ABSTRACT
This chapter focuses on more complex data analysis applications in which density and density derivative estimators are crucial components. It covers the estimation of the level sets of a density function: high threshold level sets are used in modal region estimation and bump-hunting, and low threshold sets for density support estimation. The chapter examines cluster analysis where the clusters are identified as the basins of attractions of the density gradient to local data density modes. It introduces the ridges of the density function, since they are based on the eigenvector decomposition of the density Hessian, as a tool for analysing filamentary data. The chapter places density curvature estimators into a formal inference framework to delimit significantly data dense regions, which offers an alternative to the level sets of the data density for modal region estimation. Mean shift clustering is a clustering algorithm designed to estimate the population modal clustering defined through stable manifolds.
