Modal-set estimation with an application to clustering
This addresses the problem of identifying complex density structures in noisy data for clustering tasks, though it appears incremental as it builds on existing modal-set concepts.
The paper introduces a procedure for estimating all local maxima (modal-sets) of a density with statistical consistency guarantees, applicable to various shapes and dimensions, and demonstrates its competitiveness in clustering applications with stability across tuning parameters.
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to better model the rich variety of locally-high-density structures in data. The procedure is then shown to be competitive on clustering applications, and moreover is quite stable to a wide range of settings of its tuning parameter.