Network of compression networks to extract useful information from multivariate time series

Compression networks are the result of a recently proposed method to transform univariate time series to a complex network representation by using a compression algorithm. We show how a network of compression networks can be constructed to capture relationships among multivariate time series. This network is a weighted graph with edge weights corresponding to how well the compression codewords of one time series compress another time series. Subgraphs of this network obtained by thresholding of the relative compression edge weights are shown to possess properties which can track dynamical change. Furthermore, community structures-groups of vertices more densely connected together-within these networks can identify partially synchronized states in the dynamics of networked oscillators, as well as perform genre classification of musical compositions. An additional example incorporates temporal windowing of the data and demonstrates the potential of the method to identify tipping point behaviour through the analysis of multivariate electroencephalogram time series of patients undergoing seizure.