HMM-Based Recognition of Online Handwritten Mathematical Symbols Using Segmental K-Means Initialization and a Modified Pen-Up/Down Feature

This paper presents a recognition system based on Hidden Markov Model (HMM) for isolated online handwritten mathematical symbols. We design a continuous left to right HMM for each symbol class and use four online local features, including a new feature: normalized distance to stroke edge. A variant of segmental K-means is used to get initialization of the Gaussian Mixture Models´ parameters which represent the observation probability distribution of the HMMs. The system obtains top-1 recognition rate of 82.9% and top-5 recognition rate of 97.8% on a dataset containing 20281 training samples and 2202 testing samples of 93 classes of symbols. For multi-stroke symbols, the top-1 recognition rate is 74.7% and the top-5 recognition rate is 95.5%. For single-stroke symbols, the top-1 recognition rate is 86.8% and the top-5 recognition rate is 98.9%. (MacLean et al., 2010) applied dynamic time warping algorithm on all the 70 classes of single-stroke symbols. Their top-1 recognition rate is 85.8%, and top-5 recognition rate is 97.0%. Our system gets top-1 recognition rate of 85.5% and top-5 recognition rate of 99.1% on the same 70 classes of single-stroke symbols.