The problem of mining a network of time series data naturally arises in many research areas including energy system, quantitative finance, bioinformatics, environmental monitoring, traffic monitoring, etc. Among others, two emerging challenges shared by manifold applications are (1) the modeling of temporal-spatial dependence with contextual information and (2) the design of efficient learning algorithms for big data (exceedingly long sequence) analytics. In this paper, we study a Contextual Hidden Markov Model (CHMM) that describes infinite temporal dependence and contextual spatial relations in an unified framework. More importantly, to make model training feasible for growing number of data samples, we develop an Online Expectation-Maximization (OEM) algorithm that avoids the usual forward-backward pass of the entire time sequence. Two typical applications, missing value recovery and novelty detection, are considered to test CHMM and the online algorithm. Experiments are conducted on real world data collected from power distribution network monitoring. We compare CHMM with other popular methods and the results not only justify the benefit of incorporating temporal-spatial and contextual information, but also demonstrate the effectiveness of the proposed OEM algorithm.
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