Motif Discovery in the Irregularly Sampled Time Series Data

Motifs are patterns that repeat within and across different time series. They can be used for various applications, such as clustering or discovering association rules. For example, in patient monitoring they can be used to identify features that are predictive of a diagnosis. Most of the motif definitions in literature are not applicable to the case when the data is irregularly sampled, which is often the case in the areas such as medical data. In this work, we present a generative model for unsupervised identification of motifs for the case when the observation times are highly irregular. In particular, we model each motif as a combination of a Poisson Point Process for the distribution of the timestamps and a Gaussian Process for the distribution of the observations. This allows us to use both the sampling frequency and the observation values in order to identify a motif. The whole time series is modeled as a Hidden Markov Model, in which each time step corresponds to a new motif. We present a version of the Viterbi Training procedure for the learning of the parameters of this model. We demonstrate experimentally that this procedure is able to re-learn the motifs in the data set generated from this model. Lastly, we present the results of using this model on laboratory tests data of the MIMIC-III, a well-known critical care dataset.