We present a novel scale adaptive, non-parametric approach to clustering point patterns. Clusters are detected by moving all points to their cluster cores using shift vectors. First, we propose a novel scale selection criterion based on local density isotropy which determines the neighborhoods over which the shift vectors are computed. We then construct a directed graph induced by these shift vectors. Clustering is obtained by simulating random walks on this digraph. We also examine the spectral properties of a similarity matrix obtained from the directed graph to obtain a K-way partitioning of the data. Additionally, we use the eigenvector alignment algorithm of [1] to automatically determine the number of clusters in the dataset.

• S. Shetty and N. Ahuja, Supervised and Unsupervised Clustering with Probabilistic Shift, European Conference on Computer Vision (ECCV), Crete, Greece, September 2010.
• S. Shetty and N. Ahuja, A Uniformity Criterion and Algorithm for Data Clustering, International Conference on Pattern Recognition (ICPR), Tampa, FL, December 2008.