Adaptive graph regularized non-negative Tucker decomposition for multiway dimensionality reduction

Dai Chen, Guoxu Zhou, Yuning Qiu, Yuyuan Yu

Abstract: Non-negative Tucker decomposition (NTD) is a powerful tool for data representation to capture rich internal structure information from non-negative high-dimensional tensor data. Arguing that NTD methods often give global-like information, graph constraint has been introduced to capture the important local nonlinear structure of data. However, existing methods generally use fixed graphs and lack the ability to adaptively learn the optimal graph that best benefits the learning task at hand. In this paper, we propose an Adaptive Graph Regularized Non-negative Tucker Decomposition (AGRNTD) model. Not only is the new model able to capture the global multilinear structure of tensor data, but also it adaptively learns the optimal graph to capture local manifold information. An updating rule is designed to optimize the new model with the guarantee of local convergence. By mapping and visualizing the features, our method exhibits better feature extraction compared with other algorithms. The clustering results on five real-world datasets demonstrate the effectiveness and robustness of our method.