Theses

The task of this thesis was to build a system that can classify computer-solvable mathematical tasks into predefined mathematical categories. A few years ago, a com- pany named PhotoMath released its homonymous app that is able to output solution steps to the user after recognizing the mathematical task scanned with a mobile phone. They provided me with the data set and the idea for this project. Each mathematical category represents some area of mathematics. The categories are hierarchically related. Each task is represented by a corresponding solver tree. Solver tree is a tree that consists of steps which explain task resolution to the user. There were two main ideas to implement. The first approach consisted of mapping solver trees from each task in the data set to a vector in the feature space. Although this approach may not be optimal, the results are quite successful. The cause of that might be that our transformation to feature space encoded the tree structure into feature vectors to the right extent. In contrast, the second approach avoids operating on feature space directly and uses kernel methods. I have implemented two kernel functions and passed their reference to Support Vector Machine. The first kernel function calculated a kernel based on the string similarities between trees encoded as strings. This method proved even more successful than the first approach with mapping solver trees to the feature space. Later on, I implemented a kernel function that generates a kernel matrix based on common subpaths in solver trees. Despite my expectations, this proved to be much less efficient.