Globally Maximizing Locally Minimizing unsupervised discriminant projection with applications to face and palm biometrics PAMI 2007 Bo Yang 2/25/2019.

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Presentation transcript:

Globally Maximizing Locally Minimizing unsupervised discriminant projection with applications to face and palm biometrics PAMI 2007 Bo Yang 2/25/2019

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.

Review PCA LDA

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

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

Basic Idea of UDP

Characterize the Local Scatter

Characterize the Non-local Scatter

Characterize the Nonlocal Scatter (cont’d)

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

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

Algorithmic Derivations of UDP in Small Sample Size Cases

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

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

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

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

UDP Algorithm

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

Graph with Heat kernel

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

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

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

LINKS TO LDA (cont’d)

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

EXPERIMENTS Yale Database FERET Database AR Database PolyU Palmprint Database

Yale Database

Yale Database (cont’d)

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.”

AR Database

PolyU Palmprint Database

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

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

Comment

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.

Thank you !