Gaussian Mean-Shift Is an EM Algorithm

The mean-shift algorithm, based on ideas proposed by Fukunaga and Hostetler (1975), is a hill-climbing algorithm on the density defined by a finite mixture or a kernel density estimate. Mean-shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision applications such as image segmentation or tracking. We show that, when the kernel is Gaussian, mean-shift is an expectationmaximisation (EM) algorithm, and when the kernel is non-gaussian, mean-shift is a generalised EM algorithm. This implies that mean-shift converges from almost any starting point and that, in general, its convergence is of linear order. For Gaussian mean-shift we show: (1) the rate of linear convergence approaches 0 (superlinear convergence) for very narrow or very wide kernels, but is often close to 1 (thus extremely slow) for intermediate widths, and exactly 1 (sublinear convergence) for widths at which modes merge; (2) the iterates approach the mode along the local...

• Type: Journal
• Year: 2007
• Where: PAMI
• Authors: Miguel Á. Carreira-Perpiñán
• Keywords: Algorithm, Convergence, Mean-shift, PAMI 2007