@article{Ding_Xu_2014, title={Finding Median Point-Set Using Earth Mover’s Distance}, volume={28}, url={https://ojs.aaai.org/index.php/AAAI/article/view/8985}, DOI={10.1609/aaai.v28i1.8985}, abstractNote={ <p> In this paper, we study a prototype learning problem, called Median Point-Set, whose objective is to construct a prototype for a set of given point-sets so as to minimize the total Earth Mover’s Distances (EMD) between the prototype and the point-sets, where EMD between two point-sets is measured under affine transformation. For this problem, we present the first purely geometric approach. Comparing to existing graph-based approaches (e.g., median graph, shock graph), our approach has several unique advantages: (1) No encoding and decoding procedures are needed to map between objects and graphs, and therefore avoid errors caused by information losing during the mappings; (2) Staying only in the geometric domain makes our approach computationally more efficient and robust to noise. We evaluate the performance of our technique for prototype reconstruction on a random dataset and a benchmark dataset, handwriting Chinese characters. Experiments suggest that our technique considerably outperforms the existing graph-based methods. </p> }, number={1}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Ding, Hu and Xu, Jinhui}, year={2014}, month={Jun.} }