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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)
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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
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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
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(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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