Dimension Amnesic Pyramid Match Kernel

With the success of local features in object recognition, feature-set representations are widely used in computer vision and related domains. Pyramid match kernel (PMK) is an efficient approach to quantifying the similarity between two unordered feature-sets, which allows well established kernel machines to learn with such representations. However, the approximation of PMK to the optimal feature matches deteriorates linearly with the dimension of local features, which prohibits the direct use of high dimensional features. In this paper, we propose a general, data-independent kernel to quantify the feature-set similarities, which gives an upper bound of approximation error independent of the dimension of local features. The key idea is to employ the technique of normal random projection to construct a number of low dimensional subspaces, and perform the original PMK algorithm therein. By leveraging on the invariance property of p-stable distributions, our approach achieves the desirable dimension-free property. Extensive experiments on the ETH-80 image database solidly demonstrate the advantage of our approach to high dimensional features.