Matrix Factorization Learning And Its Application In Network Community Detection

Matrix Factorization Learning is one of the most widely used method in Machine Learning,and its main goal is to express the original data matrix renewedly as the product form of two or more low rank matrix.After decomposition process,the matrix ranks are far less than the original matrix rank,and we may fulfill classification or clustering task from low dimensional matrix.Matrix factorization is an efficient way to find hidden potential factors or missing values in prediction matrix by decomposing compact data into different matrix.In recent years,more and more researchers have paid attention to matrix factorization learning methods.In task of network community detection,all network structure can be represented by the diagram,and we can describe the diagram with its adjacency matrix.Therefore,application of matrix factorization learning method can effectively aggregate the nodes from whole network into different communities,and achieves good experimental results.This article will systematically introduce existing methods of matrix factorization learning and network community detection.According to character of network data,such as less supervision,overlapping effect and network data practical problems,we put forward semi-supervised symmetric nonnegative matrix factorization algorithm and bayesian symmetric nonnegative matrix factorization algorithm,and apply two algorithms in social network and scientific network data.Comparing with relevant community detection methods,our algorithms obtain good experiment and application effects.The main contributions and innovations of this paper are listed in the following aspects:1.Semi-supervised symmetric non-negative matrix factorization algorithm.Generally,matrix factorization is an unsupervised method,but there always exists Ground-truth data in a large number of social network data,and network data matrix is usually symmetric.In this paper,a semi-supervised symmetric non-negative matrix factorization algorithm based on pairwise constraints is proposed.Compared with other matrix factorization learning algorithms,our proposed algorithm has achieved good results in community detection application of different network data types.2.Bayesian symmetric non-negative matrix factorization algorithm.In this paper,we research the bayesian inference process model with poisson prior and gaussian prior,and propose a bayesian symmetric non-negative matrix factorization learning algorithm.We also derive the updating rules of the model and verify it in experiment.Compared with other community detection algorithms,the proposed algorithm achieves better experimental results in different data sets.3.Research on automatic relevant determination method of community number in community detection process.In general,matrix factorization learning method cannot obtain the decomposition dimension information directly.In bayesian inference process of symmetric nonnegative matrix we proposed,we combine semi-normal distribution to help dimensional sparse compression,and predict the number of communities effectively.Comparing the detection results of different initial community ranks,we solve the problem that the initial communities number could not be given in real community detection.4.Overlapping community detection.Through the analysis of network data,we select appropriate value related to network density as the overlapping threshold of the mixed coefficient matrix in bayesian symmetric non-negative matrix factorization processing,and effectively obtain overlapping network communities.Finally,we conclude the matrix factorization method and theory in community detection,and analysis for demand from libraries,such as scientific community detection problem,author name disambiguation requirement in instituional scholarly output data center,and digital humanities practical application.We effectively solve all these problems with matrix factorization learning algorithm we proposed,and realize certain application achievements in specific practical field.