  How can we capture the hidden properties from a tensor and a matrix data
simultaneously in a fast, accurate, and scalable way? Coupled matrix-tensor
factorization (CMTF) is a major tool to extract latent factors from a tensor
and matrices at once. 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 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
inter-relations 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
times faster, and 2.1~4.1 times 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 recommendation tensor data coupled with 3
additional matrices to discover interesting properties.

Numerical Analysis