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.
local shape features
examples under varying conditionsSets of features
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!
Measure of difficulty of a match at level iPyramid match kernel
Approximate partial match similarity
Histogram pyramid: level i has bins of size 2iFeature extraction
matches at previous level
Difference in histogram intersections across levels counts number ofnew pairs matchedCounting new matches
number of newly matched pairs at level i
measure of difficulty of a match at level iPyramid match kernel
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