Learning to Rank using High-Order Information
Puneet K.
1Ecole
1
Dokania ,
A.
2
Behl ,
Centrale Paris and INRIA Saclay - France,
Aim
•
•
C. V.
2
Jawahar ,
M. Pawan
2IIIT
1
Kumar
Hyderabad - India
Results
HOB-SVM
•
Incorporate High-order information
• Optimizes Decomposable loss
• Encoding high-order information (joint feature map):
Optimizing Average Precision (Ranking)
Incorporating High-Order Information
Motivations and Challenges
• High-Order Information
 For example, persons in the same image are likely to have same action
Action inside
the bounding
box ?
Context helps
 Problem Formulation: Given an image and a bounding box in the image,
predict the action being performed in the bounding box.
 Dataset- PASCAL VOC 2011, 10 action classes, , 4846 images (2424 ‘trainval’ +
2422 ‘test’ images).
 Features: POSELET + GIST
 High-Order Information: “Persons in the same are likely to perform same
action”. Connected bounding boxes belonging to the same image.
• Results
• Parameter Learning:
High Order + Ranking -> No Method
• Action Classification
• Average Precision Optimization
 AP is the most commonly used evaluation metric
 AP loss depends on the ranking of the samples
 Optimizing 0-1 loss may lead to suboptimal AP
• Ranking: Single Score

Ranking ??
Sort difference of max-marginal scores to get ranking:
Use Max-marginals
AP = 1
Accuracy = 1
 Max-marginals capture high-order information
AP = 0.55
Accuracy = 1
• Optimization:
 Convex
AP doesn’t decompose
SVM
 Use dynamic graph cut for fast computation of max-marginals
HOAP-SVM
Notations
• Samples:
• Set of positive samples:
• Ranking Matrix:
• Labels:
• Set of negative samples:
• Loss function:
•
AP-SVM
• Optimizes AP (measure of ranking)
• No High-Order Information
• Key Idea: Uses SSVM to encode ranking (joint score):
•
Parameter Learning
•
HOAP-SVM
• Paired ttest:
Sample scores similar to
HOB-SVM (max-marginals)
 HOB-SVM better than SVM in 6 action classes
 HOB-SVM not better than AP-SVM
 HOAP-SVM better than SVM in 6 action classes
 HOAP-SVM better than AP-SVM in 4 actions classes
Conclusions
Parameter Learning
• Ranking:
Sort scores
• Optimization
 Non Convex - > Difference of Convex -> CCCP
Ranking: Sort scores,
Optimization
 Convex
 Cutting plane -> Most violated constraint (greedy) -> O(|P||N|)
HOB-SVM
• Optimizes AP based loss
• Incorporate high-order information
• Encode ranking and high-order information (AP-SVM + HOB-SVM):
Joint score similar to AP-SVM
•
AP-SVM
Methods
Loss
Ranking
Objective
0-1
High-Order
Information
No
SVM
Yes
Convex
AP-SVM
AP Based
No
Yes
Convex
HOB-SVM
Decomposable
Yes
Yes
Convex
HOAP-SVM
AP Based
Yes
Yes
Non-Convex
(Diff of Convex)
Code and Data: http://cvn.ecp.fr/projects/ranking-highorder/
 Dynamic graph cut for fast upper bound