Kernels for visual words histograms

Abstract

Computer vision researchers have developed several learning methods based on the bag-of-words model for image related tasks, such as image retrieval or image categorization. For such an approach, images are represented as histograms of visual words from a codebook that is usually obtained with a simple clustering method. Next, kernel methods are used to compare such histograms. Popular choices, besides the linear SVM, are the intersection, Hellinger's, χ 2 and Jensen-Shannon kernels. This paper aims at introducing a kernel for histograms of visual words, namely the PQ kernel. This kernel is inspired from a class of similarity measures for ordinal variables, more precisely Goodman and Kruskals gamma and Kendalls tau. A proof that PQ is actually a kernel is also given in this work. The proof is based on building its feature map. Object recognition experiments are conducted to compare the PQ kernel with other state of the art kernels on two benchmark datasets. The PQ kernel has the best mean average precision (AP) on both datasets. In one of the experiments, PQ and Jensen-Shannon kernels are combined to improve the mean AP score even further. In conclusion, the PQ kernel can be used with success, alone or in combination with other kernels, for image retrieval, image classification or other related tasks. © 2013 Springer-Verlag.