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arXiv Machine Learning By Michael L. Wells, Kamel Lahouel, Victor Rielly, Bruno Jedynak

The Clustering Occupation Kernel (CLOCK) Method for Time Series Arising from Dynamical Systems

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The paper introduces the Clustering Occupation Kernel (CLOCK) method, a representation-based framework that embeds time series from dynamical systems into a reproducing kernel Hilbert space using a time‑averaged occupation kernel. This embedding allows trajectory comparison via the RKHS norm and, for differential equation systems, approximates the kernel mean embedding of the invariant Sinai‑Ruelle‑Bowen measure, effectively measuring the maximum mean discrepancy between attractors. CLOCK handles unequal‑length and irregularly‑spaced data, incorporates Takens’ embedding for general time series, and demonstrates superior performance over benchmark methods on synthetic data and real intracranial EEG recordings, with ablation studies confirming theoretical convergence and noise robustness.

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