Visual Analysis of Dispersion of Multidimensional Scattered Data - Janusz OPILA (Communications of International Proceedings, 2025)
One of the goals of data dispersion analysis is the determination of the empirical probability density function based on the sampled data. The paper presents a critical discussion of four methods of analysis of the dispersion of multivariate data in the sample: classical histogram, ”inverted histogram”, ”smoothed histogram” based on the kernel density estimation function (KDE) with the Gaussian kernel, and the newly developed and hereby proposed KDE with ”algorithmic kernel” based on local density approach (aKDE). The purpose of the work is to inspect the strengths and weaknesses of the methods under consideration. In particular, the hypothesis is verified that the proposed method, aKDE, is an acceptable alternative to more classic methods. The considerations are illustrated by calculations and graphs made on samples drawn from the mixed multivariate correlated distribution for one, two, and three dimensions.
Keywords: KDE; algorithmic kernel; data visualization; data dispersion