Point Information Gain and Multidimensional Data Analysis
Renata Rycht\'arikov\'a, Jan Korbel, Petr Mach\'a\v{c}ek, Petr, C\'isa\v{r}, Jan Urban, Dmytro Soloviov, Dalibor \v{S}tys
TL;DR
This paper extends the concept of Point Information Gain and related entropy measures to Re9nyi entropy, applying them to analyze multidimensional datasets and demonstrating their properties on real image data.
Contribution
It introduces a generalized framework for Point Information Gain using Re9nyi entropy and applies it to multidimensional data analysis, showcasing its utility on real images.
Findings
PIE/PIED spectra reveal key data properties
Method effectively analyzes multidimensional datasets
Potential applications in various data processing fields
Abstract
We generalize the Point information gain (PIG) and derived quantities, i.e. Point information entropy (PIE) and Point information entropy density (PIED), for the case of R\'enyi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss possible further utilization in other fields of data processing.
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