  Mean shift is a simple interactive procedure that gradually shifts data
points towards the mode which denotes the highest density of data points in the
region. Mean shift algorithms have been effectively used for data denoising,
mode seeking, and finding the number of clusters in a dataset in an automated
fashion. However, the merits of mean shift quickly fade away as the data
dimensions increase and only a handful of features contain useful information
about the cluster structure of the data. We propose a simple yet elegant
feature-weighted variant of mean shift to efficiently learn the feature
importance and thus, extending the merits of mean shift to high-dimensional
data. The resulting algorithm not only outperforms the conventional mean shift
clustering procedure but also preserves its computational simplicity. In
addition, the proposed method comes with rigorous theoretical convergence
guarantees and a convergence rate of at least a cubic order. The efficacy of
our proposal is thoroughly assessed through experimental comparison against
baseline and state-of-the-art clustering methods on synthetic as well as
real-world datasets.
