Chapters authored
Novel Formulation of Parzen Data Analysis
The Parzen analysis associates Gaussian kernels with each data point, thus obtaining a density function which may be viewed as a possible artificial generator of the data. This probability function can be decomposed into the product of two components, weight (W) and shape (S), which represent different aspects of the data. We demonstrate how this naturally leads to a formalism of fields in data space, which are interconnected through relations in one-dimensional scale space, corresponding to the common Gaussian width. We discuss the connection of this formalism to different clustering procedures such as quantum clustering (QC) and mean shift (MS). We demonstrate on various examples the importance of these concepts in the analysis of natural data as well as in image analysis in two or three dimensions.
Part of the book: Pattern Recognition