Classification using intersection kernel support vector machines is efficient

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) with runtime complexity of the classifier logarithmic in the number of support vectors as opposed to linear for the standard approach. We further show that by precomputing auxiliary tables we can construct an approximate classifier with constant runtime and space requirements, independent of the number of support vectors, with negligible loss in classification accuracy on various tasks. This approximation also applies to 1 - chi <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and other kernels of similar form. We also introduce novel features based on a multi-level histograms of oriented edge energy and present experiments on various detection datasets. On the INRIA pedestrian dataset an approximate IKSVM classifier based on these features has the current best performance, with a miss rate 13% lower at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> False Positive Per Window than the linear SVM detector of Dalal & Triggs. On the Daimler Chrysler pedestrian dataset IKSVM gives comparable accuracy to the best results (based on quadratic SVM), while being 15times faster. In these experiments our approximate IKSVM is up to 2000times faster than a standard implementation and requires 200times less memory. Finally we show that a 50times speedup is possible using approximate IKSVM based on spatial pyramid features on the Caltech 101 dataset with negligible loss of accuracy.