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Learning Nearest Neighbor Graphs from Noisy Distance Samples Noisy - - PowerPoint PPT Presentation
Learning Nearest Neighbor Graphs from Noisy Distance Samples Noisy - - PowerPoint PPT Presentation
Learning Nearest Neighbor Graphs from Learning Nearest Neighbor Graphs from Noisy Distance Samples Noisy Distance Samples Blake Mason, Ardhendu Tripathy, & Robert Nowak Blake Mason, Ardhendu Tripathy, & Robert Nowak Motivation Wish to
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Motivation
Wish to learn ‘most similar’ or ‘closest’ items to a given from noisy measurements
amazon.com/discover
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Motivation
Wish to learn ‘most similar’ or ‘closest’ items to a given from noisy measurements
Fujitsu white paper
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Motivation
Wish to learn ‘most similar’ or ‘closest’ items to a given from noisy measurements We don’t know the given a priori. We want to answer ‘closest’ queries for any item quickly!
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The Nearest Neighbor Graph Problem
Sharma et al. (2015)
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Preliminaries and Notation
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Outline of ANNTri
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Elimination via the triangle inequality
j i l k
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Triangle Inequality Bounds
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Theoretical Results
- Worst case complexity is always O(n2)
- In general, order matters
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Theoretical Results
- Often, we can do better:
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Theoretical Results
- An example of separation:
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Theoretical Results
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Experimental Results
- Simulated data
- 100 points in ℝ2
- 10 clusters of 10 points
- Euclidean distance
- Gaussian noise, 𝜏2 =
0.1
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Experimental Results
- Compare against
Random sampling
- Test effect of triangle
inequality
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Experimental Results
- The metric is (2d)
Euclidean
- We can compare
against (distance) matrix completion
- With a distance matrix,
the graph can be computed easily
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Experimental Results
- What shoes are most similar?
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Experimental Results
- What shoes are most similar?
- 85 images from UTZappos50K dataset
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Experimental Results
- What shoes are most similar?
- 85 images from UTZappos50K dataset
- Human judgements collected by Heim et al., (2015).
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Experimental Results
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Experimental Results
- What shoes are most similar?
- 85 images from UTZappos50K dataset
- Human judgements collected by Heim et al., (2015).
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Experimental Results
- What shoes are most similar?
- 85 images from UTZappos50K dataset
- Human judgements collected by Heim et al., (2015).
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Main takeways for ANNTri
- 1. ANNTri finds the nearest neighbor graph for general
metrics using the triangle inequality
- 2. Only requires access to noisy oracle
- 3. In favorable settings, requires 𝑷(𝒐𝒎𝒑𝒉 𝒐 𝚬−𝟑) queries