Fast and memory-efficient algorithms for high-order Tucker decomposition

摘要

Multi-aspect data appear frequently in web-related applications. For example, product reviews are quadruplets of the form (user, product, keyword, timestamp), and search-engine logs are quadruplets of the form (user, keyword, location, timestamp). How can we analyze such web-scale multi-aspect data on an off-the-shelf workstation with a limited amount of memory? Tucker decomposition has been used widely for discovering patterns in such multi-aspect data, which are naturally expressed as large but sparse tensors. However, existing Tucker decomposition algorithms have limited scalability, failing to decompose large-scale high-order (\(\ge \) 4) tensors, since they explicitly materialize intermediate data, whose size grows exponentially with the order. To address this problem, which we call “Materialization Bottleneck,” we propose S-HOT, a scalable algorithm for high-order Tucker decomposition. S-HOT minimizes materialized intermediate data by using an on-the-fly computation, and it is optimized for disk-resident tensors that are too large to fit in memory. We theoretically analyze the amount of memory and the number of data scans required by S-HOT. Moreover, we empirically show that S-HOT handles tensors with higher order, dimensionality, and rank than baselines. For example, S-HOT successfully decomposes a real-world tensor from the Microsoft Academic Graph on an off-the-shelf workstation, while all baselines fail. Especially, in terms of dimensionality, S-HOT decomposes 1000 \(\times \) larger tensors than baselines.