Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries

TL;DR

This paper introduces P-Tucker, a scalable and accurate Tucker factorization method for sparse tensors, enabling efficient discovery of latent features in large-scale multi-dimensional data.

Contribution

The paper presents P-Tucker, a novel parallelized Tucker factorization algorithm with variants that improve speed and accuracy for sparse tensor data.

Findings

P-Tucker achieves 1.7-14.1x speed-up over state-of-the-art methods.

P-Tucker reduces error by 1.4-4.8x compared to existing algorithms.

P-Tucker scales near linearly with data size and computational resources.

Abstract

Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems with multi-dimensional data, which are modeled as tensors. However, most Tucker factorization algorithms regard and estimate missing entries as zeros, which triggers a highly inaccurate decomposition. Moreover, few methods focusing on an accuracy exhibit limited scalability since they require huge memory and heavy computational costs while updating factor matrices. In this paper, we propose P-Tucker, a scalable Tucker factorization method for sparse tensors. P-Tucker performs alternating least squares with a row-wise update rule in a fully parallel way, which significantly reduces memory requirements for updating factor matrices. Furthermore, we offer two variants of P-Tucker: a caching algorithm P-Tucker-Cache and an approximation algorithm P-Tucker-Approx, both of which accelerate the update process. Experimental results show that P-Tucker exhibits 1.7-14.1x speed-up and 1.4-4.8x less error compared to the state-of-the-art. In addition, P-Tucker scales near linearly with the number of observable entries in a tensor and number of threads. Thanks to P-Tucker, we successfully discover hidden concepts and relations in a large-scale real-world tensor, while existing methods cannot reveal latent features due to their limited scalability or low accuracy.