2016 International Conference on Artificial Intelligence: Techniques and Applications (AITA 2016) ISBN: 978-1-60595-389-2
Hyperspectral Images Classification via Weighted Spatial-Spectral
Principle Component Analysis
Fang
HE,
Wei-min
JIA, Qiang
YU,
Rong
WANG
and
Shan
LIU
Xi'anResearchInstituteofHigh-tech,Xi’an710025,China
Keywords: Hyperspectralimagesclassification,Weightedspatialandspectralprinciplecomponent analysis,reconstruct.
Abstract. In order to improve the Hyperspectral images (HSI) classification accuracy and to
preprocess HSI by fully using the spatial and spectral information, a new spatial-spectral
dimensionality reduction method, Weighted Spatial and Spectral Principle Component Analysis
(WSSPCA),wasproposed.ThisalgorithmreconstructedtheHSIbyusingthephysicalcharactersof
HSI.Then,principleComponentAnalysis(PCA)wasutilizedtoreducedimensionalityofHSI.The
new method not only can lower the influence of singular point in HSI, but also reduce the
redundancy between bands, which improves the HSI classification accuracy efficiently. The
benchmark tests on Indian Pines and PaviaU demonstrate that the performance of WSSPCA is
better than PCA and LPP when 10%, 5% samples in each class. The best values of kappa
coefficient obtained by WSSPCA are 89.61% and 95.59% respectively on the HSI datasets,
exceedingthebaseline20.5%and19.38%.
Introduction
Hyperspectralremotesensingtechnologyhasbeenrapidlydevelopedsinceinthe1980ofthe20th
century [1],and widely used for environmental science, geological research, precisionagriculture,
and military [2], [3]. The hyperspectral image (HSI) is the remote sensing image obtained by
imaging spectrometer.The main characteristicof HSI is fusing traditional ofspace dimension and
spectrumdimensioninformationforone,forming"mapsone"ofsuperdimensiondata[4].Thehigh
of spectrum dimension number and spectrum resolution for features brings great opportunity for
HSI classification,while also proposeschallenges to traditionalof imageclassification recognition
algorithms[5].
Hyperspectralimagesaremadeupofalargenumberofsinglebandimages.Therapidexpansion
of the amountof data increased the complexity ofdata processing, reducingthe efficiency of data
processing [6]. As the spectral resolution improves, the redundancy between adjacent bands is
increasing, whichis seriouslyreducing theaccuracy oftraditional algorithm forHSIclassification.
When the sample is limited, the HSI classification will experience “dimensionality curse” [7].
Dimensionality reduction (DR), which searches a low-dimensional representation that contains
usefulinformationforhighdimensiondata, isanimportantpartofHSIclassificationpreprocessing
[6].Meanwhile,DRcanreducetheamountofdataandlookforasimplerandclearerrepresentation
ofdata,whichmakesforHSIclassification[8].
In recent years, the traditional DR methods are linear discriminant analysis (LDA) [9],
nonparametric weighted feature extraction (NWFE) [10], principle component analysis (PCA)
[11][12][13], locality preserving projection (LPP) [14], and neighborhood preserving embedding
(NPE)[15].However,theaboveDRmethodssimplyusethespectralinformationofHSIandignore
thespatialinformationwhichcannotrevealtheintrinsicrelationshipbetweendifferentsamples.
AsthedistributionofsamplesinHSIisspatialcontinuity, thispaperproposesanewDRmethod
offusionof hyperspectralimagespaceandspectral information,weighted spatialspectralprinciple
component analysis (WSSPCA). This new algorithm uses the neighborhood space between the
HSI Reconstructed Based on Weighted Spatial and Spectral Information
The samplesof HSI arespatial continuity thatis the localcontiguous region ofneighboring pixels
are made up of the same material and belong to the same class. Using the weighted spatial and
spectralinformationtoreconstructtheHSIcansmoothHSI.
InHSI,settingthecoordinatesofpixelisxi,theneighborhoodspaceofxiis:
( ) ,
, q ,
i
i i i i
N p q
p p a p a q a q a
x x ，
， (1)
wherea(w1) / 2, w is odd number, which presents the window scale of neighborhood space.
Thepixels x xi, i1,xi2,...,xis areintheneighborspaceofN(xi).Thenumberofnearestneighborpoint issw21.
