Parzen windows: Simplest regularization algorithm

Nonparametric learning methods such as Parzen Windows have been applied to a variety of density estimation and classification problems. In this chapter we derive a "simplest" regularization algorithm and establish its close relationship with Parzen Windows. We derive the finite sample error bound for the "simplest" regularization algorithm. Because of the close relationship between the "simplest" algorithm and Parzen Windows, this analysis provides interesting insight to Parzen Windows from the view point of learning theory. Our work is a realization of the design principle of dynamic data driven applications system (DDDAS) introduced in Chapter 1. Finally, we provide empirical results on the performance of the "simplest" regularization algorithm (Parzen Windows) and other methods such as nearest neighbor classifiers, and the regularization algorithm on a number of real data sets. These results corroborate well our theoretical analysis.