用最优多路决策树实现高准确率且易懂的聚类，适合关键决策场景。
Interpretable clustering via optimal multi-way decision trees
- 通过一维K均值对数值特征分箱，更好捕捉数据分布
- 构建二元线性规划模型，确保树结构全局最优
- 在4个公开数据集上表现更优，树更深但更简洁易读
聚类是发现数据结构、支持知识发现与决策的基础无监督学习方法。尽管聚类精度至关重要，可解释性在高风险决策中同样影响实际价值。基于决策树的聚类方法虽具备明确分裂规则，提升可解释性，但现有方法多依赖局部贪心搜索或需高昂计算成本，仅支持二叉分裂，导致树深度增加、可读性下降。为此，我们提出高性能计算框架「可解释聚类最优多路树」（ICOMT）。首先，提出一种新离散化方法，利用一维K均值聚类捕捉数值特征分布；其次，构建二元线性优化（BLO）问题，保证树结构全局最优；最后，在四个公开数据集上的广泛验证表明，ICOMT优于现有基线方法，在保持浅层简洁树结构的同时，实现了更高聚类精度。
原文摘要 · Abstract (English)
Clustering is a fundamental unsupervised learning technique for uncovering data structures to facilitate knowledge discovery and decision-making. While clustering accuracy is crucial, interpretability significantly impacts the practical value of clustering results, particularly in high-risk decision-making contexts. Although decision-tree-based clustering methods offer high interpretability through explicit splitting rules, existing approaches often rely on local greedy search or require expensive computational costs limited to binary splits, resulting in deeper, less interpretable trees. To overcome these limitations, we establish a high-performance computational framework named Interpretable Clustering via Optimal Multi-way Trees (ICOMT). We make three primary contributions. First, we propose a new discretization method for numerical features using one-dimensional K-means clustering to capture data distributions. Second, we formulate a binary linear optimization (BLO) problem to guarantee tree optimality. Third, extensive validation on four public datasets demonstrates that our ICOMT method outperforms existing baselines, achieving superior clustering accuracy while maintaining shallow, concise tree structures.
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