The Pyramid Match: Efficient Learning with Partial Correspondences

It is often useful to represent a single example by a set of the local features that comprise it. However, this representation poses a challenge to many conventional learning techniques, since sets may vary in cardinality and the elements are unordered. To compare sets of features, researchers often resort to solving for the least-cost correspondences, but this is computationally expensive and becomes impractical for large set sizes. We have developed a general approximate matching technique called the pyramid match that measures partial match similarity in time linear in the number of feature vectors per set. The matching forms a Mercer kernel, making it valid for use in many existing kernel-based learning methods. We have demonstrated the approach for various learning tasks in vision and text processing, and find that it is accurate and significantly more efficient than previous approaches.