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The pyramid match kernel: Efficient learning with sets of features (2007)
| Venue: | Journal of Machine Learning Research |
| Citations: | 136 - 10 self |
BibTeX
@ARTICLE{Grauman07thepyramid,
author = {Kristen Grauman and Trevor Darrell and Pietro Perona},
title = {The pyramid match kernel: Efficient learning with sets of features},
journal = {Journal of Machine Learning Research},
year = {2007},
volume = {8},
pages = {2007}
}
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Abstract
In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kernel methods can learn complex functions, but a kernel over unordered set inputs must somehow solve for correspondences—generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function called the pyramid match that measures partial match similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3-D human pose inference, and time of publication estimation for documents, and we show that the proposed method is accurate and significantly more efficient than current approaches.
Keyphrases
pyramid match kernel error relative expensive task regression task kernel method single example current approach time linear weighted histogram intersection many conventional machine publication estimation 3-d human pose inference matched pair new fast kernel function large set size pyramid match implicit correspondence partial match similarity mercer kernel numerous domain complex function resolution histogram cell unordered set input object recognition meaningful ordering optimal partial matching cost multi-resolution histogram local feature pyramid match yield
