Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections

TL;DR

This paper introduces a discriminant dynamic mode decomposition method that incorporates label information into the extraction of coherent spatio-temporal patterns, enhancing class separation and interpretability.

Contribution

It develops a novel discriminant DMD approach by integrating discriminant analysis with kernel functions on dynamic mode subspaces, tailored for labeled spatio-temporal data.

Findings

Effective pattern extraction demonstrated on synthetic data

Improved class separation in real-world datasets

Potential for enhanced exploratory analysis of spatio-temporal data

Abstract

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.