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Unsupervised Discriminant Projection: Maximizing Global and Minimizing Local Scatter

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dalton
36 diapositives · 515 Views · Jan 29, 2014

A novel method for Unsupervised Discriminant Projection (UDP), addressing the limitations of existing manifold algorithms in classification tasks. By maximizing the ratio of non-local (global) scatter to local scatter, it enhances discrimination in high-dimensional data. Notably, the method is connected to Locality Preserving Projections (LPP) and Linear Discriminant Analysis (LDA). Experiments demonstrate its efficacy in biometrics, particularly in face and palmprint recognition. Algorithmic derivations and the extension of UDP with kernel weighting are also discussed.

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  1. Globally Maximizing Locally Minimizing unsupervised discriminant projection with applications to face and palm biometricsPAMI 2007 Bo Yang 6/7/2014

  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 ofNonlocal 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

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

  32. 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

  33. Comment

  34. 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.

  35. Thank you !