Parzen Windows classifiers have been applied to a variety of density estimation as well as classification tasks with considerable success. Parzen Windows are known to converge in the asymptotic limit. However, there is a lack of theoretical analysis on their performance with finite samples. In this paper we show a connection between Parzen Windows and the regularized least squares algorithm, which has a well-established foundation in computational learning theory. This connection allows us to provide useful insight into Parzen Windows classifiers and their performance in finite sample settings. Finally, we show empirical results on the performance of Parzen Windows classifiers using a number of real data sets.