🤖 AI Summary
This paper addresses the challenging problem of clustering multivariate, irregularly sampled time series with missing observations—common in healthcare and psychology. We propose the first mixture-clustering framework based on linear Gaussian state-space models (LGSSMs). Our method explicitly embeds parameterized LGSSMs into a mixture model, derives a closed-form log-likelihood function, and designs an expectation-maximization (EM) algorithm tailored to irregular sampling, thereby ensuring both theoretical interpretability and empirical robustness. The approach naturally accommodates varying sampling rates and models missing data via the underlying probabilistic structure. Extensive evaluation on synthetic data and real-world applications—including wearable sensing, ecological momentary assessment, and epidemiological cohort studies—demonstrates significant improvements over existing time-series clustering methods. The implementation is publicly available.
📝 Abstract
We introduce VISTA, a clustering approach for multivariate and irregularly sampled time series based on a parametric state space mixture model. VISTA is specifically designed for the unsupervised identification of groups in datasets originating from healthcare and psychology where such sampling issues are commonplace. Our approach adapts linear Gaussian state space models (LGSSMs) to provide a flexible parametric framework for fitting a wide range of time series dynamics. The clustering approach itself is based on the assumption that the population can be represented as a mixture of a given number of LGSSMs. VISTA's model formulation allows for an explicit derivation of the log-likelihood function, from which we develop an expectation-maximization scheme for fitting model parameters to the observed data samples. Our algorithmic implementation is designed to handle populations of multivariate time series that can exhibit large changes in sampling rate as well as irregular sampling. We evaluate the versatility and accuracy of our approach on simulated and real-world datasets, including demographic trends, wearable sensor data, epidemiological time series, and ecological momentary assessments. Our results indicate that VISTA outperforms most comparable standard times series clustering methods. We provide an open-source implementation of VISTA in Python.