  Many clustering algorithms exist that estimate a cluster centroid, such as
K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters
data by returning exactly K meaningful modes. We propose a natural definition
of a K-modes objective function by combining the notions of density and cluster
assignment. The algorithm becomes K-means and K-medoids in the limit of very
large and very small scales. Computationally, it is slightly slower than
K-means but much faster than mean-shift or K-medoids. Unlike K-means, it is
able to find centroids that are valid patterns, truly representative of a
cluster, even with nonconvex clusters, and appears robust to outliers and
misspecification of the scale and number of clusters.
