  Sparse coding (Sc) has been studied very well as a powerful data
representation method. It attempts to represent the feature vector of a data
sample by reconstructing it as the sparse linear combination of some basic
elements, and a $L_2$ norm distance function is usually used as the loss
function for the reconstruction error. In this paper, we investigate using Sc
as the representation method within multi-instance learning framework, where a
sample is given as a bag of instances, and further represented as a histogram
of 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's
distance (EMD) instead of $L_2$ norm distance as a measure of the
reconstruction error. By minimizing the EMD between the histogram of a sample
and the its reconstruction from some basic histograms, a novel sparse coding
method is developed, which is refereed as SC-EMD. We evaluate its performances
as a histogram representation method in tow multi-instance learning problems
--- abnormal image detection in wireless capsule endoscopy videos, and protein
binding site retrieval. The encouraging results demonstrate the advantages of
the new method over the traditional method using $L_2$ norm distance.