Thereconstructedpixelcanbegottenbyusingthefollowingrule:
2 2 1 1 1 1 ˆ 1 j i j i w j j
N i k k ik
i w j N k k
xx xx
x x x
x (2)
where the weight of any pixel xik to the center pixel xi in the neighbor space of is
2 0
exp{ }
k i ik
x x . The parameter 0 is the spectral factor which can be used to measure the
degree of interaction between the different pixels in the same neighborhood space. The physical
meaningof 0 is thecloser thespectral curvesbetween thepixels, themore interaction witheach
other,whereasthesmaller.
This algorithm can adjust the size of neighborhood space by the neighbors window scale and
gives the smaller weight to reduce the interference of singular points by the spectral factor,
achievingtosmooththeHSI.Parameter w and 0 areimportantforthefinalresult,thusweused
experimentalresearchmethodtoselect.
Thepixels inthe edgesor cornersarepreprocessed asFig.1. Eachsquare gridrepresentsa pixel
inHSI, thelightgraygrid asthecenterpixelandthedark graygridasthefilledmethod.Whenthe
pixelisattheedgeorcornerlocation,itsneighborpixelisfilledwith.
i1 j1
x
x
i1 j 1 1
i j
x
1
i j
x
x
ij 1
i j
x
i1 j1
x
x
i1 jx
i 1 j1(a) Normalposition
i1 j1
x
1
i j
x
x
ij 1
i j
x
i1j1
x
x
i1 jx
i 1 j1ij
x
x
i j 1(b) Ontheedge (c) Atthecorner
Figure1.Neighborspaceofpixelunderdifferentconditions.
The Algorithm of Weighted Spatial and Spectral Information Principle Component Analysis
PCA, a classical and effective method for feature extraction, can reduce the correlation between
HSI databy usingseveral principal components whichare unrelatedto present theoriginal energy
information of multiple bands, when applied in HSI DR. WSSPCA integrates the spatial and
spectralinformationofHSItoreducethedimension,whichishelpfulforHSIclassification.
The procedures of WSSPCA are as follows. The reconstructed HSI can be represented as Xˆ
whose size is n d , where n is the total pixel in each band and d is the number of all bands.
ThenthemeanofeachimageinHSIis
1
1 n ˆ
i i n
μ X
T 1
1 n ˆ ˆ
i i
i n
S x μ x μ
(3)
Thentheeigenvaluesandeigenvectorsofthecovariancematrixare:
= , 1, 2,...,
i i i i n
Sν ν
(4)
Choosing k componentsofHSItoformthefeaturespace: w w1, 2,...,wk
Thereconstructeddataareprojectedonthefeaturespace:
T ˆ
y W x μ
(5)
The nearest neighbor classifier is used to classify the projected data and the classification
accuracyevaluationindexiscountedtomeasuretheresult.
HSI Classification by Weighted Spatial and Spectral Information Principle Component Analysis
The concrete steps of HSI classification by weighted spatial and spectral information principle
componentanalysisisasthefollows:
Input:HSIdata
1,...,
T,n d n
X x x X R ,thescaleparameter w andspectralfactor0
.
Output:theclassificationaccuracyevaluationindex.
Step1:thedataset’sneighboringspaceisselectedaccordingtoEq.1;
Step 2: forany pixel xi in datasetX,the xi is reconstructed according toEq.2 toget the new
dataXˆ ;
Step3:thecovariancematrixof Xˆ iscountedaccordingtoEq.3andcomputingtheeigenvalues
and eigenvectors of the covariance matrix. k components of HSI are chosen to form the feature
space.
Step 4: the train and test samples are chosen from the data set according to certain rules. The
reconstructed data are projected on the feature space and the nearest neighbor classifier is used to
classifytheprojecteddata.Theclassificationaccuracyevaluationindexiscounted.
（a）Falsecolor （b）Correspondinggroundtruth （a）Falsecolor （b）Correspondinggroundtruth
Figure2.TheIndian-pineshyperspectralimage. Figure3.ThePaviaUhyperspectralimage.
Experiment Result and Analysis
Hyperspectral Data Sets
Indian Pines. The data set was acquired by the AVIRIS sensor in 1992. The image has 220
bands, inwhich 20bandsare discardedbecauseof thewaterandatmospheric affection. Eachband
has 145 145 pixels.The total numberof samples is10249 rangingfrom 20 to 2455in each class.
Thefalsecolorcompositionofbands50,27,and17andtheground-truthmapareshowninFig.2(a)
andFig.2(b).
