The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can enforce nonnegativity of the computed low-rank factors. The principal task is to parallelize the matricized-tensor times Khatri-Rao product (MTTKRP) bottleneck subcomputation. The algorithm is computation efficient, using dimension trees to avoid redundant computation across MTTKRPs within the alternating method. Our approach is also communication efficient, using a data distribution and parallel algorithm across a multidimensional processor grid that can be tuned to minimize communication. We benchmark our software on synthetic as well as hyperspectral image and neuroscience dynamic functional connectivity data, demonstrating that our algorithm scales well to 100s of nodes (up to 4096 cores) and is faster and more general than the currently available parallel software.
FCNCP: A Coupled Nonnegative CANDECOMP/PARAFAC Decomposition Based on Federated Learning
School of Biomedical Engineering, Faculty of Medicine, Dalian University of Technology（大连理工大学医学院生物医学工程学院）；Key Laboratory of Integrated Circuit and Biomedical Electronic System, Liaoning Province, Dalian University of Technology（大连理工大学辽宁省集成电路与生物医学电子系统重点实验室）；Stem Cell Clinical Research Center, the First Affiliated Hospital of Dalian Medical University（大连医科大学附属第一医院干细胞临床研究中心）；Dalian Innovation Institute of Stem Cell and Precision Medicine（大连干细胞与精准医学创新研究院）；Key Laboratory of Social Computing and Cognitive Intelligence (Dalian University of Technology), Ministry of Education, China（教育部社会计算与认知智能重点实验室（大连理工大学））
Improved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correction
Graduate School of Science and Engineering（研究生院）；PAF-Karachi Institute of Economics and Technology（卡拉奇经济和技术学院）；Department of Mathematics and Operational Research（数学与运筹学系）
Randomized Algorithms for Symmetric Nonnegative Matrix Factorization
School of Computational Science and Engineering, Georgia Institute of Technology（佐治亚理工学院计算科学与工程学院）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Dept. of Computer Science, Wake Forest University（维克森林大学计算机科学系）
