Solving sparse non-negative tensor equations： algorithms and applications

作     者：Xutao LI Michael K. NG 

作者机构：School of Computer Engineering Nanyang Technological University Singapore 639798 Singapore Centre for Mathematical Imaging and Vision and Department of MathematicsHong Kong Baptist University Hong Kong China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2015年第10卷第3期

页      面：649-680页

核心收录：

学科分类：08[工学] 0801[工学-力学（可授工学、理学学位）] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported in part by grants from Hong Kong Baptist University (FRG) and the Research Grant Council of Hong Kong 

主　　题：Nonnegative tensor multi-dimensional network information retrieval community iterative method multivariate polynomial equation 

摘      要：We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.