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![Page 1: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/1.jpg)
Presented by Relja Arandjelović
The Power of Comparative Reasoning
University of Oxford 29th November 2011
Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin
ICCV 2011
![Page 2: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/2.jpg)
Overview
Ordinal embedding of features based on partial order statistics Non-linear embedding Simple extension for polynomial kernels
Data independent Very easy to implement
![Page 3: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/3.jpg)
Idea
Compare feature vectors based on the order of dimensions, sorted by magnitude
Ranking is invariant to constant offset, scaling, small noise Use local ordering statistics; example pair-wise measure:
WTA (Winner Takes All) hashing scheme produces vectors comparable via Hamming distance.
The distance approximates: For K=2,
![Page 4: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/4.jpg)
Similarity function
![Page 5: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/5.jpg)
Winner Takes All (WTA)
![Page 6: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/6.jpg)
K parameter
Increasing K biases the similarity towards the top of the list
![Page 7: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/7.jpg)
WTA with polynomial kernel
Simple to do WTA on the polynomial expansion of the feature space
Computed in O(p), where p is the polynomial kernel degree
![Page 8: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/8.jpg)
Results: Descriptor matching (SIFT / DAISY)
Descriptor matching task, Liberty dataset K=2, 10k binary codes
RAW: +11.6% SIFT: +10.4% DAISY: +11.2%
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
![Page 9: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/9.jpg)
Results: VOC
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%
![Page 10: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/10.jpg)
Results: Image retrieval LabelMe dataset: 13,500 images; 512-D Gist descriptor K=4, p=4
![Page 11: Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung.](https://reader030.fdocuments.net/reader030/viewer/2022032518/56649ccd5503460f94997571/html5/thumbnails/11.jpg)
Conclusions
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
My note for SIFT/DAISY: Can just discard all this hashing stuff and encode all pair-wise relations