caa a22 4500 605477981 CHVBK 20210128100403.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10994-014-5435-2 doi (NATIONALLICENCE)springer-10.1007/s10994-014-5435-2 AliyariGhassabeh Youness Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada aut Asymptotic stability of equilibrium points of mean shift algorithm [Elektronische Daten] [Youness AliyariGhassabeh] The mean shift (MS) algorithm is a popular non-parametric technique that has been widely used in statistical pattern recognition and machine learning. The algorithm iteratively tries to find modes of an estimated probability density function. These modes play an important role in many applications, such as clustering, image segmentation, feature extraction, and object tracking. The modes are fixed points of a discrete, nonlinear dynamical system. Although the algorithm has been successfully used in many applications, a theoretical study of its convergence is still missing in the literature. In this paper, we first consider the iteration index as a continuous variable and, by introducing a Lyapunov function, show that the equilibrium points are asymptotically stable. We also show that the proposed function can be considered as a Lyapunov function for the discrete case with the isolated stationary points. The availability of a Lyapunov function for continuous and discrete cases shows that if the MS iterations start in a neighborhood of an equilibrium point, the generated sequence remains close to that equilibrium point and finally converges to it. The Author(s), 2014 Mean shift algorithm nationallicence Lyapunov function nationallicence Mode estimate sequence nationallicence Asymptotically stable nationallicence Convex function nationallicence Equilibrium point nationallicence Fixed point nationallicence Machine Learning Springer US; http://www.springer-ny.com 98/3(2015-03-01), 359-368 0885-6125 98:3<359 2015 98 10994 https://doi.org/10.1007/s10994-014-5435-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-014-5435-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- AliyariGhassabeh Youness Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 98/3(2015-03-01), 359-368 0885-6125 98:3<359 2015 98 10994