Continuous CP decomposition of sparse tensor streams

Abstract

Tensors with a time mode are widely used for modeling and analyzing multi-aspect data streams that grow over time. However, the main drawback of such tensors is that they can be updated only once per period, which is often a day or even a year, even if the new data arrive in real-time. This discreteness of tensors has limited their usage for real-time applications with the sparse data streams, where new data have to be immediately analyzed as they arrive. How can we analyze time-evolving multi-aspect sparse data 'continuously' using 'discrete-time' tensors? In this work, we propose SliceNStitch for the continuous tensor model and its CANDECOMP/PARAFAC (CP) decomposition, which has numerous time-critical applications, including anomaly detection and recommender systems. SliceNStitch changes the starting point of each period adaptively based on the current time and updates outputs of CP decomposition instantly as new data arrives. We show, theoretically and experimentally, that SliceNStitch is (1) Any time: updating outputs of CP decomposition immediately without having to wait until the current period ends, (2) Fast: with constant-time updates up to 464× faster than online methods, and (3) Accurate: with fitness comparable (specifically, 72-100%) to offline methods.