On Thursday, May 11th, the seminar series hosted a talk from Joshua Tobin, a postdoctoral researcher in Trinity College Dublin, discussing theoretical properties of the density peaks clustering algorithm and extensions to the peak-finding framework for clustering. Details for the talk are below.
Title
Consistent Mode-Finding for Parametric and Non-Parametric Clustering
Abstract
Density peaks clustering detects modes as points with high density and large distance to points of higher density. To cluster the observed samples, points are assigned to the same cluster as their nearest neighbor of higher density. This efficient and intuitive approach has, in recent years, grown in popularity in applications. Despite its widespread use, little work has been completed to understand the theoretical properties of the density peaks method, as well as its strengths and limitations when clustering. We prove that it recovers consistent estimates of the modes of the underlying density and correctly clusters the data with high probability. Deficiencies of the density peaks clustering method are also highlighted, notably how noise in the density estimates can lead to errors when estimating modes and incoherent cluster assignments.
An adaptation of the density peaks clustering approach is proposed to remedy these issues. The method detects modal sets rather than point modes in the data, thus reducing the sensitivity of the clusterings to fluctuations in the density estimate. The approach is analyzed theoretically and its superior performance is demonstrated.
Finally, motivated by the consistent estimates of the modes provided by the density peaks clustering algorithm, a novel model-based clustering algorithm is proposed. This approach uses a set of high density points as initial mean parameters, and iteratively prunes them to return a sequence of nested clusterings. The method outperforms popular model-based clustering methods.