A Bayesian semi-parametric approach to cluster heterogeneous time series

Majority of time series clustering research is focused on calculating similarity metrics between individual series, which in conjunction with traditional clustering algorithm partitions the data into similar groups (clusters). A major challenge lies in obtaining partitions when the number of clusters is not known in advance. Another challenge in such a clustering problem is to apply known hierarchies and heterogeneities in the data to refine clustering. In this work, we aim to alleviate both challenges using a Bayesian semi-parametric model for clustering of time series from data sources with known heterogeneity (e.g. different sensors). We apply a hierarchical normal model to represent the heterogeneity of sensor types within the sensor network and a dynamic linear model to represent the time series. The clustering is based on subset of parameters of the dynamic linear model, rest of the parameters are used for incrementing the likelihood of data to the model. We present a Gibbs Sampling algorithm to train the model and learn its parameters. We illustrate our approach with a dataset of EMG measurements recorded during different trials of locomotion. Our evaluation shows that the model learns significant clusters present within the data, filtering out the variances resulting from heterogeneity and random noise.