Transactions of the Japanese Society for Artificial Intelligence
Original Paper
Learning Non-linear Dynamical Systems by Alignment of Local Linear Models
Masao JokoYoshinobu KawaharaYairi Takehisa
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Volume 26 (2011) Issue 6 Pages 638-648

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Abstract

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.

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© 2011 JSAI (The Japanese Society for Artificial Intelligence)
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