### Slides (PPT) - University of Oxford

```The Power of Comparative Reasoning
Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin
ICCV 2011
Presented by Relja Arandjelović
University of Oxford
29th November 2011
Overview
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Ordinal embedding of features based on partial order statistics
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Non-linear embedding
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Simple extension for polynomial kernels
Data independent
Very easy to implement
Idea
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Compare feature vectors based on the order of dimensions,
sorted by magnitude
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Ranking is invariant to constant offset, scaling, small noise
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Use local ordering statistics; example pair-wise measure:
WTA (Winner Takes All) hashing scheme produces vectors
comparable via Hamming distance.
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The distance approximates:
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For K=2,
Similarity function
Winner Takes All (WTA)
K parameter
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Increasing K biases the similarity towards the top of the list
WTA with polynomial kernel
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Simple to do WTA on the polynomial expansion of the
feature space
Computed in O(p), where p is the polynomial kernel degree
Results: Descriptor matching (SIFT / DAISY)
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Descriptor matching task, Liberty dataset
K=2, 10k binary codes
RAW: +11.6%
 SIFT: +10.4%
 DAISY: +11.2%
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Note: SIFT is 128-D so there are 8128 possible pairs, might as
well compute PO exactly in this case; similar for 200-D DAISY
I tried briefly for SIFT on a different task: works
Results: VOC
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VOC 2010
Bag-of-words of their descriptor based on Gabor wavelet
responses
K=4
Linear SVM
χ2 for 1000-D: 40.1%
WTA for 1000-D: +2%
Results: Image retrieval
LabelMe dataset: 13,500 images; 512-D Gist descriptor
 K=4, p=4
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Conclusions
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Partial order statistics could be a good way to compare vectors
Data independent: no training stage
Non-linear embedding: could use a linear SVM in this space
Simple to implement and try out
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My note for SIFT/DAISY:
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Can just discard all this hashing stuff and encode all pair-wise relations
```