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Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle.

Francisco J Valverde-Albacete¹, Carmen Peláez-Moreno¹

¹Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganés 28911, Spain.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study introduces an information-theoretic model to evaluate machine learning data transformations. It uses entropy diagrams to visualize and quantify information transfer efficiency for feature selection methods like PCA and ICA.

Keywords:

Shannon-type relations data transformation entropy balance equation entropy, entropy visualization machine learning evaluation multivariate analysis

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Area of Science:

Machine Learning
Information Theory
Data Science

Background:

Data transformation is crucial for machine learning.
Assessing the quality of these transformations, especially in unsupervised settings, remains challenging.
Existing methods may not fully capture the information flow during transformation.

Purpose of the Study:

To develop an information-theoretic framework for assessing data transformation quality.
To introduce novel tools, including entropy diagrams, for visualizing and quantifying information transfer.
To provide a method for evaluating unsupervised feature transformation and selection techniques.

Main Methods:

Decomposition of maximal potential entropy into transferable and non-transferable parts.
Representation of these decompositions using de Finetti entropy diagrams.
Application to analyze information transfer in Principal Component Analysis (PCA) and Independent Component Analysis (ICA).

Main Results:

A balance equation is derived to partition information potential.
The aggregate channel multivariate entropy triangle serves as a visual tool for assessing transformation effectiveness.
Entropy triangles are generated for input and output variables to analyze information flow.

Conclusions:

The proposed information-theoretic model and tools offer a robust method for evaluating data transformations.
Entropy diagrams provide intuitive insights into information transfer efficiency.
The framework is applicable to common unsupervised feature selection methods in machine learning.