Technical Report: Learning to Rank using High-Order Information

The problem of ranking a set of visual samples according to their relevance to a query plays an important role in computer vision. The traditional approach for ranking is to train a binary classifier such as a support vector machine (svm). Binary classifiers suffer from two main deficiencies: (i) they do not optimize a ranking-based loss function, for example, the average precision (ap) loss; and (ii) they cannot incorporate high-order information such as the a priori correlation between the relevance of two visual samples (for example, two persons in the same image tend to perform the same action). We propose two novel learning formulations that allow us to incorporate high-order information for ranking. The first framework, called high-order binary svm (hob-svm), allows for a structured input. The parameters of hob-svm are learned by minimizing a convex upper bound on a surrogate 0-1 loss function. In order to obtain the ranking of the samples that form the structured input, hobsvm sorts the samples according to their max-marginals. The second framework, called high-order average precision svm (hoap-svm), also allows for a structured input and uses the same ranking criterion. However, in contrast to hob-svm, the parameters of hoap-svm are learned by minimizing a difference-of-convex upper bound on the ap loss. Using a standard, publicly available dataset for the challenging problem of action classification, we show that both hob-svm and hoap-svm outperform the baselines that ignore high-order information.