Fast Mean Shift with Accurate and Stable Convergence

Mean shift is a powerful but computationally expensive method for nonparametric clustering and optimization. It iteratively moves each data point to its local mean until convergence. We introduce a fast algorithm for computing mean shift based on the dual-tree. Unlike previous speed-up attempts, our algorithm maintains a relative error bound at each iteration, resulting in significantly more stable and accurate convergence. We demonstrate the benefit of our method in clustering experiments with real and synthetic data.