PaviaU. Thedatasetwasacquiredin2001bytheROSISinstrumentoverthecityofPavia, Italy.
This image scene corresponds to the University of Pavia and has the size of 610 340 pixels and
experiments.Thedatacontains9ground-truthclasses.Thefalsecolorcomposition ofbands50,27,
and17andtheground-truthmapareshowninFig.3(a)andFig.3(b).
Experimental Result and Analysis
WSSPCA, PCA, and LPP are used to reduce the dimension of HSI and the nearest neighbor
classifier isused to classify thedata after DR.The result withoutDR is actedas the baseline. The
best parameter of WSSPCA is chosen by experimental analysis. The weight matrix W of LPP is
constructed by the heart method.The HSI classification accuracy evaluations are overall accuracy
(OA), average accuracy (AA), and kappa coefficient (k). OA is the percentage of correctly
classifiedpixelsinthetestset, whereasAAisthemeanofclass-specific accuracyvalues. k isthe
percentageof agreement correctedby the numberof agreements thatwould be expectedpurely by
chance.
HSI Classification on Indian Pines Data Set. Thenearestwindow scaleandspectral factorare
twomainparametersinWSSPCA,whichcanbechosenfromexperiment.Weselectrandomly10%
of samples per class for training, and the remaining samples are used for testing. For very small
classes,wetake aminimumoftentrainingsamplesperclass. Fig.4 showstherelationshipbetween
classification accuracy and differentparameter on Indian Pines dataset. As shown in Fig.4a, when
the neighbor window scale is 9, AA, OA, and kappa coefficient can get the optimal result. From
Fig.4b, whenthe spectral factor is1, AA, OA, and kappacoefficient reached the maximum value.
ThebestparametersonIndianPinesdatasetare w9, 1.0.
（a）TherelationshipbetweenClassification
Accuracy(%)andneighborhoodscale
（b）TherelationshipbetweenClassification
Accuracy(%)andspectralfactor
Figure4.TherelationshipbetweenClassificationAccuracy(%)anddifferentparameteronIndianPinesdataset.
To compare the performance of different algorithms, we repeated 10 times classification
experiments, and computed the mean of AA, OA, and kappa coefficient. Fig.5 shows the
relationshipbetweenclassificationaccuracyanddimensions onIndianPines datasetinthefirst100
dimensions under the different algorithms. Tab.1 shows the best result and the corresponding
dimensionsobtainedbyeachalgorithmontheIndianPinesdataset.
From Fig.5, we can know that the classification results obtained by WSSPCA algorithm are
superiorto PCA,LPPalgorithms. The maximumclassification accuracygottenby WSSPCA isfar
beyondthebaseline,buttheresults obtainedbyPCA,andLPPareslightlylowerthanthe baseline.
The reason is that WSSPCA effectively used the spatial and spectral information, which can
improvetheclassificationaccuracy.
FromTable1,we canseethatWSSPCA,as anewspatial-spectralalgorithm ofHSI,can getthe
best resultunder the sameconditions. Themaximum value of OAwhich is obtainedby WSSPCA
algorithm is90.90%, exceeding the baseline17.93%, and kappacoefficient is 89.61%, beyondthe
baseline20.50%.Fig.5showsthatWSSPCAproposedinthispaperperformsbest.
Fig.6showstheclassificationmapsofthegroundtruth,trainsamples,testsamples,theresultsof
noDR,PCA,LPP,WSSPCAwhenthekappacoefficientismaximum.
3 5 7 9 11 13 15
83 85 87 89 91 93
Neighborhood Scale
Cl
as
si
fi
ca
ti
on A
cc
ura
cy (%)
AA OA kappa
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 80
82 84 86 88 90 92 94
Spectral factor
Cl
as
si
fi
ca
ti
on A
cc
ura
cy (%)
（a）Therelationshipbetween
AA(%)anddimensions
（b）Therelationshipbetween
OA(%)anddimensions
（c）Therelationshipbetween
kappa(%)anddimensions
Figure5.Therelationshipbetweenclassificationaccuracy(%)anddimensionsonIndianPinesdataset.
（a）Groundtruth （b）Trainsamples （c）Testsamples （d）Baseline
（e）PCA （f）LPP （g）WSSPCA
Figure6.ClassificationresultsofdifferentalgorithmsinIndianPinesdataset.
