A multi-dimensional similarity scoring function for mathematical information retrieval

Similarity measurement plays a important role in mathematical information retrieval (MIR), where measuring the similarity between two entities or mathematical formulas is important for effective search and knowledge discovery. The existing similarity metrics, although widely used in text and data mining applications, often fail to capture the structural, semantic, and contextual relationships that are intrinsic to mathematical information. Most existing approaches primarily depend on surface-level lexical matching or vector-based distance computations, which limits their ability to represent the hierarchical structure of formulas, the semantic equivalence of expressions, and contextual dependencies within mathematical information. This paper systematically implemented and mathematically formulated 17 widely used similarity measurement metrics on mathematical formulas and demonstrate their mathematical modeling. This mathematical modeling reveals that existing metrics inadequately address the combined influence of structural organization, semantic meaning, and contextual relevance in mathematical information. To overcome these limitations, we propose a multi-dimensional similarity scoring function that integrates four core pillars: structural similarity, semantic similarity, contextual similarity and differential divergence. The proposed similarity scoring function assigns adaptive weights to each component and computes a unified similarity score that more accurately reflects the true relationship between mathematical information. The experimental results and analysis shows that the proposed similarity scoring function provides improved performance compared to existing similarity measurement metrics.