CT-Miner: Fast and Coarse-Grained Time-Series Pattern Mining via Cartesian Trees

Abstract:Time series often contain recurring structural patterns, and efficiently mining such patterns into compact representations is essential for scalable analysis of long sequences. Cartesian tree (CT) equivalence provides a well-established structural abstraction that preserves hierarchical order structure while discarding exact values and fine-grained ordinal variations. By grouping multiple ordinal patterns into a shared structural form, CT equivalence offers a principled way to compress recurring temporal structure. However, mining frequent CT-equivalent patterns at scale remains computationally expensive. A naive pairwise approach repeatedly constructs and counts CT representations over subsequences, requiring $O(n^4)$ time for a sequence of length $n$, which severely limits its applicability to long sequences. We propose a new Cartesian pattern mining algorithm based on a Cartesian suffix tree that compactly organizes CT-equivalent subsequences and reuses shared structural information. Our method reduces exhaustive CT-pattern occurrence collection from $O(n^4)$ to $O(n^2)$ time, and we formally prove the correctness and complexity bounds. We further show that this computational gain translates into effective compact representations. Across diverse time-series datasets, a small set of mined CT patterns preserves meaningful clustering structure, and comparisons with finer-grained order-preserving representations show that CT equivalence reduces redundant ordinal distinctions under limited feature budgets. Our implementation is available at this https URL .

Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG)

arXiv:2610.05330 [cs.DS]

(or arXiv:2610.05330v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2610.05330 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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