Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections
This work provides a tool for exploratory data analysis in spatio-temporal domains where label information is available, but it is incremental as it builds on existing DMD methods.
The authors tackled the problem of extracting coherent patterns from labeled spatio-temporal data by incorporating discriminant analysis into dynamic mode decomposition, resulting in a method that identifies distinctive patterns contributing to differences in labeled dynamics, as demonstrated on synthetic and real-world datasets.
Extracting coherent patterns is one of the standard approaches towards understanding spatio-temporal 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 spatio-temporal data. In this work, we propose a new method for extracting distinctive coherent patterns from labeled spatio-temporal 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 spatio-temporal data.