Straightforward classification using kernelized SVMs requires evaluating the kernel for a test vector and each of the support vectors. For a class of kernels we show that one can do this much more efficiently. In particular we show that one can build histogram intersection kernel SVMs (IKSVMs

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, which is time consuming. In this paper, we propose a novel approach for learning non-linear SVM corresponding to the histogram intersection kernel without using the kernel trick. We formulate the exact non-linear problem in the original space and show how to perform classification directly in this space

usual images contain sev-eral millions of pixel, the use of kernel-based methods for the task of semantic segmentation is limited due to the involved computation times. In this paper, we over-come this drawback by exploiting efficient kernel calcu-lations using the histogram intersection kernel for fast

for correspondences – generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function which maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in this space. This “pyramid match” computation is linear

Abstract. An important advantage of Gaussian processes is the ability to directly estimate classification uncertainties in a Bayesian manner. In this paper, we develop techniques that allow for estimating these un-certainties with a runtime linear or even constant with respect to the number of training examples. Our approach makes use of all training data without any sparse approximation technique while needing only a linear amount of memory. To incorporate new information over time, we further derive online learning methods leading to significant speed-ups and allowing for hyperparameter optimization on-the-fly. We conduct several experiments on public image datasets for the tasks of one-class classification and active learning, where computing the uncertainty is an essential task. The experimental results highlight that we are able to compute classification uncertainties within microseconds even for large-scale datasets with tens of thousands of training examples. 1

Measuring image similarity is a central topic in computer vision. In this paper, we learn similarity from Flickr groups and use it to organize photos. Two images are similar if they are likely to belong to the same Flickr groups. Our approach is enabled by a fast Stochastic Intersection Kernel

that the Histogram Intersection Kernel (HIK) is more effective than the Euclidean distance in supervised learning tasks with histogram features. In this paper, we demonstrate that HIK can also be used in an unsupervised manner to significantly improve the generation of visual codebooks. We propose a histogram kernel

Maji and Berg [13] have recently introduced an explicit feature map approximating the intersection kernel. This enables efficient learning methods for linear kernels to be applied to the non-linear intersection kernel, expanding the applicability of this model to much larger problems. In this paper

Let ~ be a t-wise s-intersecting family, i.e., [F a N" " N F t I> s holds for every t members of ~¢~. Then there exists a set Y such that I Fx N.'- N F, N Y [ _> _ s still holds for every Fl..... F, e ~. Here exponential lower and upper bounds are proven for the possible sizes