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The Pyramid Match Kernel: Discriminative Classification with Sets of Image Features by Kristen Grauman and Trevor Darrell Presentation by Guy Tannenbaum
Kernel Methods (e.g. SVM, kPCA) are a class of algorithms for pattern analysis, which find different types of relations on the input data (for example classification).
KM approach the problem by using an implicit mapping of the input data into high dimensional feature space , and searching there for relations.
KM operate in the feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space .
A kernel is a function such that for all
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Positive definite kernel A kernel is positive definite if The matrix G who's elements are is a positive definite matrix. i.e It is sufficient to show that there exist some mapping to a vector space such that
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Counting new matches Histogram intersection Difference in histogram intersections across levels counts number of new pairs matched matches at this level matches at previous level
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100 sets with 2D points, cardinalities vary between 5 and 100 Trial number (sorted by optimal distance) [Indyk & Thaper] Matching output Approximation of the optimal partial matching
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