Research On Geometric Mathematical Problems Similarity Measurement Method Based On Logical Relation Modeling

Against the background of Big Data and nationally educational informatization,there is already a large number of mathematical problem resources on the Internet.The mathematical problems similarity measurement is the key technology to accurately retrieve the required mathematical problems from these resources.Existing mathematical problem retrieval applications are mainly based on the text similarity measurement,without considering the logical relation of the mathematical problem and the diagram of the geometric problem.Although sentences with the same meaning in mathematical problems would have different natural language expressions,the logical relation is consistent.In addition,the diagram information of geometric mathematical problems should also be included in the similarity measurement.Therefore,mathematical problems similarity measurement focusing on logical relation and diagram has important research significance and application value.The feature representation of problems required for mathematical problems similarity measurement can be obtained by automatic understanding of mathematical problems.We model automatic understanding of mathematical problems as the task of logical diagram element extraction,where the elements in the logical diagram include mathematical entities and logical relations between entities.The research mainly consists of two parts.First,because the logical relations of mathematical problems are generally expressed by logical feature words directly or indirectly,this study proposes a method for logical diagram element extraction of mathematical problems based on the attention enhancement of logical feature words.In the training phase,logical feature words are adopted to guide the learning of the weight parameters in the attention layer,so words that have a strong correlation with mathematical logical relation would automatically obtain greater attention weight.Our experimental results on mathematical problem datasets show that our method is superior to several baselines in terms of precision,recall,and F1-score for logical relation extraction.Besides,diagrams of geometric mathematical problems would contain information missing from the text description.We propose a method for mathematical problems similarity measurement that combines text and diagram bimodal information.We identify the geometric units and geometric relations in the diagrams,and then check the consistency with the text information,finally filter out the geometric relations with high confidence.Based on relation modeling,we transform mathematical problems similarity measurement into logical diagram elements similarity measurement and propose a method for logical relations similarity measurement.We select the geometric mathematical problem dataset containing diagram for testing,and the results show that the text and diagram bimodal method combined with diagram information has improved accuracy,recall,and F1-score by 6.8%,as compared with the text unimodal method.Based on the above research,we have implemented a similar mathematical problems retrieval tool.Compared with other applications,our tool is based on the logical relations of mathematical problems and combines text and diagram information for retrieval.The tool can handle mathematical problems with the same meaning but different expressions or containing diagram information,so it can match similar problems more accurately from the massive problem database.