Grassmannian Geometry Meets Dynamic Mode Decomposition in DMD-GEN: A New Metric for Mode Collapse in Time Series Generative Models

TL;DR

This paper introduces DMD-GEN, a novel metric based on Dynamic Mode Decomposition and Optimal Transport to quantify mode collapse in time series generative models, providing better insights into dynamic data generation.

Contribution

It defines mode collapse specifically for time series and proposes DMD-GEN, a new metric that assesses dynamic mode preservation and collapse in generative models.

Findings

DMD-GEN correlates with traditional metrics on static data.

DMD-GEN effectively detects mode collapse in time series models.

Validated on synthetic and real-world datasets with various models.

Abstract

Generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) often fail to capture the full diversity of their training data, leading to mode collapse. While this issue is well-explored in image generation, it remains underinvestigated for time series data. We introduce a new definition of mode collapse specific to time series and propose a novel metric, DMD-GEN, to quantify its severity. Our metric utilizes Dynamic Mode Decomposition (DMD), a data-driven technique for identifying coherent spatiotemporal patterns, and employs Optimal Transport between DMD eigenvectors to assess discrepancies between the underlying dynamics of the original and generated data. This approach not only quantifies the preservation of essential dynamic characteristics but also provides interpretability by pinpointing which modes have collapsed. We validate DMD-GEN on both synthetic and real-world datasets using various generative models, including TimeGAN, TimeVAE, and DiffusionTS. The results demonstrate that DMD-GEN correlates well with traditional evaluation metrics for static data while offering the advantage of applicability to dynamic data. This work offers for the first time a definition of mode collapse for time series, improving understanding, and forming the basis of our tool for assessing and improving generative models in the time series domain.