The Power of Comparative Reasoning
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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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The Power of Comparative Reasoning

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

@ Google

ICCV 2011

Presented by Relja Arandjelović

29th November 2011

University of Oxford


Overview
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
K parameter

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


Wta with polynomial kernel
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
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
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
Results: Image retrieval

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

  • K=4, p=4


Conclusions
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


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