[2508.02330] A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps

Computer Science > Machine Learning arXiv:2508.02330 (cs) [Submitted on 4 Aug 2025 (v1), last revised 25 Mar 2026 (this version, v3)] Title:A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps Authors:Parth Naik, Harikrishnan N B View a PDF of the paper titled A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps, by Parth Naik and Harikrishnan N B View PDF HTML (experimental) 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 syntheti...