Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

By David Hallac, Sagar Vare, Stephen P. Boyd, Jure Leskovec. Knowledge Discovery and Data Mining, 2017

309 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Economics and Econometrics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/00e589a575526a0dca7b458c16bbb1c27524666f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jindong Wang
2. Tao Qin
3. Wenjie Feng
4. Dongjin Song
5. Renjun Xu
6. Nitesh V. Chawla
7. Wei Cheng
8. Sinno Jialin Pan

In Economics and Econometrics

1. Wei Cheng
2. Haifeng Chen
3. Dongjin Song

In Signal Processing

1. Jindong Wang
2. Tao Qin
3. Sinno Jialin Pan
4. Dongjin Song
5. Xu Tan
6. Tie-Yan Liu
7. Sheng Zhao
8. Yi Ren

Citations in the corpus

• AdaRNN: Adaptive Learning and Forecasting of Time Series (2021, background): “Time-series clustering [16, 34], on the other hand, aims at finding different groups consisting of similar (segments of) time series, which is clearly different from our situation.”
• A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data (2018, background): “This paper is also related to other time series applications such as clustering/classification (Li and Prakash 2011; Hallac et al. 2017; Karim et al. 2018), segmentation (Keogh et al. 2001; Lemire 2007), and so on.”