Object Classification using pyramid match kernel
The pyramid match kernel does not operate on the sets of feature vectors directly.  It operates on multi-level histograms of feature vectors. Let's say you are using the SIFT descriptors, which live in 128-dimensional space.  First you divide each dimension into 2 bins, which divides the entire feature space into $2^{128}$ bins. Then you count how many features fall into each bin.  This is the first level of your histogram.  Then you divide each dimension into 4 bins, and so on. Luckily, this histogram is going to be very sparse, so you only need to allocate the memory for non-zero bins.

You do this for the training images, and the images that you want to classify.  Then the pyramid match kernel is simply the intersection of two histograms.