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The Power of Comparative Reasoning. Jay Yagnik , Dennis Strelow , David Ross, Ruei -sung Lin @ Google ICCV 2011. Presented by Relja Arandjelovi ć. 29 th November 2011. University of Oxford. Overview. Ordinal embedding of features based on partial order statistics

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Presented by Relja Arandjelovi ć

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#### Presentation Transcript

The Power of Comparative Reasoning

Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin

ICCV 2011

Presented by Relja Arandjelović

29th November 2011

University of Oxford

### Overview

• Ordinal embedding of features based on partial order statistics

• Non-linear embedding

• Simple extension for polynomial kernels

• Data independent

• Very easy to implement

### 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,

### K parameter

• Increasing K biases the similarity towards the top of the list

### 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

### 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

### 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%

### Results: Image retrieval

• LabelMe dataset: 13,500 images; 512-D Gist descriptor

• K=4, p=4

### 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