Topological features greatly reduce parameters for time series classification
TopTimeNet: Topologically-assisted time-series classification model
Machine LearningComputational Geometry
Summary
Distinguishing whether a time series comes from a periodic or chaotic system is hard but important. The authors introduce TopTimeNet, which first turns the time series into a fixed geometric and topological summary before learning to classify it, unlike usual end-to-end methods. This approach matches or beats standard neural networks on many test cases while using far fewer trainable parameters. They also show the system's sensitivity depends on where noise affects the data pipeline, revealing new insights about robustness.
What this means in practice
- •For signal processing engineers: Implement low-parameter models to classify complex dynamical behaviors in sensor data using precomputed topological features.
- •For industrial automation teams: Use geometric and topological summaries to quickly detect system states with fewer data-driven parameters, reducing computational load in monitoring sensors.
Authors
Sharareh Sayyad, Sophia Bazzi
Abstract
Distinguishing periodic from chaotic dynamics in a time series is a fundamental challenge in both physics and engineering. Yet, end-to-end learned architectures must discover both a representation and a decision boundary from data, at substantial cost. We introduce TopTimeNet, which decouples these tasks: a fixed, non-learned stage extracts a $42$-dimensional geometric and topological descriptor from Takens delay embeddings and persistent homology, and a lightweight learnable stage performs classification. On a benchmark of $49$ nonlinear dynamical systems, a $1{,}638$-parameter configuration matches the mean accuracy of one with $33\times$ more trainable parameters. Additionally, this approach delivers mean accuracy comparable to convolutional neural networks and surpasses the average performance of converged Transformer models, while requiring three to four orders of magnitude fewer trainable parameters. Robustness also depends sharply on where noise is introduced: TopTimeNet degrades gracefully under perturbations to its precomputed features, but degrades sharply when noise is introduced into the raw signal and the full feature-extraction pipeline is recomputed, showing that robustness to perturbations of the precomputed features does not imply robustness of the complete raw-signal-to-prediction pipeline. These results show that decoupling fixed geometric and topological feature construction from a lightweight discriminative stage can achieve comparable classification accuracy with substantially fewer trainable parameters.