Simultaneous Ground Metric Learning and Matrix Factorization with Earth Mover´s Distance

Non-negative matrix factorization is widely used in pattern recognition as it has been proved to be an effective method for dimensionality reduction and clustering. We propose a novel approach for matrix factorization which is based on Earth Mover´s Distance (EMD) as a measure of reconstruction error. Differently from previous works on EMD matrix decomposition, we consider a semi-supervised learning setting and we also propose to learn the ground distance parameters. While few previous works have addressed the problem of ground distance computation, these methods do not learn simultaneously the optimal metric and the reconstruction matrices. We demonstrate the effectiveness of the proposed approach both on synthetic data experiments and on a real world scenario, i.e. addressing the problem of complex video scene analysis in the context of video surveillance applications. Our experiments show that our method allows not only to achieve state-of-the-art performance on video segmentation, but also to learn the relationship among elementary activities which characterize the high level events in the video scene.