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Some Evidence That LSH May Not Be Useful. Another Option: Bayesian Sequential Hypothesis Testing. What To Do Next? (Two Choices). Outline. Outline. Review. Outline. Review Why this problem may not be a good match for the LSH algorithm. Outline. Review - PowerPoint PPT Presentation
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What To Do Next?(Two Choices)
Some Evidence That LSH May Not Be Useful.
Another Option: Bayesian Sequential Hypothesis Testing.
Outline
Outline
• Review
Outline
• Review
• Why this problem may not be a good match for the LSH algorithm
Outline
• Review
• Why this problem may not be a good match for the LSH algorithm
• Another possible direction
Outline
• Review
• Why this problem may not be a good match for the LSH algorithm
• Another possible direction
Outline
• Review
• Why this problem may not be a good match for the LSH algorithm
• Another possible direction
• Decision to make…
observed patch part model
Euclidean distance?
observed patch part model
Euclidean distance?
observed patch
0.00.2
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0.0
0.0
0.0 0.1
0.0 0.2
0.00.1
0.2
0.0
0.0
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0.2
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0.2
0.0
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0.6 0.9 0.6 1.0
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0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
foreground
observed patch
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0.5
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0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
foreground
observed patch
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0.2
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0.5
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0.0
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0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
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0.6 0.9 0.6 1.0
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0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
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0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
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0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
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0.2
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0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
0.1 0.0 0.1 0.0
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0.0 0.2
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0.10.1
0.0 0.2
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0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
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0.0 0.0 0.2 0.0
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0.2
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0.10.1
0.0 0.2
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0.2
0.0
0.0
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0.2 0.1
0.0
0.0 0.2
0.0
0.00.2
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.2
0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
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0.2
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0.2
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0.10.1
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0.2
0.0
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0.2 0.1
0.0
0.0 0.2
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0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.2
0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.0 0.1
0.0
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0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
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0.00.1
0.00.00.1
0.2
0.0
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0.0 0.1
0.0
0.0 0.2
0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
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0.1
0.0 0.2
0.00.0
0.00.00.0
0.2
0.0
0.0
0.1 0.1 0.0 0.0
0.1 0.0 0.2 0.0
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0.0 0.0
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0.0 0.2
0.0
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0.1
0.10.1
0.0 0.2
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0.2
0.0
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0.2 0.1
0.0
0.0 0.2
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0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.2
0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
observed patch
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.0 0.1
0.0
0.0 0.2
0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.1
0.2
0.0
0.0
0.1 0.0 0.2 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.0 0.1
0.0
0.0 0.2
0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.0
0.00.00.0
0.2
0.0
0.0
0.1 0.1 0.0 0.0
0.1 0.0 0.2 0.0
0.0 0.2
0.0 0.0
0.0
0.0 0.2
0.0
0.00.0
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.0
0.00.00.0
0.2
0.0
0.0
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.2 0.1
0.0
0.0 0.2
0.0
0.00.2
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.2
0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
patch“goodness”
observed patch
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.0 0.1
0.0
0.0 0.2
0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.1
0.2
0.0
0.0
0.1 0.0 0.2 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.0 0.1
0.0
0.0 0.2
0.0
0.00.1
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.0
0.00.00.0
0.2
0.0
0.0
0.1 0.1 0.0 0.0
0.1 0.0 0.2 0.0
0.0 0.2
0.0 0.0
0.0
0.0 0.2
0.0
0.00.0
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.0
0.00.00.0
0.2
0.0
0.0
0.1 0.0 0.1 0.0
0.0 0.0 0.2 0.0
0.0 0.2
0.2 0.1
0.0
0.0 0.2
0.0
0.00.2
0.1
0.10.1
0.0 0.2
0.0
0.0
0.1
0.0 0.2
0.00.1
0.00.00.2
0.2
0.0
0.0
0.6 0.9 0.6 1.0
0.9 0.6 0.8 0.7
0.5 0.9
0.8 0.7
0.5
0.8 0.6
0.0
060.5
0.9
0.10.1
0.5 0.7
0.9
0.5
0.6
1.0 0.2
0.40.8
0.80.70.7
0.6
0.8
0.5
part model
Euclidean distance?
