Model Based Clustering of Time Series Utilizing Expert ODEs

In practical system identification scenarios, partially observed time series are often acquired from a set of similar dynamical systems forming clusters in the parameter space (e.g., healthy vs. diseased patients). The problem of identifying these clusters and that of identifying the model parameters are tightly coupled. In this work, we propose a novel model-based clustering method that makes it possible to utilize expert knowledge in the form of parameterized ODEs. It is challenging to learn complex dynamics from a single short time series, while the correct grouping of these segments is not known a priori. Our method clusters the data and results in parameter estimates corresponding to the cluster centroids. We demonstrate that our model has higher performance than state-of-the-art time series clustering methods, and the naive application of clustering to the output of parameter estimation methods.