Table1.Thebestresults(%)withoptimaldimensions.
method OA(dimension) kappa(dimension)
baseline 72.97(1) 69.11(1)
PCA 72.94(20) 69.08(20)
LPP 72.91(3) 68.29(3)
WSSPCA 90.90(21) 89.61(21)
HSI Classification on PaviU Data Set. Inthisexperiment,we chooserandomly5% ofsamples
perclassfortraining,andtheremainingsamplesareusedfortesting.ThesameasIndianPinesdata
set,theparametersarechosenbyexperiments.Theoptimalparametersare w15, 2.0.
Werepeated10timesclassificationexperiments, andcomputedthemean ofAA,OA, andkappa
coefficient as the final result. Fig.7 shows the relationship between classification accuracy and
dimensions on PaviU dataset in different dimensions under the different algorithms. Tab.2 shows
thebestresultandthecorrespondingdimensionsobtainedbyeachalgorithmonPaviUdataset.
From Fig.7 and Table 2, we can know that the classification results obtained by WSSPCA
algorithm are superior to PCA,LPP algorithms. Themaximum valueof OA which is obtained by
WSSPCA algorithm is 96.69%, exceeding the baseline 14.36%, and kappa coefficient is 95.59%,
beyondthebaseline19.38%. However,theresultsobtainedbyPCAand LPParealwayslowerthan
thebaseline.
Fig.8showstheclassificationmapsofthegroundtruth,trainsamples,testsamples,theresultsof
noDR,PCA,LPP, WSSPCA whenthekappacoefficient ismaximum.From Fig.8,wecan seethe
classificationmapobtained byWSSPCA performsbest. Theerrorormissed phenomenonobtained
byWSSPCAistheleast.
0 20 40 60 80 100
20 40 60 80 100
Reduced dimensionality
A
ve
ra
ge
Cl
as
si
fi
ca
ti
on A
cc
ura
cy (%)
Baseline PCA LPP WSSPCA
0 20 40 60 80 100
20 40 60 80 100
Reduced dimensionality
O
ve
ra
ll
Cl
as
si
fi
ca
ti
on A
cc
ura
cy (%)
Baseline PCA LPP WSSPCA
0 20 40 60 80 100
20 40 60 80 100
Reduced dimensionality
(%)
（a）Therelationshipbetween
AA(%)anddimensions
（b）Therelationshipbetween
OA(%)anddimensions
（c）Therelationshipbetween
kappa(%)anddimensions
Figure7.Therelationshipbetweenclassificationaccuracy(%)anddimensionsonPaviUdataset.
（a）Groundtruth （b）Trainsamples （c）Testsamples （d）Baseline
（e）PCA （f）LPP （g）WSSPCA
Figure8.ClassificationresultsofdifferentalgorithmsinPaviUdataset.
Table2.Thebestresults(%)withoptimaldimensions.
method OA(dimension) kappa(dimension)
baseline 82.33(1) 76.21(1)
PCA 82.35(20) 76.25(16)
LPP 82.42(5) 76.48(5)
WSSPCA 96.69(20) 95.59(21)
Conclusion
This paperproposeda newweighted spatialand spectralprinciple component analysis(WSSPCA)
algorithm. Thisalgorithm considersthephysical characteristicstoreconstruct theHSIby usingthe
nearestwindowscaleandspectralfactor,whichcaneffectivelyeliminatingtheinfluenceofsingular
point. PCA is used to reduce the dimension of the reconstructed data, which can lower the
redundancy among the bands. On the Indian Pines and PaviU data sets, the experimental results
showthatthenewmethodproposedinthispaperissuperiortoPCAandLPPalgorithms.OnIndian
Pinesdataset,themaximumOAis90.90%andkappacoefficientis89.61%when10%samplesare
randomly selected as training samples in each class. On PaviU data set, when 5% samples are
randomly selected as training samples in each class, the maximum OA is 96.69% and kappa
coefficientis95.59%.TheWSSPCAalgorithmeffectivelyimprovedtheclassificationaccuracy.
0 10 20 30 40
40 60 80 100
Reduced dimensionality
A
ve
ra
ge
Cl
as
si
fi
ca
ti
on A
cc
ura
cy (%)
Baseline PCA LPP WSSPCA
0 10 20 30 40
20 40 60 80 100
Reduced dimensionality
O
ve
ra
ll
c
la
ss
ifi
ca
ti
on A
cc
ura
cy (%)
Baseline PCA LPP WSSPCA
0 10 20 30 40
20 40 60 80 100
Reduced dimensionality
(%)
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