[ammai] week9/10 Semi-Supervised Hashing for Scalable Image Retrieval

Paper:
    J. Wang et al, "Semi-Supervised Hashing for Scalable Image Retrieval," CVPR, 2010.


     
     SSH(Semi-Supervised Hashing) is based on two idea:
     (1) distribute the similar label images to the closer hash
     (2) make each hash bucket balanced.

     Assume that  is the images pairs set in which have same label, and  is the images pairs set where have different labels. The following objective function is main to the first criterion: for pairs with same label, maximize the probability such that they have fall into the closer buckets; for pairs with different, minimize such probability.
     Besides, they add a regularization to constraint such that each bucket size should be balanced: hash functions should be orthogonal.

      Because this work uses is going to learn a projection matrix W for hashing, so J becomes...

      And the author transform the constraint into a soft one like....

     ,which can maximize the variance of mapping space.

     

     The result is terrific in author's experiments as followed....

    

     SSH can maintain the semantic meanings consistency, unlike LSH method, and do not require too much time like supervised learning methods like RBM and SH.