# x - Department of Computer Science by hcj

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```									   Tag Ranking

Present by Jie Xiao

Dept. of Computer Science
Univ. of Texas at San Antonio
Outline
Problem
Probabilistic tag relevance estimation
Random walk tag relevance refinement
Experiment
Conclusion

jxiao@cs.utsa.edu        1
Problem
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.

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Problem (Cont.)

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Tag relevance
There are two types of relevance to be
considered.

The relevance between a tag and an image

The relevance between two tags for the same
image.

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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

jxiao@cs.utsa.edu                             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

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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
Histogram
Kernel density estimator

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Histogram

Credit: All of Nonparametric Statistics via UTSA library

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Kernel Density Estimation
Smooth function K is used to estimate the density

jxiao@cs.utsa.edu                          9
Kernel Density Estimation (Cont.)
Its kernel density estimator is

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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

jxiao@cs.utsa.edu                            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

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Relevance between tags (Cont.)

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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

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Relevance between tags (Cont.)

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Relevance between tags (Cont.)
Relevance score between two tags

where

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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

jxiao@cs.utsa.edu                               17
Random walk

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Random walk over tag graph (Cont.)

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Experiments
Dataset: 50,000 image crawled from Flickr
Popular tags:
Raw tags: more than 100,000 unique tags
Filtered tags: 13,330 unique tags

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Performance Metric
Normalized Discounted Cumulative Gain
(NDCG)

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.

jxiao@cs.utsa.edu                                21
Experimental Result
Comparison among different tag ranking
approaches

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Conclusion
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.

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Thank you!

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