Chaotic Map based Compression Approach to Classification

TL;DR

This paper presents a novel, interpretable data classification method using chaotic maps for encoding, achieving competitive accuracy with simpler models compared to traditional machine learning approaches.

Contribution

It introduces a chaos-based compression classifier that reinterprets learning as encoding data via dynamical systems, offering a simpler and more interpretable alternative to complex models.

Findings

Achieves 92.98% accuracy on breast cancer dataset

Performance closely approaches traditional machine learning methods

Demonstrates the viability of chaos-based encoding for classification

Abstract

Modern machine learning approaches often prioritize performance at the cost of increased complexity, computational demands, and reduced interpretability. This paper introduces a novel framework that challenges this trend by reinterpreting learning from an information-theoretic perspective, viewing it as a search for encoding schemes that capture intrinsic data structures through compact representations. Rather than following the conventional approach of fitting data to complex models, we propose a fundamentally different method that maps data to intervals of initial conditions in a dynamical system. Our GLS (Generalized L\"uroth Series) coding compression classifier employs skew tent maps - a class of chaotic maps - both for encoding data into initial conditions and for subsequent recovery. The effectiveness of this simple framework is noteworthy, with performance closely approaching that of well-established machine learning methods. On the breast cancer dataset, our approach achieves 92.98\% accuracy, comparable to Naive Bayes at 94.74\%. While these results do not exceed state-of-the-art performance, the significance of our contribution lies not in outperforming existing methods but in demonstrating that a fundamentally simpler, more interpretable approach can achieve competitive results.