Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data (1706.03161v2)

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.

• The paper introduces TICC, a novel method for clustering multivariate time series data by defining clusters based on learning dependency structures using inverse covariance matrices.
• TICC simultaneously segments and clusters multivariate time series data using a dynamic programming strategy, solving the optimization problems via alternating minimization with ADMM.
• TICC achieves at least 41% higher accuracy than baselines on synthetic data using fewer samples, making it valuable for applications like anomaly detection and behavioral analytics.

Toeplitz Inverse Covariance-Based Clustering for Multivariate Time Series Data

The paper "Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data" presents a novel method for subsequence clustering in multivariate time series data, proposing an innovative approach called Toeplitz Inverse Covariance-based Clustering (TICC). The authors, affiliated with Stanford University, aim to address the challenges associated with discovering patterns in high-dimensional temporal data and interpreting the clusters that define these patterns.

The underlying principle of TICC is to define each cluster using a correlation network, specifically a Markov random field (MRF), which characterizes the interdependencies within a typical subsequence of that cluster. This approach is significant because it focuses on the graphical structure of data rather than merely assessing raw values, allowing for more nuanced and interpretable insights into complex datasets such as automobile sensor readings or financial market data.

Technical Contributions

1. Model-Based Clustering Approach: TICC utilizes a model-based approach to capture the dependency structure of multivariate time series data. This is achieved by learning sparse Gaussian inverse covariance matrices that define an MRF for each cluster. This methodological choice is pivotal in preventing overfitting and ensuring the interpretability of clusters.
2. Simultaneous Segmentation and Clustering: The paper addresses the challenge of simultaneously segmenting and clustering time series data, a task made complex due to the need for multiple segments to belong to the same cluster. TICC resolves this by employing a dynamic programming strategy to optimize clustering assignments across the time series timeline.
3. Optimization Methodology: The authors propose solving the clustering problem through alternating minimization, akin to an expectation maximization (EM) approach. The use of the Alternating Direction Method of Multipliers (ADMM) allows for the scalable solution of the resulting convex optimization problems.
4. Validation and Performance: The authors validate TICC against state-of-the-art baselines across synthetic datasets, reporting at least a 41% improvement in clustering accuracy. Furthermore, TICC requires significantly fewer samples to achieve similar performance levels compared to alternative methods.

Implications and Future Directions

The practical implications of TICC are substantial, particularly in areas requiring the analysis of complex, high-dimensional data. The method's ability to transform long sequences of raw sensor data into a concise representation of a few distinct states holds potential for varied applications, ranging from behavioral analytics in wearable technology to anomaly detection in vehicular systems.

Theoretically, this work opens pathways to extend model-based clustering approaches to more diversified data types and structures. Future research could aim to apply the TICC framework to different data-object classes, such as boolean or categorical datasets, utilizing other exponential family MRFs to broaden the scope and applicability of the method. This could lead to significant advancements in the fields of bioinformatics, cybersecurity, and beyond, where the interpretability and accuracy of model-based approaches are increasingly valued.

In summary, the TICC methodology provides a sophisticated tool for uncovering and interpreting repeating patterns within multivariate time series data. Its emphasis on the structural relationships intrinsic to data signals a progressive step forward in computational approaches to time series analysis, offering a newly refined lens through which complex datasets can be understood and leveraged.