2014/06/06 by Yen‐Chi Chen, Chen, Yen-Chi, Christopher R. Genovese +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1406.1803
openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose a method for studying the geometric structure of generalized densities. In particular, we show how to find the modes and ridges of a generalized density function using a modification of the mean shift algorithm and its variant, subspace constrained mean shift. Our method can be used to perform clustering and to calculate a measure of connectivity between clusters. We establish consistency and rates of convergence for our estimator and apply the methods to data from two astronomical problems.