Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper, we analyze convergence properties of the BMS algorithm by leveraging its interpretation as an optimization procedure, which is known but has been underutilized in existing convergence studies. Whereas existing results on convergence properties applicable to multi-dimensional data only cover the case where all the blurred data point sequences converge to a single point, this study provides a convergence guarantee even when those sequences can converge to multiple points, yielding multiple clusters. This study also shows that the convergence of the BMS algorithm is fast by further leveraging geometrical characterization of the convergent points.

翻译：模糊均值漂移（BMS）算法是均值漂移算法的一种变体，是一种基于核的迭代数据聚类方法，其中数据点通过迭代模糊处理根据其收敛点进行聚类。本文利用BMS算法作为优化过程的解释（该解释已知但未在现有收敛性研究中得到充分利用），分析了其收敛性质。现有适用于多维数据的收敛性结果仅覆盖所有模糊处理后的数据点序列收敛至单点的情况，而本研究在序列可能收敛至多点（从而产生多个聚类）时也提供了收敛性保证。此外，本研究通过进一步刻画收敛点的几何特征，证明了BMS算法的收敛速度较快。