发表机构
Università degli Studi di Napoli Federico II; Centre for Studies in Economics and Finance (CSEF)（那不勒斯费德里科二世大学; 经济与金融研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出几何感知的圆柱数据聚类框架，通过弦距离和测地距离实例化K-means，精确计算Frechet均值，在模拟和真实数据上优于欧几里得K-means。
AI 中文摘要
圆柱数据将角度与线性测量配对。忽略角度周期性的聚类会破坏跨越其原点的分组。我们针对圆柱上的通用距离公式化K-means算法，并将其分别实例化为环境空间的弦距离和沿曲面的测地距离，使得两个版本仅度量不同。质心是使用已知工具计算的精确Frechet均值：弦的均值方向，弧的圆Frechet均值。以K-means++为种子，该算法在有限次迭代内收敛，成本与经典K-means相当。在模拟数据的大量实证分析中，欧几里得K-means从未有意义的更好，并且在簇跨越原点时崩溃；两个版本在角度集中时一致，弦仅在角度无信息时偶然占优；基于模型的圆柱混合方法是最可变的，但能更好地描述细长、相关的簇。在色调-值彩色图像量化中，圆柱版本在基于颜色分割的目标检测上表现更好；在风向和氮氧化物数据上，它们恢复了欧几里得K-means切分的两个污染状态。
英文摘要
Cylindrical data pair an angle with a linear measurement. Clustering that ignores the periodicity of the angle breaks up groups lying across its origin. We formulate the K-means algorithm for a generic distance on the cylinder and instantiate it with the chordal distance of the ambient space and the geodesic distance along the surface, so that the two versions differ in the metric alone. Centroids are exact Frechet means computed with known tools: the mean direction for the chord, the circular Frechet mean for the arc. Seeded by K-means++, the algorithm converges in finitely many iterations at a cost comparable to classical K-means. Over an extensive empirical analysis on simulated data, Euclidean K-means is never meaningfully better and breaks down when clusters cross the origin; the two versions agree for concentrated angles, the chord incidentally prevailing only when the angle is uninformative; a model-based cylindrical mixture is the most variable method but describes elongated, correlated clusters better. In hue-value color image quantization, the cylindrical versions performs better on object detection based on color segmentation; on wind direction and nitrogen oxides data they recover two pollution regimes that Euclidean K-means cuts apart.
