Explicit Path CGR: Maintaining Sequence Fidelity in Geometric Representations

Abstract: We present a novel information-preserving Chaos Game Representation (CGR) method, also called Reverse-CGR (R-CGR), for biological sequence analysis that addresses the fundamental limitation of traditional CGR approaches - the loss of sequence information during geometric mapping. Our method introduces complete sequence recovery through explicit path encoding combined with rational arithmetic precision control, enabling perfect sequence reconstruction from stored geometric traces. Unlike purely geometric approaches, our reversibility is achieved through comprehensive path storage that maintains both positional and character information at each step. We demonstrate the effectiveness of R-CGR on biological sequence classification tasks, achieving competitive performance compared to traditional sequence-based methods while providing interpretable geometric visualizations. The approach generates feature-rich images suitable for deep learning while maintaining complete sequence information through explicit encoding, opening new avenues for interpretable bioinformatics analysis where both accuracy and sequence recovery are essential.