Kernel methods for weakly supervised mean shift clustering

Mean shift clustering is a powerful unsupervised data analysis technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the clusters. The data association criteria is based on the underlying probability distribution of the data points which is defined in advance via the employed distance metric. In many problem domains, the initially designed distance metric fails to resolve the ambiguities in the clustering process. We present a novel semi-supervised kernel mean shift algorithm where the inherent structure of the data points is learned with a few user supplied constraints in addition to the original metric. The constraints we consider are the pairs of points that should be clustered together. The data points are implicitly mapped to a higher dimensional space induced by the kernel function where the constraints can be effectively enforced. The mode seeking is then performed on the embedded space and the approach preserves all the advantages of the original mean shift algorithm. Experiments on challenging synthetic and real data clearly demonstrate that significant improvements in clustering accuracy can be achieved by employing only a few constraints.