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Dictionary plays an important role in multi-instance data representation. Itmaps bags of instances to histograms. Earth mover's distance (EMD) is the mosteffective histogram distance metric for the application of multi-instanceretrieval. However, up to now, there is no existing multi-instance dictionarylearning methods designed for EMD based histogram comparison. To fill this gap,we develop the first EMD-optimal dictionary learning method using stochasticoptimization method. In the stochastic learning framework, we have one tripletof bags, including one basic bag, one positive bag, and one negative bag. Thesebags are mapped to histograms using a multi-instance dictionary. We argue thatthe EMD between the basic histogram and the positive histogram should besmaller than that between the basic histogram and the negative histogram. Baseon this condition, we design a hinge loss. By minimizing this hinge loss andsome regularization terms of the dictionary, we update the dictionaryinstances. The experiments over multi-instance retrieval applications shows itseffectiveness when compared to other dictionary learning methods over theproblems of medical image retrieval and natural language relationclassification.

Stochastic Learning of Multi-Instance Dictionary for Earth Mover's Distance based Histogram Comparison