The Pyramid Match Kernel and Its Improvement. Guo LiJun. PMK: Kristen Grauman,Trevor Darrell ICCV’05, Oral Projects that use LIBPMK Multiple Kernel Learning from Sets of Partially Matching Image Features, UKACC Control 2008.
How to build a discriminative classifier using the set representation?
Measuring Similarity Between Sets of Features
2)Bags of Prototypical Features
High complexityExisting set kernels
Kondor & Jebara, Moreno et al., Lafferty & Lebanon, Cuturi & Vert,
Wolf & Shashua
Compare sets by computing a partialmatching between their features.
Robust to clutter, segmentation errors, occlusion…
Pyramid match kernel measures similarity of a partial matching between two sets:
No explicit search for matches!
For sets with m features of dimension d, and pyramids with L levels, computational complexity of
Pyramid match kernel:
Existing set kernel approaches:
[Indyk & Thaper]
Trial number (sorted by optimal distance)
100 sets with 2D points, cardinalities vary between 5 and 100
Convergence is guaranteed since pyramid match kernel is positive-definite.
Eichhorn and Chapelle 2004
(1% chance performance)
optimal partial matching between sets of features
difficulty of a match at level i
number of new matches at level i
Disregard all information about the spatial layout of the features
Spatial Pyramid Matching
Learn Method: PMK or EMD-NN