Convergence and clustering analysis for Mean Shift with radially symmetric, positive definite kernels

The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In this paper, we show that for$\mathit{\text{sufficiently}}\mathit{\text{large}}\mathit{\text{bandwidth}}$ convergence is guaranteed in any dimension with $\mathit{\text{any}}\mathit{\text{radially}}\mathit{\text{symmetric}}\mathit{\text{and}}\mathit{\text{strictly}}\mathit{\text{positive}}\mathit{\text{definite}}\mathit{\text{kernels}}$. Although the author acknowledges that our result is partially more restrictive than that of \cite{YT} due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in \cite{YT}, and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at $\mathit{\text{large}}\mathit{\text{bandwidths}}$ is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.