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**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）

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**Learning with Ambiguity**

Single-label Learning Multi-label Learning ? Label Ambiguity Less Ambiguity More Ambiguity

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**Label Ambiguity Multi-label Learning “What describes the instance?”**

cloud sky water building Multi-label Learning

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**More Ambiguity? “How to describe the instance?” some cloud mostly sky**

much water a bit of building

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**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

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**LDL – Problem Formulation**

Description Degree A real number is assigned to the label for the instance WLOG Label Distribution Complete label set

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**LDL – Problem Formulation**

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**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

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**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

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**Conditional Probability Mass Function**

Directly minimizing the K-L divergence between predicted and real LDs MaxEnt Model

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**Conditional Probability Mass Function**

IIS-LLD [Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]

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**Conditional Probability Mass Function**

BFGS-LLD [Geng and Ji, ICDMW’13]

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**Conditional Probability Mass Function**

CPNN [Geng, Yin, and Zhou, TPAMI’13] 3

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**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

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**Multivariate Support Vector Regression**

Sigmoid model Target function of SVR Loss Function

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**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.

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**Multivariate Support Vector Regression**

The loss function Multivariate Insensitive Zone Problem: Difficult to optimize and apply the kernel trick

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**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

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**Multivariate Support Vector Regression**

The loss function Replacing ui with u′i/4 Insensitive Zone

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**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?

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**Age Estimation Experiment**

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

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**Head Pose Estimation Bivariate Label Distribution**

[Geng and Xia, CVPR’14] Bivariate Label Distribution

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

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**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”

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**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

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**Multilabel Ranking for Natural Scene Images**

[Geng and Luo, CVPR’14] Experiment

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

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

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**Pre-release Prediction of Crowd Opinion on Movies**

[Geng and Hou, submitted to IJCAI’15] Pre-release Metadata Crowd Rating Distribution

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**Pre-release Prediction of Crowd Opinion on Movies**

[Geng and Hou, submitted to IJCAI’15] Experiment

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**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 ……

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**Download the LDL Matlab package from**

Interested? Download the LDL Matlab package from

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Thank You palm.seu.edu.cn

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