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Joint Problems in Learning Multiple Dynamical Systems

Created by
  • Haebom

Author

Mengjia Niu, Xiaoyu He, Petr Ry\v{s}av y, Quan Zhou, Jakub Marecek

Outline

This paper presents a novel approach to the problem of clustering time series. Specifically, we propose a method for partitioning a given set of time series into subsets using a given number of subsets and learning a linear dynamical system (LDS) model for each subset. The goal is to minimize the maximum error across all models. We present a globally convergent method and the EM heuristic, and the computational results show promising results. Key features include the elimination of the need for a predefined hidden state dimension and the provision of guidelines for determining regularization during system identification.

Takeaways, Limitations

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Takeaways:
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Time series clustering and LDS model training are possible without the need to predefine hidden state dimensions.
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Provides guidance on normalization decisions in system identification.
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We contribute to practical problem solving by presenting globally convergent algorithms and EM heuristics.
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It has high applicability in various fields (metabolic modeling, quantum information theory, etc.).
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Limitations:
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There is a lack of analysis of the computational complexity of the proposed method.
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Extensive experimental results on real-world data are required.
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Minimizing the maximum error does not always guarantee optimal clustering results.
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Performance evaluation on relatively high-dimensional time series data is required.
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