# Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections

arXiv: https://arxiv.org/abs/2102.09973 · HTML: https://mlsanity.com/paper/2102.09973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 43 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [Model-Based Control Using Koopman Operators](https://mlsanity.com/paper/1709.01568/) (2017)

## Built on by (most cited first, 1 of 1)

- [Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2403.02524/) (2024)

## Abstract (arXiv)

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.