Explicit Path CGR: Maintaining Sequence Fidelity in Geometric Representations

2025-09-22

AI Summary

Traditional Chaos Game Representation (CGR) suffers from information loss, preventing lossless reconstruction of the original biological sequence from its geometric trajectory. To address this, we propose Reversible CGR (R-CGR), the first fully invertible mapping within the CGR framework. R-CGR achieves reversibility through explicit path encoding, exact rational arithmetic, and a geometric trajectory inversion algorithm. It rigorously preserves both positional and symbolic information, yielding high-fidelity, interpretable geometric visualizations while enabling end-to-end deep learning feature extraction. Experimental evaluation on biological sequence classification tasks demonstrates that R-CGR matches the performance of state-of-the-art sequence models—such as Transformers and LSTMs—while uniquely supporting exact sequence reconstruction and human-interpretable visualization. By unifying theoretical soundness with practical utility, R-CGR establishes a new paradigm for geometric sequence representation that bridges interpretability, fidelity, and learnability.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Addressing sequence information loss in traditional geometric mapping methods
• Enabling perfect sequence reconstruction from geometric representations through encoding
• Providing interpretable geometric visualizations while maintaining complete sequence fidelity

Innovation

• Reverse-CGR with explicit path encoding
• Rational arithmetic precision for sequence recovery
• Complete path storage maintaining positional information