Linear Convergence of the Subspace Constrained Mean Shift Algorithm: From Euclidean to Directional Data

Autor:	Zhang, Yikun, Chen, Yen-Chi
Rok vydání:	2021
Předmět:	Statistics - Machine Learning Mathematics - Optimization and Control Mathematics - Statistics Theory Statistics - Methodology 62G05 49Q12 62H11
Druh dokumentu:	Working Paper
Popis:	This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm. Comment: Substantial revision. The updated version has 93 pages, 12 figures, and 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.14977 Zobrazit plný text záznamu View this record from Arxiv