Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification
This addresses time series classification problems in systems and control engineering for applications like health monitoring and fault detection, representing a novel method for a known bottleneck.
The paper tackles the challenge of classifying time series from dynamic systems without known models, with noise, and long signals by developing a non-parametric classifier using topological signatures. The result is accurate discrimination between states of chaotic systems close in parameter space, with robust performance to noise.
Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new trajectory labels using Sinkhorn divergences on the space of diagram KDEs to quantify proximity. We show that this approach accurately discriminates between states of chaotic systems that are close in parameter space, and its performance is robust to noise.