S-HOT: Scalable High-Order Tucker Decomposition

Abstract

Multi-aspect data appear frequently in many web-related applications. For example, product reviews are quadruplets of (user, product, keyword, timestamp). How can we analyze such web-scale multi-aspect data? Can we analyze them on an off-the-shelf workstation with limited amount of memory? Tucker decomposition has been widely used for discovering patterns in relationships among entities in multi-aspect data, naturally expressed as high-order tensors. However, existing algorithms for Tucker decomposition have limited scalability, and especially, fail to decompose high-order tensors since they explicitly materialize intermediate data, whose size rapidly grows as the order increases (≥ 4). We call this problem M-Bottleneck ("Materialization Bottleneck"). To avoid M-Bottleneck, we propose S-HOT, a scalable high-order tucker decomposition method that employs the on-the-fly computation to minimize the materialized intermediate data. Moreover, S-HOT is designed for handling disk-resident tensors, too large to fit in memory, without loading them all in memory at once. We provide theoretical analysis on the amount of memory space and the number of scans of data required by S-HOT. In our experiments, S-HOT showed better scalability not only with the order but also with the dimensionality and the rank than baseline methods. In particular, S-HOT decomposed tensors 1000× larger than baseline methods in terms dimensionality. S- HOT also successfully analyzed real-world tensors that are both large-scale and high-order on an off-the-shelf workstation with limited amount of memory, while baseline methods failed. The source code of S-HOT is publicly available at http://dm.postech.ac.kr/shot to encourage reproducibility.