用角度分区均值法确定性初始化聚类中心，提速超70%且不损失精度
Sector-Mean: Deterministic Initialization of K-Means Centroids via Angular Sector Partitioning
- 以全局中心为原点划分二维数据角度扇区，用各扇区均值确定初始聚类中心
- 相比K-Means++和Max-Min，初始化时间减少74.9%和59.8%，迭代次数降低5%~16%
- 适合对初始化速度敏感、需可重复结果的工程化聚类场景
K-Means是应用最广泛的聚类算法之一，但其对初始中心选择敏感，严重影响收敛速度与聚类精度。本文提出一种确定性初始化策略——Sector-Mean，该方法以全局中心为原点，将二维数据空间划分为角度扇区，并利用各扇区内的数据均值作为初始聚类中心，时间复杂度为O(N)。在标准二维基准数据集（SIPU、Birch）及多个真实世界数据集上，与随机初始化、K-Means++、Max-Min方法在相同Lloyd迭代次数下对比。统计分析显示，尽管聚类质量与K-Means++和Max-Min相当，但Sector-Mean显著提升计算效率：初始化时间分别比K-Means++和Max-Min减少74.9%和59.8%；平均迭代次数比K-Means++少约5%，比Max-Min少16%。结果表明，Sector-Mean在保持聚类质量的同时，提供了一种高效且可复现的确定性初始化方案。
原文摘要 · Abstract (English)
K-Means is one of the most widely used clustering algorithms, but its susceptibility to initial centroid selection remains a primary bottleneck for its convergence speed and clustering accuracy. This paper proposes Sector-Mean Initialization, a deterministic initialization strategy with O(N) time complexity that partitions the two-dimensional data space into angular sectors around the global centroid and initializes centroids using sector-wise means. We evaluate the method on established two-dimensional benchmarks (SIPU, Birch) and multiple real-world datasets, comparing against random, K-Means++, and Max-Min initialization under identical Lloyd iterations. The statistical analysis of Friedman's test (p<0.05) and Nemenyi post-hoc comparison indicates that, while delivering equivalent clustering quality as K-Means++ and Max-Min, Sector-Mean offers significant computational efficiency. Experimental results show that Sector-Mean reduces the initialization time by 74.9% and 59.8% in comparison to K-Means++ and max-min, respectively. And, it yields the lowest average number of iterations, achieving approximately 5% fewer iterations than K-Means++ and 16% fewer than max-min. These results highlight that Sector-Mean initialization offers a deterministic and computationally efficient initialization strategy while preserving cluster quality.
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