A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps

TL;DR

This paper introduces a new classification framework based on symbolic dynamics and data compression using chaotic maps, modeling classes with symbolic sequences and selecting the class with the most efficient symbolic encoding.

Contribution

It presents a novel dynamical systems approach to classification that leverages symbolic dynamics and compression, providing a new perspective beyond traditional machine learning methods.

Findings

Competitive performance on synthetic and real datasets

Effective modeling of classes with symbolic sequences from chaotic maps

Demonstrates the potential of dynamical systems in classification tasks

Abstract

We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are then evolved through a one-dimensional chaotic map. For each class, we compute the transition probabilities of symbolic patterns (e.g., `00', `01', `10', and `11' for the second return map) and aggregate these statistics to form a class-specific probabilistic model. During testing phase, the test data are thresholded and symbolized, and then encoded using the class-wise symbolic statistics via back iteration, a dynamical reconstruction technique. The predicted label corresponds to the class yielding the shortest compressed representation, signifying the most efficient symbolic encoding under its respective chaotic model. This approach fuses concepts from dynamical systems, symbolic representations, and compression-based learning. We evaluate the proposed method: \emph{ChaosComp} on both synthetic and real-world datasets, demonstrating competitive performance compared to traditional machine learning algorithms (e.g., macro F1-scores for the proposed method on Breast Cancer Wisconsin = 0.9531, Seeds = 0.9475, Iris = 0.8469 etc.). Rather than aiming for state-of-the-art performance, the goal of this research is to reinterpret the classification problem through the lens of dynamical systems and compression, which are foundational perspectives in learning theory and information processing.