A Geometry-Aware Framework for Clustering Cylindrical Data

2026-09-22

AI Summary

本文提出了一种考虑角度周期性的圆柱数据聚类框架，通过改进K-means算法并使用两种不同的距离度量方法解决了传统聚类方法在处理跨越角度原点的数据时的失效问题。

Abstract

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.

Problem

• Cylindrical Data
• Clustering
• Periodicity
• Angle

Innovation

• cylindrical data
• chordal distance
• geodesic distance
• Frechet means
• K-means++