An Improved Non-negative Matrix Factorization Method of Blind Unmixing for Hyperspectral Imagery.pdf

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http://www.j-es.org/

Scientific Journal of Earth Science December 2013, Volume 3, Issue 4, PP.107-118

An Improved Non-negative Matrix Factorization

Method of Blind Unmixing for Hyperspectral

Imagery Jingjing Cao, Li Zhuo

Center of Integrated Geographic Information Analysis, Guangdong Key Laboratory for Urbanization and Geo-simulation, School

of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, PR China

Email: [email protected]

Abstract

An improved non-negative matrix factorization method of blind unmixing for hyperspectral imagery (ATGP-NMF) was proposed

in this paper, concerning the fact that the blind unmixing of Non-negative Matrix Factorization(NMF) is easily reduced to the local

minimum, by which the spectra and abundance of the target endmember that were obtained by using Automatic Target Generation

Process (ATGP) algorithm based on unsupervised orthogonal subspace projection and Non-negative Least Squares (NNLS) were

then regarded as initial values by NMF to get the corresponding endmember. The validity and feasibility of the proposed method

were analyzed based on the data of both simulation and remote sensing imagery; and then the result was compared with that from

VCA-FCLS algorithm which extracted the endmember matrix by using the Vertex Component Analysis (VCA) algorithm and the

abundance matrix by using the Fully Constrained Least Squares (FCLS) algorithm. It was indicated that the optimization of the

target endmember initial value not only promotes the algorithm accuracy, but also strengthens its feasibility in the ATGP-NMF

algorithm.

Keywords: Hyperspectral Remote Sensing; Mixed Pixel; Target Endmember; Non-negative Matrix Factorization; Blind Unmixing

510275

(NMF)

(ATGP-NMF)(ATGP)(NNLS)

NMF

VCA-FCLSATGP-NMF

S20120100105172011-2014-B08008

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[1]

[2]Blind Source Separation, BSS

[3, 4]BSS

Independent Component Analysis, IC[5-10]

Non-negative matrix factorization, NMF[11-13]Complexity Analysis, CA[14]

Sparse Component Analysis, SCA[15, 16]NMF

NMF

NMF[17] NMF[11] NMF[18]

[19][13] NMF

NMF

NMF

Automatic Target Generation

Process-Non-negative matrix factorization, ATGP-NMF NMF

1

NMF 20 Lee Seung 1999Nature

[20]

[21]n mX r

n rA r mS

n m n r r m n mX A S E (1)

nm r ( min( , ))r n m n rA

r n mX n mE

NMF

n m n r r mX A S (2)

NMF NMF

(4) NMF

A S

221 1( , ) ( ( ) )

2 2ij ij

ij

Euc X AS X AS X AS (3)

21min ( , )

2

0, 0

F

ij ij

f A S X AS

a s

(4)

- 109 -


2

F Frobenius

( )

( )

T

pb

pb pb T

pb

A XS S

A AS (5)

( )

( )

T

lp

lp lp T

lp

XSA A

ASS (6)

NMF

2 ATGP-NMF

1

NMF NMF

ATGP [22] NMF NMF

1

2.1

- 110 -


Harsanyi, Farrand Chang[23]-Neyman-Pearson

Hsrsanyi-Farrand-Chang, HFCHFC

PCA, ICA, AkaikeAkaike Information Criterion, AIC[24]

Minimum Description Length, MDL[25]HFC

2.2

ATGP[22, 26]

ATGP

(1) x HFC q

(2)

0t 0 arg max[ ]Tx

t x x

(3) 0t 0 0U t 0 0=U tP P

0 01 arg max[( ) ( )]TU Uxt P x P x

(4) 1i i ( 1,2, , 1i q ) i it 1 1arg max[( ) ( )]i iTi U Uxt P x P x

(5) it 0 1[ , , , ]i iU t t t #

iU i iP I UU

(6) q

0 1 1[ , , , ]qt t t

2.3 NMF

NMF

NMF

(1) A S ATGP NMF A NNLS

S

(2)

0 A S

( )

( )

T

pb

pb pb T

pb

A XS S

A AS

(7)

( )

( )

T

lp

lp lp T

lp

XSA A

ASS

(8)

(3) A S(7) S (8) A

- 111 -


(4) 1

(9) S S 1

pb

pb P

pb

p

SS

S

(9)

(5) A S 0

2( ) ( ) ( )1 ( , )

2

k k kEuc X X X X (10)

