Tensor rank learning in CP decomposition via convolutional neural network

作     者：Zhou, Mingyi Liu, Yipeng Long, Zhen Chen, Longxi Zhu, Ce 

作者机构：Univ Elect Sci & Technol China Ctr Informat Med Ctr Robot Sch Informat & Commun Engn Xiyuan Ave 2006 Chengdu Sichuan Peoples R China 

出 版 物：《SIGNAL PROCESSING-IMAGE COMMUNICATION》 (信号处理：图像通信)

年 卷 期：2019年第73卷

页      面：12-21页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

基　　金：National Natural Science Foundation of China (NSFC) [61602091, 61571102] Fundamental Research Funds for the Central Universities [ZYGX2016J199, ZYGX2014Z003] 

主　　题：CANDECOMP/PARAFAC decomposition Convolutional neural network Deep learning Low rank tensor approximation Tensor rank estimation 

摘      要：Tensor factorization is a useful technique for capturing the high-order interactions in data analysis. One assumption of tensor decompositions is that a predefined rank should be known in advance. However, the tensor rank prediction is an NP-hard problem. The CANDECOMP/PARAFAC (CP) decomposition is a typical one. In this paper, we propose two methods based on convolutional neural network (CNN) to estimate CP tensor rank from noisy measurements. One applies CNN to the CP rank estimation directly. The other one adds a pre-decomposition for feature acquisition, which inputs rank-one components to CNN. Experimental results on synthetic and real-world datasets show the proposed methods outperforms state-of-the-art methods in terms of rank estimation accuracy.