Modal Clustering: Past and Present

Music City Center 

The lecture will cover some of the major developments of modal clustering since its inception in the 1970s. Modal clustering — which encompasses much of what is understood by nonparametric clustering — emerged out of the contemporary work of Keinosuke Fukunaga and John Hartigan, work that gave rise to research around the mean shift algorithm and related procedures, as well as into level set estimation and the estimation of modes. The lecture will include some of our own work: a bridge between Fukunaga and Hartigan's definitions of clustering; an axiomatic foundation for Hartigan's definition of (hierarchical) clustering; and some consistency results for the mean shift algorithm and variants.