Chaotic Map based Compression Approach to Classification

2025-02-17

AI Summary

To address the poor interpretability and high computational cost of complex machine learning models, this paper proposes an information compression classification framework grounded in chaotic dynamical systems. Methodologically, input data are mapped to initial-value intervals of a skewed tent map; compact, invertible representations are then generated via Generalized Lüroth Series (GLS) encoding, while class structure is modeled through sensitivity to initial conditions. The key contribution lies in the first integration of GLS encoding with chaotic maps for supervised classification—achieving a principled balance among model simplicity, intrinsic interpretability, and discriminative power. Evaluated on the breast cancer dataset, the method attains 92.98% accuracy, comparable to Naïve Bayes (94.74%), thereby demonstrating that this minimalist chaotic encoding paradigm effectively reconciles predictive performance with transparency.

Technology Category

• Machine Learning: Learning with Manifolds
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Representation Learning for Vision

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Simplifies complex machine learning models
• Enhances interpretability through chaotic maps
• Achieves competitive classification accuracy

Innovation

• Chaotic map encoding
• Dynamical system intervals
• Skew tent maps