Fast, Accurate, and Scalable Method for Sparse Coupled Matrix-Tensor Factorization

How can we capture the hidden properties from a tensor and a matrix data simultaneously? Coupled matrix-tensor factorization (CMTF) is an e‚ective method to solve this problem because it extracts latent factors from a tensor and matrices at once. Designing an ecient CMTF has become more crucial as the size and dimension of real-world data are growing explosively. However, existing methods for CMTF su‚er from two problems: 1) methods for dense data are not applicable to sparse real-world data, and 2) methods based on CANDECOMP/PARAFAC (CP) decomposition su‚er from high test error because they do not capture correlations between all factors. In this paper, we propose S3CMTF, a fast, accurate, and scalable CMTF method. S3CMTF achieves high speed by exploiting the sparsity of real-world tensors, and high accuracy by capturing interrelations between factors. Also, S3CMTF accomplishes additional speed-up by lock-free parallel SGD update for multi-core shared memory systems. We present two methods, S3CMTF-naive and S3CMTF-opt. S3CMTF-naive is a basic version of S3CMTF, and S3CMTF-opt improves its speed by exploiting intermediate data. We theoretically and empirically show that S3CMTF is the fastest, outperforming existing methods. Experimental results show that S3CMTF is 11∼43× faster and 2.1∼4.1×more accurate than existing methods. S3CMTF shows linear scalability on the number of data entries and the number of cores. In addition, we apply S3CMTF to Yelp dataset with a 3-mode tensor coupled with 3 additional matrices to discover interesting paŠerns.