Sparse coding with earth mover’s distance for multi-instance histogram representation

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 $$L_2$$L2 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 $$L_2$$L2 norm distance is not suitable, and propose to use the earth mover’s distance (EMD) instead of $$L_2$$L2 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 $$L_2$$L2 norm distance.