1. Label Distribution Learning and Its Applications
Xin Geng （耿新）
Pattern Learning and Mining (PALM) Lab
（模式学习与挖掘实验室,
School of Computer Science and Engineering
Southeast University, Nanjing, China
（东南大学）

2. Learning with Ambiguity
Single-label Learning
Multi-label Learning ?
Label Ambiguity
Less Ambiguity
More Ambiguity

3. Label Ambiguity Multi-label Learning “What describes the instance?”
cloud
sky
water
building
Multi-label Learning

4. More Ambiguity? “How to describe the instance?” some cloud mostly sky
much water
a bit of building

5. How to learn? Not a good choice! Keep more, learn more MLL
Thresholding Positive labels MLL
Label Distribution Learning (LDL)
Assign a real number to each label
Importance
Confidence
Level ……
Not a good choice!
Keep more, learn more

6. LDL – Problem Formulation
Description Degree
A real number is assigned to the label for the instance
WLOG
Label Distribution
Complete label set

7. LDL – Problem Formulation

8. LDL – Algorithms Two Categories
Conditional Probability Mass Function (Classification)
Model the mapping from the instance x to the label distribution d via a conditional PMF
Multivariate Support Vector Regression (Regression)
Model the mapping from the instance x to the label distribution d via a multivariate support vector machine

9. Conditional Probability Mass Function
Learning from Label Distribution
Training set:
Goal: learn a conditional mass function that can generate label distributions similar to given the instance
K-L divergence

10. Conditional Probability Mass Function
Directly minimizing the K-L divergence between predicted and real LDs
MaxEnt Model

11. Conditional Probability Mass Function
IIS-LLD [Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]

12. Conditional Probability Mass Function
BFGS-LLD [Geng and Ji, ICDMW’13]

13. Conditional Probability Mass Function
CPNN [Geng, Yin, and Zhou, TPAMI’13] 3

14. Multivariate Support Vector Regression
Two issues
How to output a distribution composed by multiple components?
Multivariate Support Vector Regression (M-SVR) [Fernandez et al., TSP’04]
How to constrain each component of the distribution within the range of a probability, i.e., [0, 1]?
Model the regression by a sigmoid function
Solve the two problems simultaneously
LDSVR [Geng and Hou, submitted to IJCAI’15]
Fit a sigmoid function to each component of the label distribution simultaneously by a support vector machine

15. Multivariate Support Vector Regression
Sigmoid model
Target function of SVR
Loss Function

16. Multivariate Support Vector Regression
The loss function
Dimension by dimension
Insensitive Zone
Problem: Examples falling into the area ρ1 will be penalized once while those falling into the area ρ2 will be penalized twice.

17. Multivariate Support Vector Regression
The loss function
Multivariate
Insensitive Zone
Problem: Difficult to optimize and apply the kernel trick

18. Multivariate Support Vector Regression
The loss function
Measure the loss by calculating how far away from zi another point z′i∈ Rc should move to get the same output with the ground truth

19. Multivariate Support Vector Regression
The loss function
Replacing ui with u′i/4
Insensitive Zone

20. Age Estimation Aging is a slow and gradual progress
[Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]
Aging is a slow and gradual progress
The faces at close ages look quite similar
Can we use the neighboring ages to relieve the ‘lack of training samples’ problem?

21. Age Estimation Experiment
[Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]
Experiment

22. Head Pose Estimation Bivariate Label Distribution
[Geng and Xia, CVPR’14]
Bivariate Label Distribution

23. Head Pose Estimation
[Geng and Xia, CVPR’14]
Experiment

24. Multilabel Ranking for Natural Scene Images
[Geng and Luo, CVPR’14]
Multilabel Ranking
A bipartition of the relevant (positive) and irrelevant (negative) labels
A proper ranking over relevant labels
Multiple Rankers: Subjective Inconsistent “Ground Truth”

25. Multilabel Ranking for Natural Scene Images
[Geng and Luo, CVPR’14]
Multilabel Ranking by Preference Distribution
Virtual labels as split point between relevant and irrelevant labels

26. Multilabel Ranking for Natural Scene Images
[Geng and Luo, CVPR’14]
Experiment

27. Crowd Counting [Wang, Zhang and Geng, Neurocomputing’15]

28. Crowd Counting [Wang, Zhang and Geng, Neurocomputing’15]

29. Pre-release Prediction of Crowd Opinion on Movies
[Geng and Hou, submitted to IJCAI’15]
Pre-release Metadata
Crowd Rating Distribution

30. Pre-release Prediction of Crowd Opinion on Movies
[Geng and Hou, submitted to IJCAI’15]
Experiment

31. Conclusion Label distribution learning It is useful when
More general framework than single-label and multi-label learning
Deals with different importance of labels
Matches certain problems better
Needs special design
It is useful when
There is a natural measure of description degree
There are multiple labeling sources for one instance
The labels are correlated to each other ……

32. Download the LDL Matlab package from
Interested?
Download the LDL Matlab package from

33. Thank You
palm.seu.edu.cn