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LLooccaall PPrreesseerrvviinngg PPrroojjeeccttiioonn

R94922011

R94922025

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Local Preserving Projection ..(by R94922011 )

.. 3

.. 4

.. 5

LPP Application .(by R94922025 )

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. 7

... .7

LPP Face Recognition 9

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Locality Preserving Projections1 R94922011

I.

1. LPP

2.

(1) Local Structure LPP PCA LDA Global Structuremanifold

(2) LPP Linear Isomap

3. Laplacian Eigenmap

1 Xiaofei He, Partha Niyogi, Locality Preserving Projection, NIPS, 2003.

Xiaofei He, Shuicheng Yan, Yuxiao Hu, Hong-Jiang Zhang, Learning a Locality Preserving Subspace for Visual Recognition, ICCV, 2003.

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II.

1. Xx1, x2, ( xi Nx1 N )

2. A [a1, a2, , aM] ( aj Nx1 aj 0 M )

3.

(1) Adjacency Undirected Graph

i. -neighborhoods

ii. k k-nearest neighbors k

(2) Wij(1) 0

i.

1i =jW

ii. heat kernel

txx

j

ji

eW2||||

i

=

(3) A

ijij

jT

iT

AWxAxAinrg 2)(ma

aj

ijij

jT

iT Wxaxain 2a )(marg

a yi=aTxi

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Ly2y W)y -(D2y

Wyy2-Dy2

WyWyy2-Wy W)y-(y

TT

ijijji

iii

2i

ijij

2j

ijijji

ijij

2i

ijij

2ji

==

=

+=

D =j

ijii WD

L = D-W Laplacian Matrix y a y = aTX

D Dii i 1y =DyT 0

amina1 a

TT

XDXaa

XLXargTT =

( ) 0= aXDXaaXLXaa

TTTT

aXDXXLX TT =a Generalized Eigenvector Problem == aXDXaaXLX TTTTa

aTXLXTa a M 0

III.

1. ??

2. Incremental Semi-Supervised

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Subspace Learning for Image Retrieval2

(1) k k-nearest neighbors S0

(2) A B(1)

=

=

B xandA x

or B, xandA xif 0

A x, xif 1

j)(i,S ii.

S S i.

ij

ji

ji

k

1-kk

(3) S W

=j

kkk j)(i,Sj)/(i,S j)(i,W

D L

kkkk

k

WIWDLID

===

(4) (2)(3)

(5)

2 Xiaofei He, Incremental Semi-Supervised Subspace Learning for Image Retrieval, ACM Multimedia, 2004.

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LPP(Local Preserving Projection) Application by R94922025

LPP Application LPP(p.s LP !) LPP tutorial LPP Machine Learning (compare with other method)

(!) Linear method PCA LDA non-linear method LLEIsomap Linear methodLPP linear method PCA LDA local PCA LDA Global classify local LPP linear method discriminating power!! non-linear method (LLE)LLE LPP linear LPP adjacency matrix Local structure LLE discriminating power LPP

LLE Face Recognition LPP LPP (p.s !!!) LPP

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LPP

LPPpower

PCA

LPP

PCAPCAoutliernoiseLPP PCALPPLPPlocal sturcturePCA 2DLPP0~92Laplacian eigenmapsLPPPCA discriminating powerLPPPCALPPLaplacian eigenmapsLaplacian eigenmapsLPPlinearnon-linear

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LPPFace Recognition (paper: Xiaofei He, Shuicheng Yan, Yuxiao Hu, Partha Niyogi, and Hong-Jiang

Zhang,Face Recognition Using Laplacianfaces, IEEE TRANSACTIONS ON PATTERN

ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 3, MARCH 2005)

LPPFace RecpgmitonLPPFace Recogniton LPP 1) PCA Projection:LPPPCAXDXTsungular(sample)eigen vectorPCAXDXTnonsingularnoise(XDXTtutorial! ) 2)Construct the nearest-neighbor graph: neighborhood

k-nearest-neighborhoodk-neighborhood

k-nearest-neighborhoodapplicationkk-nearest-neighborhood-neighborhood

3)Choosing weights: weightweight

node

eS tijxx ji

2

= nodeweight0

4)Eigenmap:generalized eigenvector

eigenvalueeigenvector

wXDXwXLX TT = nmmeigenvalueeigenvector

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xy

LPP

Face Recognition

trainingLPPtrainging

2LPP

LPP

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LPP

Face Recognition

LPPYale DatabasePIE DatabaseMSRA DatabasePCALDAshowMSRA databasedatabase DimError RateLPPFace RecognitionLPP

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LPP training data training data training data LPP PCA LDA LPP

LPP LPP tutorial LPP

! GOOD LUCK! tutorial (!)

!!