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SphericalHashing
Jae‐Pil Heo1,Youngwoon Lee1,Junfeng He2,Shih‐FuChang2,andSung‐Eui Yoon1
1KAIST 2ColumbiaUniv.
IEEEConf.onComputerVisionandPatternRecognition(CVPR)2012
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Introduction
• Approximatek‐nearestneighborsearchinhighdimensionalspace– widelyusedinvariousapplications– highcomputationcost,memoryrequirement– tree‐basedmethodsdonotgiveanybenefit(curseofdimensionality)
– spatialhashingtechniquesgetmoreattention
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ImageRetrieval
Findingvisuallysimilarimages
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ImageDescriptorsHighdimensionalpoint(BoW,GIST,ColorHistogram,etc.)
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ImageDescriptorsHighdimensionalpoint(BoW,GIST,ColorHistogram,etc.)Imageretrievalisreducedto
nearestneighborsearchinhighdimensionalspace
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Challenge
BoW GISTDim 1000+ 300+1image 4KB+ 1.2KB+1B images 3TB+ 1TB+
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BinaryCodes
11000
11000
11001
00001
00011
00111
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BinaryCodes11000
11000
11001
00001
00011
00111
* Benefits‐ High compression ratio (scalability)‐ FastsimilaritycalculationwithHammingdistance(efficiency)
*Issue‐ Howwelldobinarycodespreservedatapositionsandtheirdistances(accuracy)
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BinaryCodewithHyper‐Planes
0
1
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BinaryCodewithHyper‐Planes10
10
10
111
011
010
110000
100
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GoodandBadHyper‐Planes
Previousworkfocusedonhowtodeterminegoodhyper‐planes
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State‐of‐the‐artMethods• Randomhyper‐planesfromaspecificdistribution[Indyk – STOC1998,Raginsky – NIPS2009]
• Spectralgraphpartitioning[Yeiss – NIPS2008]
• Minimizingquantizationerror(ITQ)[Gong– CVPR2011]
• Independentcomponentanalysis(ICA)[He– CVPR2011]
• Supportvectormachine(SVM)[Joly – CVPR2011]
• Allofthemusehyper‐planes!
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OurContributions
• SphericalHashing
• Iterativeoptimizationschemetodeterminehyper‐spheres
• SphericalHammingdistance
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OurContributions
• SphericalHashing
• Iterativeoptimizationschemetodeterminehyper‐spheres
• SphericalHammingdistance
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SphericalHashing
01
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PartitioningExample
111
011
010
110000
100 001101
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BoundingPowerofHyper‐Sphere
Average of maximum distances within a partition:‐ Hyper‐spheres gives tighter bound!
openclosed
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OurContributions
• SphericalHashing
• Iterativeoptimizationschemetodeterminehyper‐spheres
• SphericalHammingdistance
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TwoCriteria[Yeiss 2008,He2011]
1. Balancedpartitioning
2.Independence
<
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TwoCriteriawithHyper‐Spheres
1.Balance 2.Independence
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IterativeOptimization
1.Balance‐ bycontrollingradiusfor
2.Independence‐ bymovingtwohyper‐spheresfor ∩
Repeatstep1,2untilconvergence.
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OurContributions
• SphericalHashing
• Iterativeoptimizationschemetodeterminehyper‐spheres
• SphericalHammingdistance
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IntuitionofSphericalHD
Boundedby1hyper‐sphere
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IntuitionofSphericalHD
Boundedby2hyper‐spheres
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IntuitionofSphericalHD
Boundedby2hyper‐spheres
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IntuitionofSphericalHD
Boundedby2hyper‐spheres
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IntuitionofSphericalHD
Boundedby3hyper‐spheres
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MaxDist.andCommon‘1’
111
011110
101
Common‘1’s
:2
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MaxDist.andCommon‘1’
111
011
010
110
100 001101
Common‘1’s
:1
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MaxDist.andCommon‘1’
Common‘1’s:1 Common‘1’s:2
Average of maximum distances between two partitions:decreases as number of common ‘1’
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SphericalHammingDistance(SHD)
SHD: Hamming Distance divided by the number ofcommon ‘1’s.
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Result(1M,384dimGIST)
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Result(1M,960dimGIST)
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Result(75M,384dimGIST)