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					   Tag Ranking

   Present by Jie Xiao

 Dept. of Computer Science
Univ. of Texas at San Antonio
    Probabilistic tag relevance estimation
    Random walk tag relevance refinement
    Conclusion        1
    There are millions of social images on
    internet, which are very attractive for the
    research purpose.

    The tags associated with images are not
    ordered by the relevance.          2
    Problem (Cont.)     3
    Tag relevance
    There are two types of relevance to be

           The relevance between a tag and an image

           The relevance between two tags for the same
           image.             4
    Probabilistic Tag Relevance Estimation

      Similarity between a tag and an image

       x     : an image
       t     : tag i associated with image x
       P(t|x) : the probability that given an image x, we have the tag t.
       P(t) : the prior probability of tag t occurred in the dataset

       After applying Bayes’ rule, we can derive that                             5
    Probabilistic Relevance Estimation (Cont)

   Since the target is to rank that tags for the individual
   image and p(x) is identical for these tags, we refine it
   as             6
    Density Estimation
    Let (x1, x2, …, xn) be an iid sample drawn from
    some distribution with an unknown density ƒ.

    Two types of methods to describe the density
           Kernel density estimator              7

                    Credit: All of Nonparametric Statistics via UTSA library                   8
    Kernel Density Estimation
     Smooth function K is used to estimate the density                          9
    Kernel Density Estimation (Cont.)
    Its kernel density estimator is        10
    Probabilistic Relevance Estimation (Cont)
    Kernel Density Estimation (KDE) is adopted to
    estimate the probability density function p(x|t).

      Xi    : the image set containing tag ti
      xk    : the top k near neighbor image in image set Xi
      K     : density kernel function used to estimate the probability
      |x|    : cardinality of Xi                            11
    Relevance between tags

    ti, tag i associated with image x
    tj, tag j associated with image x
          , the image set containing tag i
          , the image set containing tag j
    N: the top N nearest neighbor for image x        12
    Relevance between tags (Cont.)       13
    Relevance between tags (Cont.)
    Co-occurrence similarity between tags

   f(ti) : the # of images containing tag ti
   f(ti,tj) : the # of images containing both tag ti and tag tj
   G        : the total # of images in Flickr                   14
    Relevance between tags (Cont.)       15
    Relevance between tags (Cont.)
    Relevance score between two tags

  where       16
    Random walk over tag graph

 P: n by n transition matrix.
 pij : the probability of the transition from node i to j

               rk(j): relevance score of node i at iteration k                               17
    Random walk   18
    Random walk over tag graph (Cont.)       19
    Dataset: 50,000 image crawled from Flickr
    Popular tags:
    Raw tags: more than 100,000 unique tags
    Filtered tags: 13,330 unique tags        20
    Performance Metric
  Normalized Discounted Cumulative Gain

        r(i) : the relevance level of the i - th tag

        Zn : a normalization constant that is chosen so that the optimal
        ranking’s NDCG score is 1.                                21
    Experimental Result
    Comparison among different tag ranking
    approaches         22   23
    Estimate the tag - image relevance by kernel
    density estimation.

    Estimate the tag – tag relevance by visual
    similarity and tag co-occurrence.

    A random walk based approach is used to
    refine the ranking performance.        24
                    Thank you!         25

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