Discovering Synchronized Subsets of Sequences: A Large Scale Solution
Evangelos Sariyanidi,  Casey J. Zampella,  Keith G. Bartley,  John D. Herrington,  Theodore D. Satterthwaite,  Robert T. Schultz,  Birkan Tunc

Finding the largest subset of sequences (i.e., time series) that are correlated above a certain threshold, within large datasets, is of significant interest for computer vision and pattern recognition problems across domains, including behavior analysis, computational biology, neuroscience, and finance. Maximal clique algorithms can be used to solve this problem, but they are not scalable. We present an approximate, but highly efficient and scalable, method that represents the search space as a union of sets called epsilon-expanded clusters, one of which is theoretically guaranteed to contain the largest subset of synchronized sequences. The method finds synchronized sets by fitting a Euclidean ball on epsilon-expanded clusters, using Jung's theorem. We validate the method on data from the three distinct domains of facial behavior analysis, finance, and neuroscience, where we respectively discover the synchrony among pixels of face videos, stock market item prices, and dynamic brain connectivity data. Experiments show that our method produces results comparable to, but up to 300 times faster than, maximal clique algorithms, with speed gains increasing exponentially with the number of input sequences.