Fast and Accurate PARAFAC2 Decomposition for Time Range Queries on Irregular Tensors

Jun-Gi Jang, Yong-chan Park, U Kang

Abstract: How can we efficiently analyze a specific time range on an irregular tensor? PARAFAC2 decomposition is widely used when analyzing an irregular tensor which consists of several matrices with different row sizes. A crucial task related to PARAFAC2 decomposition is to analyze sub-tensors corresponding to various time ranges of a given tensor, instead of analyzing the entire tensor. Although many recent works have developed efficient PARAFAC2 decomposition methods, existing PARAFAC2 decomposition methods are inappropriate for addressing various time range queries, as they need to decompose sub-tensors from scratch.In this paper, we propose Repeat, a fast and accurate PARAFAC2 decomposition method for handling arbitrary time range queries on irregular tensors. To avoid decomposing sub-tensors of queries from scratch, Repeat obtains preprocessed results that support efficient query answering before time ranges are given. For time range queries, Repeat efficiently computes the PARAFAC2 decomposition for the sub-tensors corresponding to the queries by using preprocessed results rather than the original irregular tensor. We experimentally demonstrate that Repeat outperforms existing PARAFAC2 methods, providing up to 12x faster speed while having comparable errors. We also present a case study for the use of Repeat in detecting locally appearing patterns through a variety of time range queries.