Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Google ICCV 2011

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,

Similarity function

Winner Takes All (WTA)

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  χ 2 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