Minimum distance classification for nonlinear dynamical systems
This work addresses classification challenges in nonlinear dynamical systems for applications like sensor data analysis, though it appears incremental as it builds on existing kernel methods and Koopman operator approximations.
The paper tackles the problem of classifying trajectory data from nonlinear dynamical systems by proposing Dynafit, a kernel-based method that learns a distance metric between trajectories and underlying dynamics, achieving effective classification in examples such as chaos detection and recognition tasks.
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.