Graph matching over Hypothesis Graphs for the Analysis of Handwritten Arithmetic Operations

This paper presents a preliminary research work for the analysis of handwritten arithmetic operations in the context of e-education. Given a mathematical exercise, an answer in the form of an arithmetical operation is expected from a child. This answer can be represented by a graph containing both expected numbers and their corresponding relationship one to another. We propose to compute several hypotheses Fuzzy Visibility Graph of symbols over a child\u0027s input. The widely used A* algorithm to compute exact graph edit distance is applied over those graphs to match the expected answer. To reduce the search complexity, simplified graphs of operands are first generated and used. Each operand is a sub-graph of the original graph, the algorithm is then applied on the pairs of matched sub-graphs. The hypothesis graph with the smallest graph edit distance with the expected graph and the matched differences can be used to produce an adapted feedback. The result of an experiment over a given example is presented.