Prediction of Mathematical Expression Declarations based on Spatial, Semantic, and Syntactic Analysis

Mathematical expressions (ME) and words are carefully bonded together in most science, technology, engineering, and mathematics (STEM) documents. They respectively give quantitative and qualitative descriptions of a system model under discussion. This paper proposes a general model for finding the co-reference relations between words and MEs, based on which we developed a novel algorithm for predicting the natural language declarations of MEs-the ME-Dec. The prediction algorithm is applied in a three-level framework, where the first level is a customized tagger to identify the syntactic roles of MEs and the part-of-speech (POS) tags of words in the ME-word mixed sentences. The second level screens the ME-Dec candidates based on the hypothesis that most ME-Dec are noun phrases (NP). A shallow chunker is trained from the fuzzy process mining algorithm, which uses the labeled POS tag series in the NTCIR-10 dataset as input to mine for the frequent syntactic patterns of NP. In the third level, using distance, word stem, and POS tag respectively as the spatial, semantic, and syntactic features, the bonding model between MEs and ME-Dec candidates is trained on the NTCIR-10 training set. The final prediction results are made upon the majority votes of an ensemble of Naive Bayesian classifiers based on the three features. Evaluation of the model on the NTCIR-10 test set, the proposed algorithm achieved 75% and 71% average F1 score in soft matching and strict matching, respectively, which outperforms the state-of-the-art solutions by a margin of 5-18%.(1)