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 |
|---|---|
| Pages (from-to) | 2856-2866 |
| Number of pages | 11 |
| Journal | Advances in Neural Information Processing Systems |
| Volume | 2018-December |
| Publication status | Published - Jan 1 2018 |
| Externally published | Yes |
| Event | 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: Dec 2 2018 → Dec 8 2018 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Information Systems
- Signal Processing
Cite this
Metric on nonlinear dynamical systems with Perron-Frobenius operators. / Ishikawa, Isao; Fujii, Keisuke; Ikeda, Masahiro; Hashimoto, Yuka; Kawahara, Yoshinobu.
In: Advances in Neural Information Processing Systems, Vol. 2018-December, 01.01.2018, p. 2856-2866.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Metric on nonlinear dynamical systems with Perron-Frobenius operators
AU - Ishikawa, Isao
AU - Fujii, Keisuke
AU - Ikeda, Masahiro
AU - Hashimoto, Yuka
AU - Kawahara, Yoshinobu
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85061367637&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061367637&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85061367637
VL - 2018-December
SP - 2856
EP - 2866
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
SN - 1049-5258
ER -