From Exponential to Efficient: A Novel Matrix-Based Framework for Scalable Medical Diagnosis

Modern diagnostic systems face computational challenges when processing exponential disease-symptom combinations, with traditional approaches requiring up to 2n evaluations for n symptoms. This paper presents MARS (Matrix-Accelerated Reasoning System), a diagnostic framework combining Case-Based Reasoning with matrix representations and intelligent filtering to address these limitations. The approach encodes disease-symptom relationships as matrices enabling parallel processing, implements adaptive rule-based filtering to prioritize relevant cases, and features automatic rule generation with continuous learning through a dynamically updated Pertinence Matrix. MARS was evaluated on four diverse medical datasets (41 to 721 diseases) and compared against Decision Tree, Random Forest, k-Nearest Neighbors, Support Vector Classifier, Bayesian classifiers, and Neural Networks. On the most challenging dataset (721 diseases, 49,365 test cases), MARS achieved the highest accuracy (87.34%) with substantially reduced processing time. When considering differential diagnosis, accuracy reached 98.33% for top-5 suggestions. These results demonstrate that MARS effectively balances diagnostic accuracy, computational efficiency, and interpretability, three requirements critical for clinical deployment. The framework’s ability to provide ranked differential diagnoses and update incrementally positions it as a practical solution for diverse clinical settings.