Study On Fuzzy Clustering Algorithm Based On Mixture Of Matrix Normal Distributions Model

Clustering analysis is an important part of non-supervised pattern classification in pattern recognition,it aims to handle classification problem by mathematical methods,and has been widely used as a tool for Knowledge Discover and Data Mining(KDD).Clustering analysis has been developed drastically in the recent 20 years,fuzzy clustering algorithm which can describe and analyze the uncertain relation more accurately has become the focus of research these years.The mainstream of practical research and application is fuzzy clustering algorithm based on objective function method,this method the problem of clustering are expressed as an optimization problem with constraints,through the optimization of concrete ways of solution to determine the division of data set and the clustering results.Acting on this kind of algorithm design is simple and easy application has good clustering effect,and by using mathematical theory to arrive at the solution of optimization problem of nonlinear programming,easy to programming implementation process.Among the various fuzzy clustering algorithms,fuzzy c-means(FCM)clustering algorithm with the characteristics of high efficiency,strong data adaptability and simpleness make it one of the most studied and frequently-used cluster analysis algorithms.Finite mixture models provide a particularly suitable method for clustering data coming from different sub-populations,for continuous observed variables,finite mixtures of normals have been widely investigated and applied in many situations,under the framework of model-based clustering.Matrix-variate distributions represent a natural way for modeling random matrices.Realizations from random matrices are generated by the simultaneous observation of variables in different situations or locations,and are commonly arranged in three-way data structures.Among the matrix-variate distributions,the matrix normal density plays the same pivotal role as the multivariate normal distribution in the family of multivariate distributions.In this work we have sorted out and reviewed the essential properties of the fuzzy clustering model and the matrix-variate distribution,and the understanding and exploration of them by scholars.Giving a detailed introduction on fuzzy clustering based objective function,especially the fuzzy c-means clustering algorithm,and the concept of information entropy regularization is introduced.We define and explore matrix-variate distribution,and the fuzzy clustering algorithm based on finite mixtures of matrix normals has been improved,and the maximum likelihood estimation and the expectation-maximization algorithm are introduced in the parameter estimation of the model.We Finally use several algorithms to cluster the matrix handwritten data sets.In this paper,the influence of parameters on fuzzy algorithm and the performance of different algorithms on this data set are compared,and demonstrate that the improved fuzzy c-mean algorithm based on K-L information entropy regularization and finite mixtures of matrix normals model has better clustering effect.