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

arXiv: https://arxiv.org/abs/2610.05330 · HTML: https://mlsanity.com/paper/2610.05330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [OPP-Miner: Order-preserving sequential pattern mining](https://mlsanity.com/paper/2202.03140/) (2022)
- [OPR-Miner: Order-preserving rule mining for time series](https://mlsanity.com/paper/2209.08932/) (2022)
- [Cartesian Tree Matching and Indexing](https://mlsanity.com/paper/1905.08974/) (2019)
- [Scalable Order-Preserving Pattern Mining](https://mlsanity.com/paper/2411.19511/) (2024)

## Abstract (arXiv)

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(n4) 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(n4) to O(n2) 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 https://github.com/hyundong98/CT-Miner .