Pyramid Match Kernels: Discriminative Classification with Sets of Image Features (version 2)
Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernel-based classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondences -- generally a computationally expensive task that becomes impractical for largeset 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 in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kerneldoes not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positive-definite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels. We demonstrate our algorithm on object recognition tasks and show it to be accurate and dramatically faster than current approaches. (This tech report updates MIT-CSAIL-TR-2005-017 and the paper "The Pyramid Match Kernel: Discriminative Classification with Sets of Images Features" which appeared in the proceedings of ICCV 2005.)