Abstract
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric includes the existing fundamental metrics for dynamical systems, which are basically defined with principal angles between some appropriately-chosen subspaces, as its special cases. We also describe the estimation of our metric from finite data. We empirically illustrate our metric with an example of rotation dynamics in a unit disk in a complex plane, and evaluate the performance with real-world time-series data.
Original language | English |
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Pages (from-to) | 2856-2866 |
Number of pages | 11 |
Journal | Advances in Neural Information Processing Systems |
Volume | 2018-December |
Publication status | Published - 2018 |
Externally published | Yes |
Event | 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: Dec 2 2018 → Dec 8 2018 |
All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Information Systems
- Signal Processing