Non-Linear Mining of Competing Local Activities

Given a large collection of time-evolving activities, such as Google search queries, which consist of d keywords/activities for m locations of duration n, how can we analyze temporal patterns and relationships among all these activities and find location-specific trends? How do we go about capturing non-linear evolutions of local activities and forecasting future patterns? For example, assume that we have the online search volume for multiple keywords, e.g., "Nokia/Nexus/Kindle" or "CNN/BBC" for 236 countries/territories, from 2004 to 2015. Our goal is to analyze a large collection of multi-evolving activities, and specifically, to answer the following questions: (a) Is there any sign of interaction/competition between two different keywords? If so, who competes with whom? (b) In which country is the competition strong? (c) Are there any seasonal/annual activities? (d) How can we automatically detect important world-wide (or local) events? We present COMPCUBE, a unifying non-linear model, which provides a compact and powerful representation of co-evolving activities; and also a novel fitting algorithm, COMPCUBE-FIT, which is parameter-free and scalable. Our method captures the following important patterns: (B)asic trends, i.e., non-linear dynamics of co-evolving activities, signs of (C)ompetition and latent interaction, e.g., Nokia vs. Nexus, (S)easonality, e.g., a Christmas spike for iPod in the U.S. and Europe, and (D)eltas, e.g., unrepeated local events such as the U.S. election in 2008. Thanks to its concise but effective summarization, COMPCUBE can also forecast long-range future activities. Extensive experiments on real datasets demonstrate that COMPCUBE consistently outperforms the best state-of- the-art methods in terms of both accuracy and execution speed.