Clustering online handwritten mathematical expressions

Abstract To help human markers mark many answers in the form of online handwritten mathematical expressions (OHMEs), this paper proposes bag-of-features for clustering OHMEs. It consists of six levels of features from low-level pattern features to high-level symbolic and structural features obtained from a state-of-the-art OHME recognizer. Then, it introduces distance-based representation (DbR) to reduce the dimensionality of our proposed feature spaces. Moreover, it presents a method for combining the proposed features to improve the performance. Experiments using the k-means++ algorithm are conducted on a set of 3,150 OHMEs (Dset_50) and an answer dataset (Dset_Mix) of 200 OHMEs intermixed between real patterns and synthesized patterns for each of 10 questions. When the number of clusters is set as the true number of categories, the best purity around 0.99 is produced by bag-of-symbols with DbR for Dset_50, which is better than state-of-the-art methods for clustering offline patterns converted from their OHMEs. The combination of both low-level and high-level features with DbR achieves a purity of around 0.777, increases to more than 0.90 and reduce the marking cost by more than 0.35 point than manually marking OHME answers by adjusting the number of clusters for Dset_Mix.