Learning Stable Linear Dynamical Systems with the Weighted Least Square Method

Huang, Wen-bing; Cao, Le-le; Sun, Fuchun; Zhao, Deli; Liu, Huaping; Yu, Shanshan

Learning Stable Linear Dynamical Systems with the Weighted Least Square Method

Wen-bing Huang, Le-le Cao, Fuchun Sun, Deli Zhao, Huaping Liu, Shanshan Yu

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Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence. Pages 1599-1604.

Abstract

Standard subspace algorithms learn Linear Dynamical Systems (LDSs) from time series with the least-square method, where the stability of the system is not naturally guaranteed. In this paper, we propose a novel approach for learning stable systems by enforcing stability directly on the least-square solutions. To this end, we first explore the spectral-radius property of the least-square transition matrix and then determine the key component that incurs the instability of the transition matrix. By multiplying the unstable component with a weight matrix on the right side, we obtain a weighted-least-square transition matrix that is further optimized to minimize the reconstruction error of the state sequence while still maintaining the stable constraint. Comparative experimental evaluations demonstrate that our proposed methods outperform the state-of-the-art methods regarding the reconstruction accuracy and the learning efficiency.

Wen-bing Huang, Le-le Cao, Fuchun Sun, Deli Zhao, Huaping Liu, and Shanshan Yu. 2016. Learning Stable Linear Dynamical Systems with the Weighted Least Square Method. In Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-16. IJCAI, 1599–1604. https://ijcai.org/proceedings/2016/229

@inproceedings{ijcai2016p229,
  title     = {Learning Stable Linear Dynamical Systems with the Weighted Least Square Method},
  author    = {Huang, Wen-bing and Cao, Le-le and Sun, Fuchun and Zhao, Deli and Liu, Huaping and Yu, Shanshan},
  booktitle = {Proceedings of the Twenty-Fifth International Joint Conference on
               Artificial Intelligence, {IJCAI-16}},
  publisher = {AAAI Press / International Joint Conferences on Artificial Intelligence},
  editor    = {Subbarao Kambhampati},
  pages     = {1599--1604},
  year      = {2016},
  month     = {7},
  url       = {https://ijcai.org/proceedings/2016/229},
}

TY  - CPAPER
TI  - Learning Stable Linear Dynamical Systems with the Weighted Least Square Method
AU  - Huang, Wen-bing
AU  - Cao, Le-le
AU  - Sun, Fuchun
AU  - Zhao, Deli
AU  - Liu, Huaping
AU  - Yu, Shanshan
T2  - Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-16
PB  - AAAI Press / International Joint Conferences on Artificial Intelligence
PY  - 2016
SP  - 1599
EP  - 1604
UR  - https://ijcai.org/proceedings/2016/229
ER  -