Parabolic Weighting Mechanism in Information Retrieval: A Mathematical Analogy to Lenz’s Law

Abstract

Conventional term-weighting techniques in information retrieval, such as term frequency-inverse document frequency and the probabilistic ranking framework, often place excessive emphasis on extreme term frequencies, which can distort document ranking. Inspired by Lenz’s Law in electromagnetism, which naturally resists sudden fluctuations in magnetic flux, this work introduces a novel parabolic weighting mechanism. By applying a parabolic function to reduce the impact of excessively frequent terms while enhancing moderately occurring words, the proposed method achieves a balanced contribution of term frequency. The mathematical formulation promotes equilibrium in term weighting by integrating term frequency with inverse document frequency. Experiments conducted on benchmark datasets, including BBC News and 20 Newsgroups, demonstrate that the parabolic weighting mechanism outperforms traditional techniques, yielding measurable improvements in accuracy with classification models such as the support vector classifier (0.44 percent increase) and logistic regression (0.30 percent increase). Furthermore, statistical validation using Cohen’s effect size measure confirms the significance of performance improvements, while bootstrap analysis ensures the reliability of the observed gains. These results establish a strong foundation for future integration with neural information retrieval models and highlight the potential of the proposed approach in domain-specific applications, such as legal document analysis and biological literature search.