1. Human age ranking from pairwise comparison data via HodgeRank
Lui Go Nam
Department of Mechanical and Aerospace Engineering
Hong Kong University of Science and Technology

2. Introduction
Pairwise comparison is a comfort way for volunteers to present their opinions.
However, when the number of subjects increases, the difficulty of direct pairwise comparison is impossible.
Thus, effective pairwise comparison analysis framework is needed.

3. Introduction
HodgeRank on Random Graphs (HRRG) is proposed as a general framework for incomplete pairwise comparison data analysis.
Every subjects (portraits e.g.) in comparison is regarded as a graph node.
An assessor collects random samples of node pairs or edges independently with a distribution (I.I.D. e.g.).

4. Content of the project
1. Global score generated by four generalized linear model.
(Uniform model, Bradley-Terry, Thurstone-Mosteller, Arcsin)
2.Comparions with real age distribution after standardization.
3.Inconsistency analysis.
4.Error analysis.

5. Dataset description
14,011 pairwise comparisons from 94 annotators of 30 portrait photos.
* I didn’t consider the impact of “hard to judge” option into the model
After rearrangement, there are sets of pairwise comparison left.

7. Global Score
Bradley-Terry model has a similar trend as Thurstone-Mosteller model while uniform model’s trend is likely to angular transform model’s.

8. Comparison

9. Inconsistency Analysis
, Brad-Terry model has the highest total inconsistency and uniform model has the lowest. Harmonic inconsistency are small for each models

10. Error Analysis
each model has similar RMSE which is around 0.49 and Thurstone-Mosteller model has the lowest which close to 0.48.

11. Error Analysis
This figure shows that the No.21, No.24, No.20 and No.3 is relatively hard to recognize their real age.

12. Interesting fact
The left is No.21, which is 20 years old and the right is No.24, which is 18 years old. Actually it’s hard to tell their real age. :)

13. Conclusion
HHRG is a suitable framework for managing the incomplete pairwise comparison data on the human age ranking.
Based on the Error analysis and Inconsistency analysis, I am convinced that Thurstone-Mosteller model is the most appropriate GLM on human age ranking.