Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

TL;DR

This paper introduces TICC, a novel model-based clustering method for multivariate time series that simultaneously segments and identifies interpretable clusters using correlation networks, validated on synthetic and real-world data.

Contribution

The paper proposes TICC, a new scalable clustering approach that models clusters with Markov random fields and combines segmentation with clustering in a unified framework.

Findings

TICC outperforms state-of-the-art baselines in synthetic experiments.

TICC effectively learns interpretable clusters in real-world sensor data.

The method is scalable and efficient due to closed-form solutions and optimization techniques.

Abstract

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.