Convergence Analysis of Mean Shift
This work provides incremental theoretical improvements for researchers in statistics and machine learning focusing on density estimation and clustering.
The study tackled the problem of proving convergence guarantees and evaluating convergence rates for the mean shift algorithm under mild conditions, extending existing results to cover the biweight kernel and showing it is optimal for asymptotic statistical efficiency in KDE-based mode estimation.
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 Łojasiewicz inequality. Our findings extend existing ones covering analytic kernels and the Epanechnikov kernel. Those are significant in that they cover the biweight kernel, which is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.