The pyramid match kernel: Discriminative classification with sets of image features

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The pyramid match kernel: Discriminative classification with sets of image features (2005)

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by Kristen Grauman , Trevor Darrell

Venue:	IN ICCV
Citations:	543 - 29 self

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@INPROCEEDINGS{Grauman05thepyramid,
    author = {Kristen Grauman and Trevor Darrell},
    title = {The pyramid match kernel: Discriminative classification with sets of image features},
    booktitle = {IN ICCV},
    year = {2005},
    pages = {1458--1465},
    publisher = {}
}

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Abstract

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 large set 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 kernel does 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.

Keyphrases

pyramid match kernel discriminative classification image feature optimal solution expensive task current approach weighted histogram intersection unordered feature set complex decision boundary matched pair new fast kernel function large set size object recognition task discriminative learning kernel function mercer kernel kernel-based classification method resolution histogram cell unordered set input extra feature pyramid match computation multi-resolution histogram

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