( ) kX k X

2.4

[27]

3

ATGP-NMF 2

2

VCA-FCLS NMF

VCA [28, 29] FCLS [30]

VCA-FCLS

Nascimento Dias[31]Spectral Angle Distance, SAD

Spectral Information Divergence, SID

Root Mean Square Error, RMSE[27] SE[32] d[33]

(1) SAD

1 1 1

1 1

( , ) cos cos

N

i i

i

N N

i i i i

i i

ABAB

SAD A BA B

A A B B

(11)

A BN

(2) SID

( , ) ( || ) ( || )SID A B D A B D B A (12)

AB

(3) RMSE

2

1 1

( )pN

ij ij

i j

S S

RMSEN

(13)

ijS ijS i jN

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(4) SE

1 1

pN

ij ij

i j

a a

SEp N

(14)

N p 1 2, , , pc c c ija i jc ija i jc

(5) d

2

1

2

1

( )

1.0 1.0

( )

N

t t

t

N

t t

t

O PMSE

d NPE

P O O O

(15)

MSEPEPON

d Willmott[33][01] d

2R

3.1

ENVI 5.0United States Geological Survey, USGS 5

BruciteChabazite(Olivine)Spessartine

Witherite420 2

2 USGS

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(a) VCA-FLCS

(b) ATGP-NMF

3 (a)VCA-FLCS(d)ATGP-NMF( USGS)

Dirichlet 1

Signal Noise RatioSNR 30dB 1296

3

1 SAD

Brucite Chabazite Olivine Spessartine Witherite Mean VCA-FCLS 0.0028 0.0037 0.0053 0.0042 0.0021 0.0036

ATGP-NMF 0.0056 0.0124 0.0121 0.0080 0.0046 0.0085

2 SID

Brucite Chabazite Olivine Spessartine Witherite Mean VCA-FCLS 0.097010-4 0.202410-4 0.631010-4 0.282110-4 0.045710-4 0.251610-4

ATGP-NMF 0.069610-3 0.290510-3 0.601910-3 0.094410-3 0.021910-3 0.215710-3

3

RMSE SE d

VCA-FCLS 0.0067 0.0047 0.9999

ATGP-NMF 0.0170 0.0121 0.9991

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1 2 3ATGP-NMF VCA-FCLS

SADSIDRMSE SE 1

VCA-FCLS

3.2

3.2.1

8

Hyperion 8196196 356nm2577nm 10nm 30m30m 242

3.2.2

(1)

1m1m

3m3m ENVI 5.0Feature Extraction K-

K-Nearest Neighbor, KNN[34]

ArcGIS 30m30m

(2)

11

30

3.2.3

ENVI Hyperion HFC

VD 7

Plaza Chang[35] FP =10-3 VD

7 VD

FP 10-1 10-2 10-3 10-4 10-5 10-6

VD 11 11 10 10 9 9

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HFCVD=10 ATGP-NMF

300 9

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

9 ATGP-NMF(a)(b)(c)(d)(e)(f)(g)(h)(i) 1#(j) 2#(k)

8

(SAD) (SID)

VCA-FCLS ATGP-NMF VCA-FCLS ATGP-NMF

0.1707 0.1008 0.1206 0.0310

0.3848 0.1584 0.3342 0.3849

0.1158 0.0980 0.0196 0.0113

0.2332 0.0444 0.0582 0.0022

0.1544 0.0618 0.0303 0.0039

0.0449 0.0918 0.0019 0.0104

0.5870 0.1249 0.7253 0.0167

1# 0.1107 0.0759 0.0123 0.0073

2# 0.8300 0.0796 1.1788 0.0065

0.4485 0.0705 0.2403 0.0050

0.3080 0.0906 0.2722 0.0479

3.2.4

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8 VCA-FCLS ATGP-NMF 10 SAD

SID

9

RMSE SE d

VCA-FCLS 0.2368 0.1356 0.5538

ATGP-NMF 0.1814 0.1155 0.7382

8 VCA-FCLS ATGP-NMF 10 SAD

SIDATGP-NMF

10ATGP-NMF

RMSESE d

9 VCA-FCLS ATGP-NMF

ATGP-NMF

ATGP-NMF

4

NMF ATGP-NMF

NMF NMF

VCA-FCLS

ATGP-NMF

VCA-FCLS

NMF

(1)

(2)(3)

(4)

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An Improved Non-negative Matrix Factorization Method of Blind Unmixing for Hyperspectral Imagery.pdf