Classification with Nonmetric Distances: Image
Retrieval and Class Representation
David W. Jacobs, Daphna Weinshall, Yoram Gdalyahu
IEEE TPAMI 2000
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Non-metric distances
• Experts
• Matching of shapes,
sequences, graphs…
• Lp-norm for p<1
D(A,B)
A
B
D(B,C)
D(A,C)
C
D(A,C) > D(A,B) + D(B,C)
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Class representation
• Condense a class to M (M << N) prototypes, but with same
nearest neighbor error
• Condensing algorithms
• low distance  points are representative for each other
• boundary points are important
• Developed for metric spaces, but potentially can be used with
non-metric distances
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Is it a good idea?
p=2
p=1
(still metric)
p = 0.5
(non-metric)
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In other words…
• Low distance does not imply points are representative, changing
prototypes slightly may drastically change boundary
• When using non-metric distances, do not make decisions based
on d(x1,x2) ?
• d(d(x1,{x3… xN}), d(x2, {x3… xN}) more informative
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Better…
• d(d(x1,{x3… xN}), d(x2, {x3… xN}) more informative
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Discussion
• In MIL many distances are non-metric, dissimilarity space works
well
• Reviewers: “Why don’t you just cluster the bags and select the
cluster representatives”
• How many (older) papers out there are really important to you
but you do not know about?
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