Anisotropic mean shift clustering using distance metric learning

Abstract

Mean shift is a non-parametric mode seeking procedure widely used in many computer vision problems. Mean shift clustering in particular is a well studied and established algorithm, which has many merits over the classic k-means clustering algorithm. These algorithms repeatedly calculate distance between data points to compute mean shift vector and cluster mean respectively using some distance function. In most of the cases, Euclidean distance function is used which weighs every dimension equally in the input space and thus often fails to capture the semantics of the data. To alleviate this problem, a general form of distance metric based on Mahalanobis distance is used that can be learned using the training data. Distance metric learning has received a lot of attention in recent years and has proven to be very successful in various problem domains. By learning a Mahalanobis distance metric, the input space is transformed such that, similar points get closer to each other and dissimilar points move further apart. A lot of research has been done on learning a global metric and integrating it with k-means algorithm, but there have been very few efforts of integrating metric learning with mean shift clustering. This work focuses on developing a unified framework for improving mean shift clustering by using global and local metric learning. We use a recently proposed Sparse Compositional Metric Learning (SCML) framework and integrate it with mean shift clustering to investigate the affect of using local metrics over a global metric. We also perform kernelization in the proposed framework that can handle datasets with non-linear decision boundaries. To establish the effectiveness of our approach, we performed experiments on 6 datasets of varying difficulty.