发表机构
Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间序列模式挖掘计算开销大的问题，提出基于笛卡尔后缀树的CT-Miner算法，将穷举模式收集从O(n^4)降至O(n^2)，并证明其能生成紧凑表示，保留聚类结构。
AI 中文摘要
时间序列中常常包含重复出现的结构模式，而高效地将这些模式挖掘为紧凑表示对于长序列的可扩展分析至关重要。笛卡尔树（CT）等价性提供了一种成熟的结构抽象，它在保留层级顺序结构的同时，舍弃了精确的数值和细粒度的序数变化。通过将多个序数模式归入一种共享的结构形式，CT等价性为压缩重复的时间结构提供了一种有原则的方法。然而，在大规模上挖掘频繁的CT等价模式在计算上仍然代价高昂。一种朴素的成对方法反复构造并计数子序列上的CT表示，对于长度为n的序列需要O(n^4)时间，这严重限制了其在长序列上的适用性。我们提出了一种基于笛卡尔后缀树的新笛卡尔模式挖掘算法，该算法紧凑地组织CT等价子序列并重用共享的结构信息。我们的方法将穷举CT模式出现收集从O(n^4)时间降低到O(n^2)时间，并且我们正式证明了其正确性和复杂度界。我们进一步表明，这种计算上的收益转化为有效的紧凑表示。在多样化的时间序列数据集上，一小部分挖掘出的CT模式保留了有意义的聚类结构，并且与更细粒度的保序表示的比较表明，在有限的特征预算下，CT等价性减少了冗余的序数区分。我们的实现可在以下网址获取：此https URL。
英文摘要
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 https://github.com/hyundong98/CT-Miner .
