Temporal Graph Signal Decomposition

Abstract: Temporal graph signals are multivariate time series with individual components associated with nodes of a fixed graph structure. Data of this kind arises in many domains including activity of social network users, sensor network readings over time, and time course gene expression within the interaction network of a model organism. Traditional matrix decomposition methods applied to such data fall short of exploiting structural regularities encoded in the underlying graph and also in the temporal patterns of the signal. How can we take into account such structure to obtain a succinct and interpretable representation of temporal graph signals? We propose a general, dictionary-based framework for temporal graph signal decomposition (TGSD). The key idea is to learn a low-rank, joint encoding of the data via a combination of graph and time dictionaries. We propose a highly scalable decomposition algorithm for both complete and incomplete data, and demonstrate its advantage for matrix decomposition, imputation of missing values, temporal interpolation, clustering, period estimation, and rank estimation in synthetic and real-world data ranging from traffic patterns to social media activity. Our framework achieves 28% reduction in RMSE compared to baselines for temporal interpolation when as many as 75% of the observations are missing. It scales best among baselines taking under 20 seconds on 3.5 million data points and produces the most parsimonious models. To the best of our knowledge, TGSD is the first framework to jointly model graph signals by temporal and graph dictionaries.