Time Series Search Using Hidden Markov Models

Instances of unusual behavior are often difficult to locate in large volumes of data. In a typical case, a single instance of the unusual behavior is located and additional instances are desired. We propose a method for performing this search using hidden Markov models (HMMs). This approach has the advantage that it generalizes to the detection of any signal whose behavior exhibits statistically distinguishable modes. Our method employs the following approach: first, a time series snippet containing an instance of the target behavior is used to train an HMM; this also results in a classification of the snippet observations. Second, the trained HMM is used to classify observations in the time series we are searching. Third, we calculate matches between the snippet classification and the search series classification. These matches can be ranked and returned according to a quality metric. Optimal fitting of hidden Markov models to generalized data is a difficult problem. In some cases, sufficient a priori information is available to constrain the problem and reduce the number of free parameters. Most often in exploratory data analysis such constraints are not available and standard optimization techniques are likely to become unstable. We solve this problem by employing a robust model fitting algorithm that uses regularization and annealing to stabilize the optimization procedure. This robust HMM procedure allows the method to work on a first try basis, making it applicable to real time interactive data analysis. We examine the performance of this method on selected engineering and science time series, including data from the Southern California Integrated GPS Network (SCIGN) and the Southern California Seismic Network.