1. Globally Maximizing Locally Minimizing unsupervised discriminant projection with applications to face and palm biometrics PAMI
Bo Yang
2/25/2019

2. Motivation
Shortage of existing manifold algorithms for Classification:
Locality: has no direct connection to classification
non-locality: modeling multi-manifolds
the inter-cluster scatter, may provide crucial information for discrimination
seeks to maximize the ratio of the nonlocal scatter to the local scatter.

3. Review
PCA
LDA

4. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

5. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

6. Basic Idea of UDP

7. Characterize the Local Scatter

8. Characterize the Non-local Scatter

9. Characterize the Nonlocal Scatter (cont’d)

10. Determine a Criterion: Maximizing the Ratio of Nonlocal Scatter to Local Scatter

11. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

12. Algorithmic Derivations of UDP in Small Sample Size Cases

13. Algorithmic Derivations of UDP in Small Sample Size Cases (cont’d)

14. Algorithmic Derivations of UDP in Small Sample Size Cases (cont’d)

15. Algorithmic Derivations of UDP in Small Sample Size Cases (cont’d)

16. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

17. UDP Algorithm

18. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

19. Graph with Heat kernel

20. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

21. LINKS TO LPP
UDP maximizes the ratio of the nonlocal scatter (or the global scatter) to the local scatter whereas LPP minimizes the local scatter

22. LINKS TO LDA
LDA can be regarded as a special case of UDP if we assume that each class has the same number of training samples

23. LINKS TO LDA (cont’d)

24. UNSUPERVISED DISCRIMINANT PROJECTION (UDP)
Basic Idea of UDP
Algorithmic Derivations of UDP in Small Sample Size Cases
UDP Algorithm
EXTENSION: UDP WITH KERNEL WEIGHTING
LINKS TO OTHER LINEAR PROJECTION TECHNIQUES: LDA AND LPP
BIOMETRICS APPLICATIONS: EXPERIMENTS AND ANALYSIS

25. EXPERIMENTS Yale Database FERET Database AR Database
PolyU Palmprint Database

26. Yale Database

27. Yale Database (cont’d)

28. FERET Database
This subset includes 1,000 images of 200 individuals (each one has five images). It is composed of the images whose names are
marked with two-character strings: “ba,” “bj,” “bk,” “be,” “bf.”

29. AR Database

30. PolyU Palmprint Database

32. Comment
LPP
UDP
UDP and LPP essentially share the same basic idea: simultaneously minimizing the local quantity and maximizing the global quantity.

33. Comment the numerators in (1) and (2), are two equivalent
the denominators in (1) and (2), are two similar scatters
the projections derived from UDP and LPP are identical under the assumption that the local density is uniform

34. Comment

35. Comment
we would like to conclude that UDP is an effective algorithm as a simplified, or regularized, version of LPP, but there is no reason to prefer UDP over LPP for the general classification and clustering tasks.

36. Thank you !