Modeling Dynamic Interactions over Tensor Streams

Many web applications, such as search engines and social network services, are continuously producing a huge number of events with a multi-order tensor form, {count;query, location, …, timestamp}, and so how can we discover important trends to enables us to forecast long-term future events? Can we interpret any relationships between events that determine the trends from multi-aspect perspectives? Real-world online activities can be composed of (1) many time-changing interactions that control trends, for example, competition/cooperation to gain user attention, as well as (2) seasonal patterns that covers trends. To model the shifting trends via interactions, namely dynamic interactions over tensor streams, in this paper, we propose a streaming algorithm, DISMO, that we designed to discover Dynamic Interactions and Seasonality in a Multi-Order tensor. Our approach has the following properties. (a) Interpretable: it incorporates interpretable non-linear differential equations in tensor factorization so that it can reveal latent interactive relationships and thus generate future events effectively; (b) Dynamic: it can be aware of shifting trends by switching multi-aspect factors while summarizing their characteristics incrementally; and (c) Automatic: it finds every factor automatically without losing forecasting accuracy. Extensive experiments on real datasets demonstrate that our algorithm extracts interpretable interactions between data attributes, while simultaneously providing improved forecasting accuracy and a great reduction in computational time.