1. Yu-Feng Li 1, James T. Kwok2, Ivor W. Tsang3 and Zhi-Hua Zhou1
A Convex Method for Locating Regions of Interest with Multi-Instance Learning
Yu-Feng Li 1, James T. Kwok2, Ivor W. Tsang3 and Zhi-Hua Zhou1
1 LAMDA Group, Nanjing University, China
2 Hong Kong University of Science & Technology, Hong Kong
3 Nanyang Technological University, Singapore

2. Multi-Instance Learning
MIL [Dietterich et al., AIJ97] attempts to learn from a training set consists of bags each containing many instances
- A bag is positive if it contains at least one positive instances; otherwise negative.
- The labels of training bags are known, however, the labels of instances in the bags are unknown.
Multi-instance learning
Traditional supervised learning
In MIL, identifying positive instances is an important problem
understanding the relation between the bag and input patterns.
Figure reprinted from [Zhi-Hua Zhou et al., icml09]

3. Example: ROI
In relevant feedback of CBIR, usually user is only interested in some regions, i.e., regions of interest (ROI), in the images.
Locating ROIs could be used in other area, i.e., image screening…

4. The Problem
How to develop an efficient and theoretical supported method for locating the ROIs?
…This presentation

5. Outline
Introduction
Our Methods
Experiments
Conclusion

6. Multi-Instance Learning
Introduction
Multi-Instance Learning
Originated from the research on drug activity prediction [Dietterich et al. AIJ97]
Drugs are small molecules working by binding to the target area
For molecules qualified to make the drug, one of its shapes could tightly bind to the target area
A molecule may have many alternative shapes
The difficulty:
Biochemists know that whether a molecule is qualified or not, but do not know which shape responses for the qualification
Figure reprinted from [Dietterich et al., AIJ97]

7. Multi-Instance Learning (con’t)
Introduction
Multi-Instance Learning (con’t)
Each shape can be represented by a feature vector, i.e., an instance …
[a1, a2, …, am]T
[b1, b2, …, bm]T
[u1, u2, …, um]T
one bag
one molecule
Thus, a molecule is a bag of instances
A bag is positive if it contains at least one positive instance; otherwise it is negative
The labels of the training bags are known
The labels of the instances in the training bags are unknown
Figure reprinted from [Zhi-Hua Zhou et al., icml09]

8. MIL for Image Analysis Various applications
Introduction
MIL for Image Analysis
Various applications
Image categorization [Maron & Ratan, ICML’98; Chen & Wang, JMLR04; Chen et al., PAMI06]
Image retrieval [Zhang et al., ICDE’02; Zhou et al., AJCAI’05]
Face detection [Viola et al., NIPS’05; Zhang & Viola, NIPS’07]
Computer-aided medical diagnosis [Fung et al., NIPS’06]
… …

9. Related works for locating ROIs
Introduction
Related works for locating ROIs
Diverse Density and its variants [Maron & Lozano-Pérez, NIPS98] [Maron & Ratan, ICML98] [Zhang & Goldman, NIPS02] [Ray & Craven, icml05]
Effective in locating the ROIs
Huge time cost, suffers from local minima
CKNN-ROI [zhou et al., AJCAI05]
A variation of Citation-kNN [wang & zucker,icml00]
Efficient, but based on heuristic
SVM based methods
Very few focus on locating the ROIs, except MI-SVM [Andrew et al., nips03]
Effect and efficient, but still suffers from local minima

10. Multi-Instance SVM [Andrew et al, nips03]
Introduction
Multi-Instance SVM [Andrew et al, nips03]
Main Idea : Large Margin Principle
Positive bag
Negative bag
Key instance, i.e., roi
Optimal Hyperplane

11. A set of training bags: , where and
Introduction
Problem Setup
A set of training bags: , where and
The decision function:
The goal is to learn f minimizes the structural risk
 is strictly monotonically increasing function,
l() is the loss function,
C is the regularization parameter

12. consider and square hinge loss
Introduction
Problem Setup (cont.)
consider and square hinge loss
So, (1) becomes
where
This, however, is a non-convex problem because of the max operator and it may get stuck in local solution.
In this paper, we propose a convex-relaxation method to solve such an non-convex problem.

13. Outline
Introduction
Our Methods
Experiments
Conclusion

14. Instance-level Key Instance SVM
Our Methods
Instance-level Key Instance SVM
By introducing the indicator variables d and s(i,j)
λ balances the slack variables from positive and negative bags

15. Bag-level Key Instance SVM
Our Methods
Bag-level Key Instance SVM
Ins-KI-SVM may involves large number of constraints in optimization.
Simply represent the negative bag by mean of its instances [Gartner et al., icml02] [Xu & Frank, pakdd04].

16. More General Formulation
Our Methods
More General Formulation
It involves Ins-KI-SVM and Bag-KI-SVM as special cases
when r = N and , , it reduces to Ins-KI-SVM
when r = m and , it reduces to Bag-KI-SVM
In this paper, we aim at solving above optimization problem instead!

17. Generate the most informative label
Our Methods
Convex relaxation – Intuitional View
Our main observation
efficient
hard ?
SVM 1 -1
SVM
Note that
Each label assignment corresponds to a kind of label-kernel in SVM dual.
Learn weights for different label assignments reduces to multiple kernel learning which is convex and efficient in general.
Our simple strategy 1 -1
SVM … 1 -1 ?
Generate the most informative label

18. Convex relaxation approach
Our Methods
Convex relaxation approach
Consider the dual
Consider the minimax relaxation [Li et al., AISTATS’09]
Multiple Kernel Learning

19. Convex relaxation approach (cont.)
Our Methods
Convex relaxation approach (cont.)
Exponential number of base kernels…. Too expensive
Cutting plane algorithm
Adaptive SimpleMKL
How?

20. Find the most violated d
Our Methods
Find the most violated d
To find the most violated d, we need to solve the following maximization problem
Rewritten as
It is a concave QP, and could not be solved efficiently…
However, the cutting plane method only requires to add a violated constraint at each iteration
Approximated by Inf-norm
Hence, we propose a simple and efficient method for finding a good approximation of the most violated d
Linear Problem, can be solved by sorting

21. Outline
Introduction
Our Methods
Experiments
Conclusion

22. Experiments
Two Kinds of Tasks
CBIR image data
Benchmark data sets

23. CBIR image data [zhou et al., AJCAI05]
Experiments
CBIR image data [zhou et al., AJCAI05]
Some statistics
Image size: 160 × 160
Feature representation by using SBN [Maron & Ratan ICML98]
Evaluation: success rate, i.e., the ratio of the number of successes divided by the total number of relevant images

24. Experiments
CBIR image data (cont.)
One-vs-rest, 50 train/ 450 test (10/90 are relevant, respectively), 30 runs

25. Experiments
Some examples

26. Different number of confident bags
Experiments
Different number of confident bags
Ins-KI-SVM is consistently better than all the other SVM-based methods across all the settings.

27. Average cpu time at ordinary PC
Experiments
Speed
Average cpu time at ordinary PC
Performance per time cost = (1/rank)/time
Bag-KI-SVM achieves highest performance per time cost
among all svm-type methods.

28. 10 fold Cross-validation
Experiments
Benchmark datasets
10 fold Cross-validation
The performance of KI-SVMs are competitive with all these state-of-the-art methods

29. Thanks! Conclusion Main contribution: Future work:
A convex method for locating ROIs with multi-instance learning
Future work:
Locating multiple rois or roi groups
Thanks!