Inertial Hidden Markov Models: Modeling Change in Multivariate Time Series

Faced with the problem of characterizing systematic changes in multivariate time series in an unsupervised manner, we derive and test two methods of regularizing hidden Markov models for this task. Regularization on state transitions provides smooth transitioning among states, such that the sequences are split into broad, contiguous segments. Our methods are compared with a recent hierarchical Dirichlet process hidden Markov model (HDP-HMM) and a baseline standard hidden Markov model, of which the former suffers from poor performance on moderate-dimensional data and sensitivity to parameter settings, while the latter suffers from rapid state transitioning, over-segmentation and poor performance on a segmentation task involving human activity accelerometer data from the UCI Repository. The regularized methods developed here are able to perfectly characterize change of behavior in the human activity data for roughly half of the real-data test cases, with accuracy of 94% and low variation of information. In contrast to the HDP-HMM, our methods provide simple, drop-in replacements for standard hidden Markov model update rules, allowing standard expectation maximization (EM) algorithms to be used for learning.