Discriminant Dynamic Mode Decomposition for Labeled Spatiotemporal Data Collections

Extracting coherent patterns is one of the standard approaches toward understanding spatiotemporal data. Dynamic mode decomposition (DMD) is a powerful tool for extracting coherent patterns, but the original DMD and most of its variants do not consider label information, which is often available as side information of spatiotemporal data. In this work, we propose a new method for extracting distinctive coherent patterns from labeled spatiotemporal data collections such that they contribute to major differences in a labeled set of dynamics. We achieve such pattern extraction by incorporating discriminant analysis into DMD. To this end, we define a kernel function on subspaces spanned by sets of dynamic modes and develop an objective to take both reconstruction goodness as DMD and class-separation goodness as discriminant analysis into account. We illustrate our method using a synthetic dataset and several real-world datasets. The proposed method can be a useful tool for exploratory data analysis for understanding spatiotemporal data.