The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly mild conditions, with the help of the argument concerning the {\L}ojasiewicz inequality. Our findings, which extend existing ones covering analytic kernels and the Epanechnikov kernel, are significant in that they cover the biweight kernel that is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.

翻译：均值漂移算法旨在寻找核密度估计的模态。本研究借助Łojasiewicz不等式相关论证，在相当宽松的条件下，给出了由均值漂移算法生成的模态估计序列的收敛性保证及其收敛速度评估。我们的发现扩展了现有涵盖解析核与Epanechnikov核的研究成果，其重要意义在于涵盖了双权核——该核在基于核密度估计的模态估计中，从渐近统计效率角度而言，是非负核中的最优选择。