José E. Chacón

TL;DR: It is shown that only mild conditions on a sequence of density estimators are needed to ensure that the sequence of modal clusterings that they induce is consistent and two new loss functions are presented, applicable in fact to any clustering methodology, to evaluate the performance of a data-based clustering algorithm with respect to the ideal population goal.

TL;DR: In this article, the authors provide an explicit formulation for the ideal population goal of the modal clustering methodology, which understand clusters as regions of high density, and present two new loss functions, applicable in fact to any clustering methodologies, to evaluate the performance of a data-based clustering algorithm with respect to the desired population goal, where mild conditions on a sequence of density estimators are needed to ensure that the sequence of modal clusterings that they induce is consistent.

TL;DR: A survey of the traditional approaches to mode estimation and the consequences of applying this modern modal methodology to other, seemingly unrelated, fields can be found in this paper, where an extensive survey is presented.

TL;DR: Two methods to adopt a modal clustering point of view after a mixture model fit are introduced and it is shown that mixture modeling can also be used for clustering in a nonparametric sense, as long as clusters are understood as the domains of attraction of the density modes.