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.