A dynamic hypergraph regularized non-negative tucker decomposition framework for multiway data analysis

Zhenhao Huang, Guoxu Zhou, Yuning Qiu, Yuyuan Yu, Haolei Dai

Abstract: Non-negative tensor decomposition has achieved significant success in machine learning due to its superiority in extracting the non-negative parts-based features and physically meaningful latent components from high-order data. To improve its representation ability, hypergraph has been incorporated into the tensor decomposition model to capture the nonlinear manifold structure of data. However, previous hypergraph regularized tensor decomposition methods rely on the original data space. This may result in inaccurate manifold structure and representation performance degeneration when original data suffer from noise corruption. To solve these problems, in this paper, we propose a dynamic hypergraph regularized non-negative Tucker decomposition (DHNTD) method for multiway data analysis. Specifically, to take full advantage of the multilinear structure and nonlinear manifold of tensor data, we learn the dynamic hypergraph and non-negative low-dimensional representation in a unified framework. Moreover, we develop a multiplicative update (MU) algorithm to solve our optimization problem and theoretically prove its convergence. Experimental results in clustering tasks using six image datasets demonstrate the superiority of our proposed method compared with the state-of-the-art methods.