Learning parameterized histogram kernels on the simplex manifold for image and action classification

State-of-the-art image and action classification systems often employ vocabulary-based representations. The classification accuracy achieved with such vocabulary-based representations depends significantly on the chosen histogram-distance. In particular, when the decision function is a support-vector-machine (SVM), the classification accuracy depends on the chosen histogram kernel. In this paper we focus on smoothly-parameterized kernels in the space of histograms, such as, but not limited to, kernels that are derived from smoothly-parameterized histogram-distance functions. We learn parameters of histogram kernels so that the SVM accuracy is improved. This is accomplished by simultaneously maximizing the SVM's geometric margin and minimizing an estimate of its generalization error. We validate our approach on a previously-published two-class synthetic dataset and three real-world multi-class datasets: Oxford5K, KTH, and UCF. On these datasets our approach yields results that compare favorably to or exceed the state of the art.