0.1 0.1 0.60.2 0.0
foreground
background
patch“goodness”
pixel“goodness”
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
• What if we let each observed patch and part model be a point?
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
• What if we let each observed patch and part model be a point?
• Can we arrange these points in space such that the distances represent the “goodness” values?
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
If we can arrange the points with correct distances in low-dimensional pixel space,
observed patch part model
Euclidean distance?
patch“goodness”
pixel“goodness”
If we can arrange the points with correct distances in low-dimensional pixel space,then we can append these coordinates in the high-dimensional patch space…
observed patch part model
Euclidean distance?
If we can arrange the points with correct distances in low-dimensional pixel space,then we can append these coordinates in the high-dimensional patch space…
Consider low-dimensional pixel space:
observed patch part model
Euclidean distance?
If we can arrange the points with correct distances in low-dimensional pixel space,then we can append these coordinates in the high-dimensional patch space…
e edge orientations
Consider low-dimensional pixel space:
observed patch part model
Euclidean distance?
If we can arrange the points with correct distances in low-dimensional pixel space,then we can append these coordinates in the high-dimensional patch space…
e edge orientationsn = p*o edge orientations (o object models, p parts per object)
Consider low-dimensional pixel space:
observed patch part model
Euclidean distance?
If we can arrange the points with correct distances in low-dimensional pixel space,then we can append these coordinates in the high-dimensional patch space…
e edge orientationsn = p*o edge orientations (o object models, p parts per object)
e+n points withe*n distance constraints
Consider low-dimensional pixel space:
Why this problem may not be a good match for the LSH algorithm.
Why this problem may not be a good match for the LSH algorithm.
• Theory suggests that the most straightforward optimization method is non-convex.
Why this problem may not be a good match for the LSH algorithm.
• Theory suggests that the most straightforward optimization method is non-convex.
• Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database
Why this problem may not be a good match for the LSH algorithm.
• Theory suggests that the most straightforward optimization method is non-convex.
• Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database
• LSH running time: dn1/c2+o(1)
Why this problem may not be a good match for the LSH algorithm.
• Theory suggests that the most straightforward optimization method is non-convex.
• Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database
• LSH running time: dn1/c2+o(1)
• Since d=n, LSH running time becomes n1/c2+1+o(1) which is no longer sublinear
Why this problem may not be a good match for the LSH algorithm.
• Theory suggests that the most straightforward optimization method is non-convex.
• Non-convex numerical optimization experiments suggest that the “affine dimension” for distance constraints is n, i.e. # points in the database
• LSH running time: dn1/c2+o(1)
• Since d=n, LSH running time becomes n1/c2+1+o(1) which is no longer sublinear
• However, theory says the optimization it can be made convex…
Another possible direction
Another possible direction
Recall:Winning Parts vs. Backgrounds
Background
WinningPart
Decision to make…
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
2. Try to apply Werman’s technique to the k-Fan probability model.
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
– Learn more about euclidean distance geometry & optimization
2. Try to apply Werman’s technique to the k-Fan probability model.
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
– Learn more about euclidean distance geometry & optimization
– Possible dead-end (may still not be fast)
2. Try to apply Werman’s technique to the k-Fan probability model.
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
– Learn more about euclidean distance geometry & optimization
– Possible dead-end (may still not be fast)
2. Try to apply Werman’s technique to the k-Fan probability model.
– “hacking the code” style speed-up
Decision to make…
1. Implement Dattoro’s technique to see if the “affine dimension” of our problem can be <n.
– Learn more about euclidean distance geometry & optimization
– Possible dead-end (may still not be fast)
2. Try to apply Werman’s technique to the k-Fan probability model.
– “hacking the code” style speed-up– Replacing Hamming distance may not work
![Two Choices[1]](https://img.pdfslide.us/doc/110x75/547c9a03b4af9fd3158b51fa/two-choices1.jpg)
