1. Tag Ranking Present by Jie Xiao Dept. of Computer Science Univ. of Texas at San Antonio

2. jxiao@cs.utsa.edu 1 Outline Problem Probabilistic tag relevance estimation Random walk tag relevance refinement Experiment Conclusion

3. jxiao@cs.utsa.edu 2 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.

4. Problem (Cont.) jxiao@cs.utsa.edu 3

5. 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. jxiao@cs.utsa.edu 4

6. Probabilistic Tag Relevance Estimation Similarity between a tag and an image jxiao@cs.utsa.edu 5 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

7. 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 jxiao@cs.utsa.edu 6

8. Density Estimation Let (x 1, x 2, …, x n ) 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 jxiao@cs.utsa.edu 7

9. Histogram jxiao@cs.utsa.edu 8 Credit: All of Nonparametric Statistics via UTSA library

10. Kernel Density Estimation jxiao@cs.utsa.edu 9 Smooth function K is used to estimate the density

11. Kernel Density Estimation (Cont.) Its kernel density estimator is jxiao@cs.utsa.edu 10

12. Probabilistic Relevance Estimation (Cont) Kernel Density Estimation (KDE) is adopted to estimate the probability density function p(x|t). jxiao@cs.utsa.edu 11 Xi : the image set containing tag ti x k : the top k near neighbor image in image set Xi K : density kernel function used to estimate the probability |x| : cardinality of Xi

13. 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 jxiao@cs.utsa.edu 12

14. Relevance between tags (Cont.) jxiao@cs.utsa.edu 13

15. Relevance between tags (Cont.) Co-occurrence similarity between tags jxiao@cs.utsa.edu 14 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

16. Relevance between tags (Cont.) jxiao@cs.utsa.edu 15

17. Relevance between tags (Cont.) Relevance score between two tags jxiao@cs.utsa.edu 16 where

18. Random walk over tag graph P: n by n transition matrix. pij : the probability of the transition from node i to j jxiao@cs.utsa.edu 17 r k (j): relevance score of node i at iteration k

19. Random walk jxiao@cs.utsa.edu 18

20. Random walk over tag graph (Cont.) jxiao@cs.utsa.edu 19

21. Experiments Dataset: 50,000 image crawled from Flickr Popular tags: Raw tags: more than 100,000 unique tags Filtered tags: 13,330 unique tags jxiao@cs.utsa.edu 20

22. Performance Metric Normalized Discounted Cumulative Gain (NDCG) jxiao@cs.utsa.edu 21 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.

23. Experimental Result Comparison among different tag ranking approaches jxiao@cs.utsa.edu 22

24. jxiao@cs.utsa.edu 23

25. 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. jxiao@cs.utsa.edu 24

26. jxiao@cs.utsa.edu 25 Thank you!