Name
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 Koopman operator 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. |
Year | Venue | Field |
|---|---|---|
2018 | neural information processing systems | Hilbert space,Kernel (linear algebra),Mathematical optimization,Algebra,Complex plane,Linear subspace,Dynamical systems theory,Nonlinear dynamical systems,Operator (computer programming),Unit disk,Mathematics |
DocType | Volume | Citations |
Journal | abs/1805.12324 | 0 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Isao Ishikawa | 1 | 1 | 1.37 |
| Keisuke Fujii | 2 | 2 | 1.39 |
| Masahiro Ikeda | 3 | 2 | 3.75 |
| Yuka Hashimoto | 4 | 1 | 1.37 |
| Kawahara, Yoshinobu | 5 | 317 | 31.30 |