domain indicator function while implementing nmAPG.The second work of this paper is that presenting a novel paradigms of matrix factorization called Fuzzy Cluster-NMF,which is also a fuzzy cluster algorithm based on NMF.Compared to Cluster-NMF,Fuzzy Cluster-NMF bring a more restrictive condition to the coefficient matrix in NMF to binds the basis matrix and coefficient matrix together,which removes the extra degree of freedom for the basis matrix and makes the decomposition factors are characterized by clustering center and membership degree.In this paper,the derivation of the objective function gradient of Fuzzy Cluster-NMF is given,and its convergence speed is accelerated by using the nmAPG algorithm with line search.From the numerical experimental comparison provided,we verified the effect of the algorithm AF-FCM and Fuzzy Cluster-NMF.It shows that AF-FCM greatly improves the convergence speed of F-FCM while ensuring the original clustering performance and Fuzzy Cluster-NMF not only relatively has better clustering accuracy,but has high robustness as well.