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Presented by Relja Arandjelovi ć

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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  1. 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

  2. Overview • Ordinal embedding of features based on partial order statistics • Non-linear embedding • Simple extension for polynomial kernels • Data independent • Very easy to implement

  3. 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,

  4. Similarity function

  5. Winner Takes All (WTA)

  6. K parameter • Increasing K biases the similarity towards the top of the list

  7. 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

  8. 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

  9. 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%

  10. Results: Image retrieval • LabelMe dataset: 13,500 images; 512-D Gist descriptor • K=4, p=4

  11. 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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