Minimum distance classification for nonlinear dynamical systems

TL;DR

This paper introduces Dynafit, a kernel-based method that learns a distance metric for classifying trajectories from nonlinear dynamical systems by approximating the Koopman operator, enabling effective classification even with partial prior knowledge.

Contribution

The paper presents Dynafit, a novel kernel-based approach that learns a dynamical distance metric through Koopman operator approximation for classifying nonlinear system trajectories.

Findings

Effective in chaos detection with logistic map

Recognizes handwritten dynamic patterns

Classifies visual dynamic textures accurately

Abstract

We address the problem of classifying trajectory data generated by some nonlinear dynamics, where each class corresponds to a distinct dynamical system. We propose Dynafit, a kernel-based method for learning a distance metric between training trajectories and the underlying dynamics. New observations are assigned to the class with the most similar dynamics according to the learned metric. The learning algorithm approximates the Koopman operator which globally linearizes the dynamics in a (potentially infinite) feature space associated with a kernel function. The distance metric is computed in feature space independently of its dimensionality by using the kernel trick common in machine learning. We also show that the kernel function can be tailored to incorporate partial knowledge of the dynamics when available. Dynafit is applicable to various classification tasks involving nonlinear dynamical systems and sensors. We illustrate its effectiveness on three examples: chaos detection with the logistic map, recognition of handwritten dynamics and of visual dynamic textures.