S3CMTF: Fast, accurate, and scalable method for incomplete coupled matrix-tensor factorization

Abstract

How can we extract hidden relations from a tensor and a matrix data simultaneously in a fast, accurate, and scalable way? Coupled matrix-tensor factorization ( CMTF) is an important tool for this purpose. Designing an accurate and efficient CMTF method has become more crucial as the size and dimension of real-world data are growing explosively. However, existing methods for CMTF suffer from lack of accuracy, slow running time, and limited scalability. In this paper, we propose (SCMTF)-C-3, a fast, accurate, and scalable CMTF method. In contrast to previous methods which do not handle large sparse tensors and are not parallelizable, (SCMTF)-C-3 provides parallel sparse CMTF by carefully deriving gradient update rules. (SCMTF)-C-3 asynchronously updates partial gradients without expensive locking. We show that our method is guaranteed to converge to a quality solution theoretically and empirically. (SCMTF)-C-3 further boosts the performance by carefully storing intermediate computation and reusing them. We theoretically and empirically show that (SCMTF)-C-3 is the fastest, outperforming existing methods. Experimental results show that (SCMTF)-C-3 is up to 930x faster than existing methods while providing the best accuracy. (SCMTF)-C-3 shows linear scalability on the number of data entries and the number of cores. In addition, we apply (SCMTF)-C-3 to Yelp rating tensor data coupled with 3 additional matrices to discover interesting patterns.