Categorical Exploratory Data Analysis: From Multiclass Classification and Response Manifold Analytics Perspectives of...

Area of Science:

• Data Science
• Machine Learning
• Statistical Analysis

Background:

• All data features possess an inherent categorical nature, observable through histograms.
• Feature associations can be quantified using contingency tables and rescaled conditional Shannon entropies.
• A heatmap of mutual associations serves as a roadmap for understanding feature relationships.

Purpose of the Study:

• To introduce Categorical Exploratory Data Analysis (CEDA), a novel data analysis paradigm.
• To apply CEDA to multiclass classification (MCC) and response manifold analytics (RMA).
• To compute visible and explainable information content with multiscale and heterogeneous structures.

Main Methods:

• Developing CEDA based on a heatmap of feature mutual associations.
• Utilizing histograms and contingency tables to determine feature associations.
• Applying CEDA to MCC using label embedding trees and indirect distance measures.
• Employing CEDA for RMA by analyzing multi-dimensional manifolds and identifying categorical localities.

Main Results:

• CEDA provides new resolutions for MCC and RMA.
• The method reveals asymmetric mixing geometries in high-dimensional point-clouds for MCC.
• RMA identifies major and minor effects within multi-dimensional manifolds.
• Information content and predictive inferences are computed for both MCC and RMA.

Conclusions:

• CEDA offers a robust framework for exploring categorical data structures.
• The approach enhances understanding of complex data relationships and system dynamics.
• CEDA demonstrates practical applications in diverse datasets, including Iris and PITCHf/x data.