Gaussian Graphical Model-Based Clustering of Time Series Data
Kohei Obata · 2024
Time series subsequence clustering is a useful tool for recognizing dynamic changes and uncovering interesting patterns in time series, and it can also be applied to downstream tasks. In addition to clustering the data, the interpretability of the cluster is crucial when analyzing the data, particularly because we frequently lack information about each cluster. The Gaussian Graphical Model (GGM) provides a clear explanation of the cluster as the inverse Gaussian covariance matrix (i.e., network) of the GGM encodes the conditional independence structure. In this study, we aim to enhance our understanding of the data by achieving GGM-based clustering for time series data of various types and structures. Furthermore, our objective is to utilize GGM in downstream tasks, including missing value imputation and forecasting, by taking advantage of the relationships between variables shown in the network. We aim to answer the following research questions: RQ1 : How can we obtain interpretable clusters for tensor time series? RQ2 : How can we deal with time series containing missing values? RQ3 : How can we effectively forecast a time series stream?