A C-eigenvalue problem for tensors with applications to higher-order multivariate Markov chains. (1st August 2019)

• Record Type: Journal Article
• Authors: Li, Wen; Ke, Rihuan; Ching, Wai-Ki; Ng, Michael K.
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 3(2019)
• Page Start: 1008
• Page End: 1025
• Publication Date: 2019-08-01
• Subjects: Eigenpair -- Tensor -- Higher-order -- Multivariate -- Markov chain -- Stationary probability distribution; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.03.016
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we study a new tensor eigenvalue problem, which involves E - and S -eigenvalues as its special cases. Some theoretical results such as existence of an eigenvalue and the number of eigenvalues are given. For an application of the proposed eigenvalue problem, we establish a tensor model for a higher-order multivariate Markov chain. The core issue of this problem is to study a stationary probability distribution of a higher-order multivariate Markov chain. A sufficient condition of the unique stationary positive distribution is given. An algorithm for computing stationary probability distribution is also developed. Numerical examples of applications in stock market modeling, sales demand prediction and biological sequence analysis are given to illustrate the proposed tensor model and the computed stationary probability distribution can provide a better prediction in these Markov chain applications.