1. Estimate the Number of Relevant Images Using Two-Order Markov Chain Presented by: WANG Xiaoling Supervisor: Clement LEUNG

2. Outline Introduction Introduction Objective Objective Methodology Methodology Experiment Results Experiment Results Conclusion and Future Work Conclusion and Future Work

3. Introduction Large collections of images have been made available on web. Large collections of images have been made available on web. Retrieval effectiveness becomes one of the most important parameters to measure the performance of image retrieval systems. Retrieval effectiveness becomes one of the most important parameters to measure the performance of image retrieval systems.

4. Measures: Measures: Precision Precision Recall Recall Significant Challenge: the total number of relevant images is not directly observable Significant Challenge: the total number of relevant images is not directly observable

5. Basic Models Basic Models Regression Model Regression Model Markov Chain Markov Chain Two-Order Markov Chain Two-Order Markov Chain

6. Objective To investigate the probabilistic behavior of the distribution of relevant images among the returned results for the image search engines using two-order markov chain To investigate the probabilistic behavior of the distribution of relevant images among the returned results for the image search engines using two-order markov chain

7. Methodology Test Image Search Engine: Test Image Search Engine: Query Design Query Design 70% provided by authors 70% provided by authors One word query One word query Two word query Two word query Three word query Three word query 30% suggestive term 30% suggestive term Suggestive term with largest returned results Suggestive term with largest returned results Suggestive term with least returned results Suggestive term with least returned results

8. Methodology Database Setup: Database Setup: Stochastic process {X 1, X 2, …, X J } Stochastic process {X 1, X 2, …, X J } where X J denotes the aggregate relevance of all the images in page J where X J denotes the aggregate relevance of all the images in page J Equation: Equation: where Y Ji =1 if the i th image on page J is relevant, and Y Ji =0 if the i th image on page J is not relevant. where Y Ji =1 if the i th image on page J is relevant, and Y Ji =0 if the i th image on page J is not relevant.

9. Page J XJXJXJXJ 118 219 320 419 520 619 720 818 919 1018

10. Forecast Using Two-Order Markov Chain Forecast Using Two-Order Markov Chain Markov Chain: Stochastic process {X J, J≥1} with state space S={0,1,2,…20} ， Markov Chain: Stochastic process {X J, J≥1} with state space S={0,1,2,…20} ， Two-Order Markov Chain: State space change to S 2 ， Two-Order Markov Chain: State space change to S 2 ， Forecast the state probability distribution of next page π(J) based on the original state probability distribution π(1) and transition probability matrix P. An Example Forecast the state probability distribution of next page π(J) based on the original state probability distribution π(1) and transition probability matrix P. An ExampleAn ExampleAn Example Model Test Model Test Mean Absolute Error Mean Absolute Error

11. Experiment Results Forecast Results Using Two-Order Markov Chain Forecast Results Using Two-Order Markov Chain PageGoogleYahooBing 1202020 2202020 3202020 4202020 5202020 6202017 7202017 8202017 9202017 10202017

12. Test Results--Google Test Results--Google

13. Test Results--Yahoo Test Results--Yahoo

14. Test Results--Bing Test Results--Bing

15. Measure for Forecast Accuracy Measure for Forecast Accuracy Mean Absolute Deviation (MAD): Mean Absolute Deviation (MAD):One-wordTwo-wordThree-wordGoogle2.72.31.10.80.10.81.71.90.6 Yahoo2.00.11.10.54.81.12.22.20.4 Bing1.31.91.24.52.01.21.210.51.1

16. Comparative Results Comparative Results Best Model: Two- Order Markov Chain Best Model: Two- Order Markov Chain Worst Model: Regression Model Worst Model: Regression Model

17. Conclusion Two-Order Markov Chain could well represent the distribution of relevant images among the results pages for the major web image search engine. Two-Order Markov Chain could well represent the distribution of relevant images among the results pages for the major web image search engine. Two-Order Markov Chain is the best model among three models we have worked. Two-Order Markov Chain is the best model among three models we have worked.

18. Future Work Our future work will try to apply Hidden Markov Chain to this topic Our future work will try to apply Hidden Markov Chain to this topic

19. Thank you! Q & A

20. Two-Order Markov Chain An example (cont ’ ) Suppose the stochastic process {X t, t>=0} with a state space S={A, B, C} Suppose the stochastic process {X t, t>=0} with a state space S={A, B, C} As to two-order Markov chain, the state space: As to two-order Markov chain, the state space: S 2 ={AA, AB, AC, BA, BB, BC, CA, CB, CC} S 2 ={AA, AB, AC, BA, BB, BC, CA, CB, CC} The state probabilities distribution of period zero: The state probabilities distribution of period zero:  (0)= (  AA,  AB,  AC,  BA,  BB,  BC,  CA,  CB,  CC )  (0)= (  AA,  AB,  AC,  BA,  BB,  BC,  CA,  CB,  CC )

21. An example (cont ’ ) The transition probability matrix: The transition probability matrix: P AA,BA =0

22. An example Therefore, the probability distribution of states for page J will be compute as: Therefore, the probability distribution of states for page J will be compute as: π(J)=π(J-1)*P π(J)=π(J-1)*P [Return] [Return]Return