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Kernels on histograms through the transportation polytope
Published on Feb 25, 20074913 Views
For two integral histograms and of equal sum, the Monge-Kantorovich distance MK(r,c) between r and c parameterized by a d × d cost matrix T is the minimum of all costs taken over matrices F of t
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Chapter list
Kernels on Histograms through the Transportation Polytope00:00
Outline00:11
Problem00:47
Problem 0101:21
Problem 0201:39
Problem 0302:10
Problem 0402:28
Problem 0502:58
Bag-of-components, histogram representations03:09
Bag-of-components, histogram representations 0103:36
Bag-of-components, histogram representations 0203:45
Probability representation03:59
Probability representation 0104:20
d Rd<br>+ Rd04:25
d Rd<br>+ Rd 0104:39
d Rd<br>+ Rd 0205:01
d Rd<br>+ Rd 0305:34
Dozens of classic probability metrics05:58
Dozens of classic probability metrics 0106:41
Dozens of classic probability metrics 0207:12
Dozens of classic probability metrics 0308:20
Outline08:49
MK distance between two histograms08:55
MK distance between two histograms 0109:17
MK distance between two histograms 0210:00
MK distance between two histograms 0310:29
MK distance between two histograms 0411:04
MK distance between two histograms 0511:25
MK distance between two histograms 0611:38
Permanent12:22
Permanent kernel between clouds of points12:40
Permanent kernel between clouds of points 0112:46
Permanent kernel between clouds of points 0212:52
Permanent kernel between clouds of points 0313:02
Permanent kernel between clouds of points 0513:34
Volume of U(r , c) for general histograms14:59
Volume of U(r , c) for general histograms 0115:32
Volume of U(r , c) for general histograms 0215:45
Positive definiteness of the volume15:55
Positive definiteness of the volume 0116:01
Positive definiteness of the volume 0216:16
Weighted volume of U(r , c)16:36
Weighted volume of U(r , c) 0117:13
Positive definiteness of weighted volumes17:26
Positive definiteness of weighted volumes 0117:47
Positive definiteness of weighted volumes 0217:53
2000 images, 10 classes, 20 pixels per image18:22