Parallel Candecomp/Parafac Decomposition of Sparse Tensors Using Dimension Trees

International audienceTensor factorization has been increasingly used to address various problems in many fields such as signal processing, data compression, computer vision, and computational data analysis. CANDECOMP/PARAFAC~(CP) decomposition of sparse tensors has successfully been applied to many well-known problems in web search, graph analytics, recommender systems, health care data analytics, and many other domains. In these applications, computing the CP decomposition of sparse tensors efficiently is essential in order to be able to process and analyze data of massive scale. For this purpose, we investigate an efficient computation and parallelization of the CP decomposition for sparse tensors. We provide a novel computational scheme for reducing the cost of a core operation in computing the CP decomposition with the traditional alternating least squares (CP-ALS) based algorithm. We then effectively parallelize this computational scheme in the context of CP-ALS in shared and distributed memory environments, and propose data and task distribution models for better scalability. We implement parallel CP-ALS algorithms and compare our implementations with an efficient tensor factorization library, using tensors formed from real-world and synthetic datasets. With our algorithmic contributions and implementations, we report up to 3.95x, 3.47x, and 3.9x speedups in sequential, shared memory parallel, and distributed memory parallel executions over the state of the art, and up to 1466x overall speedup over the sequential execution using 4096 cores on an IBM BlueGene/Q supercomputer

Algorithms for Large-Scale Sparse Tensor Factorization

University of Minnesota Ph.D. dissertation. April 2019. Major: Computer Science. Advisor: George Karypis. 1 computer file (PDF); xiv, 153 pages.Tensor factorization is a technique for analyzing data that features interactions of data along three or more axes, or modes. Many fields such as retail, health analytics, and cybersecurity utilize tensor factorization to gain useful insights and make better decisions. The tensors that arise in these domains are increasingly large, sparse, and high dimensional. Factoring these tensors is computationally expensive, if not infeasible. The ubiquity of multi-core processors and large-scale clusters motivates the development of scalable parallel algorithms to facilitate these computations. However, sparse tensor factorizations often achieve only a small fraction of potential performance due to challenges including data-dependent parallelism and memory accesses, high memory consumption, and frequent fine-grained synchronizations among compute cores. This thesis presents a collection of algorithms for factoring sparse tensors on modern parallel architectures. This work is focused on developing algorithms that are scalable while being memory- and operation-efficient. We address a number of challenges across various forms of tensor factorizations and emphasize results on large, real-world datasets