Learning non-linear dynamical systems by alignment of local linear models

Masao Joko, Yoshinobu Kawahara, Takehisa Yairi

Research output: Contribution to journalArticlepeer-review


In this paper, we present an algorithm for learning non-linear dynamical systems which works by aligning local linear models, based on a probabilistic formulation of subspace identification. This is achieved by the fusion of the recent works in the fields of machine learning and system control. Because the procedure for constructing a state sequence in subspace identification can be interpreted as the Canonical Correlation Analysis(CCA) between past and future observation sequences, we can derive a latent variable representation for this problem. Therefore, as in a similar manner to the recent works on learning a mixture of probabilistic models, we obtain a framework for constructing a state space by aligning local linear coordinates. This leads to a prominent algorithm for learning non-linear dynamical systems. Finally, we apply our method to motion capture data and telemetry data, and then show how our algorithm works well.

Original languageEnglish
Pages (from-to)638-648
Number of pages11
JournalTransactions of the Japanese Society for Artificial Intelligence
Issue number6
Publication statusPublished - 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence


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