Journal Article

The art of misclassification: too many classes, not enough points

Fernández, Nelson, Gershenson, Carlos, Febres, Gerardo, Franco, Mario

2025

Overview

Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is ultimately constrained by the intrinsic properties of datasets, independently of computational power or model complexity. In this work, we introduce a formal entropy-based measure of classifiability, which quantifies the inherent difficulty of a classification problem by assessing the uncertainty in class assignments given feature representations. This measure captures the degree of class overlap and aligns with human intuition, serving as an upper bound on classification performance for classification problems. Our results establish a theoretical limit beyond which no classifier can improve the classification accuracy, regardless of the architecture or amount of data, in a given problem. Our approach provides a principled framework for understanding when classification is inherently fallible and fundamentally ambiguous.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: Accuracy / Artificial intelligence / Classification / Classification limits / Complexity / Computer Appl. in Social and Behavioral Sciences / Computer Science / Data limits / Data-driven Science / Datasets / Entropy-based measure / Machine learning / Modeling and Theory Building / Neural networks / Smarter Cities and Societies: What We Can and Cannot Optimize For / Upper bounds