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Sparse coding (Sc) has been studied very well as a powerful datarepresentation method. It attempts to represent the feature vector of a datasample by reconstructing it as the sparse linear combination of some basicelements, and a $L_2$ norm distance function is usually used as the lossfunction for the reconstruction error. In this paper, we investigate using Scas the representation method within multi-instance learning framework, where asample is given as a bag of instances, and further represented as a histogramof the quantized instances. We argue that for the data type of histogram, using$L_2$ norm distance is not suitable, and propose to use the earth mover'sdistance (EMD) instead of $L_2$ norm distance as a measure of thereconstruction error. By minimizing the EMD between the histogram of a sampleand the its reconstruction from some basic histograms, a novel sparse codingmethod is developed, which is refereed as SC-EMD. We evaluate its performancesas a histogram representation method in tow multi-instance learning problems--- abnormal image detection in wireless capsule endoscopy videos, and proteinbinding site retrieval. The encouraging results demonstrate the advantages ofthe new method over the traditional method using $L_2$ norm distance.

Sparse Coding with Earth Mover's Distance for Multi-Instance Histogram Representation