Point Information Gain and Multidimensional Data Analysis
arXiv:1501.02891 · doi:10.3390/e18100372
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 Rényi 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.
arXiv comment16 pages, 6 figures
References in corpus (11)
- Rényi Divergence and Kullback-Leibler Divergence
- Computational Mechanics: Pattern and Prediction, Structure and Simplicity
- Renyi's information transfer between financial time series
- Quantifying Self-Organization with Optimal Predictors
- A Characterization of Entropy in Terms of Information Loss
- On observability of Renyi's entropy
- Interpretations of Renyi Entropies And Divergences
- On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
- Multifractal Diffusion Entropy Analysis: Optimal Bin Width of Probability Histograms
- Entropy algebras and Birkhoff factorization
- The world according to Renyi: Thermodynamics of multifractal systems