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Comparison of Vertex Componet Analysis (VCA) and Genetic Algorithm Endmember Extraction (GAEE) algorithms for Endmember Extraction

Douglas Winston R. S., Gustavo T. Laureano, Celso G. Camilo Jr.

Endmember Extraction is a critical step in hyperspectral image analysis and classification. It is an useful method to decompose a mixed spectrum into a collection of spectra and their corresponding proportions. In this paper, we solve a linear endmember extraction problem as an evolutionary optimization task, maximizing the Simplex Volume in the endmember space. We propose a standard genetic algorithm and a variation with In Vitro Fertilization module (IVFm) to find the best solutions and compare the results with the state-of-art Vertex Component Analysis (VCA) method and the traditional algorithms Pixel Purity Index (PPI) and N-FINDR. The experimental results on real and synthetic hyperspectral data confirms the overcome in performance and accuracy of the proposed approaches over the mentioned algorithms.

Paper Online in https://arxiv.org/abs/1805.10644

@ARTICLE{2018arXiv180510644D,
   author = {{Douglas Winston.~R.}, S. and {Laureano}, G.~T. and {Camilo}, Jr, C.~G.
	},
    title = "{Comparison of VCA and GAEE algorithms for Endmember Extraction}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1805.10644},
 keywords = {Computer Science - Neural and Evolutionary Computing, Electrical Engineering and Systems Science - Image and Video Processing, 68T20, 68U10},
     year = 2018,
    month = may,
   adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180510644D},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

Envirionment Setup:

Monte Carlo runs: 50

Number of endmembers to estimate: 12

Number of skewers (PPI): 1000

Maximum number of iterations (N-FINDR): 36

Parameters used in each GAEE versions

Parameters GAEE GAEE-IVFm GAEE-VCA GAEE-IVFm-VCA
Population Size 100 100 100 100
Number of Generations 1000 1000 1000 1000
Crossover Probability 1 0.7 0.5 1
Mutation Probability 0.1 0.3 0.05 0.1

alt text

Comparison between the ground-truth Laboratory Reflectances and extracted endmembers using PPI, N-FINDR, VCA, GAEE, GAEE-IVFm using SAM for the Cuprite Dataset.

Endmembers PPI NFINDR VCA GAEE GAEE-IVFm GAEE-VCA GAEE-IVFm-VCA
Alunite 0.3744 0.1122 0.0939 0.1122 0.1034 0.1043 0.1043
Andradite 0.0758 0.2068 0.1034 0.0693 0.0760 0.1694 0.1694
Buddingtonite 0.2081 0.1205 0.0786 0.0798 0.0762 0.0762 0.0762
Dumortierite 0.1907 0.0706 0.0702 0.0735 0.0719 0.0755 0.0755
Kaolinite_1 0.0795 0.0870 0.0862 0.0952 0.0935 0.0870 0.0870
Kaolinite_2 0.0820 0.0992 0.0741 0.0649 0.0723 0.0744 0.0782
Muscovite 0.2506 0.0961 0.1805 0.0861 0.1091 0.0965 0.0961
Montmonrillonite 0.1338 0.0646 0.0651 0.0671 0.0677 0.0688 0.0650
Nontronite 0.1033 0.0780 0.0801 0.0711 0.0791 0.1150 0.1150
Pyrope 0.0579 0.0865 0.0818 0.0563 0.0623 0.0793 0.0686
Sphene 0.0673 0.0542 0.0530 0.1121 0.0946 0.0795 0.0901
Chalcedony 0.0871 0.0731 0.0773 0.0738 0.0756 0.0765 0.0861

SAM Statistics for Cuprite Dataset.

Statistics PPI NFINDR VCA GAEE GAEE-IVFm GAEE-VCA GAEE-IVFm-VCA
Mean 0.1425 0.1033 0.1024 0.1016 0.0989 0.1109 0.1090
Std 0.0000 0.0225 0.0252 0.0248 0.0255 0.0117 0.0157
p-value -34.8557 -0.6562 0.0000 0.5032 2.3017 -6.4153 -4.8551
Gain 30.6303 4.2790 3.3962 2.6854 0.0000 10.8064 9.2929
Time 2.1929 7.8318 0.5106 8.9232 22.3329 8.7494 22.1761

Comparison between the ground-truth Laboratory Reflectances and extracted endmembers using PPI, N-FINDR, VCA, GAEE, GAEE-IVFm using SID for the Cuprite Dataset.

Endmembers PPI NFINDR VCA GAEE GAEE-IVFm GAEE-VCA GAEE-IVFm-VCA
Alunite 0.0000 0.0000 0.0105 0.0170 0.0000 0.0000 0.0145
Andradite 0.0000 0.0117 0.0052 0.0055 0.0092 0.0077 0.0056
Buddingtonite 0.0477 0.0196 0.0077 0.0076 0.0108 0.0072 0.0072
Dumortierite 0.0562 0.0071 0.0298 0.0072 0.0181 0.0077 0.0077
Kaolinite_1 0.0114 0.0104 0.0139 0.0139 0.0128 0.0131 0.0131
Kaolinite_2 0.0114 0.0058 0.0042 0.0049 0.0029 0.0111 0.0086
Muscovite 0.0969 0.0317 0.0148 0.0086 0.0286 0.0285 0.0171
Montmonrillonite 0.0230 0.0053 0.0047 0.0052 0.0048 0.0057 0.0060
Nontronite 0.0126 0.0083 0.0093 0.0065 0.0082 0.0155 0.0155
Pyrope 0.0071 0.0438 0.0229 0.0057 0.0279 0.0593 0.0593
Sphene 0.0076 0.0912 0.0096 0.0165 0.0086 0.0099 0.0067
Chalcedony 0.0088 0.0093 0.0069 0.0069 0.0096 0.0070 0.0070

SID Statistics for Cuprite Dataset.

Statistics PPI NFINDR VCA GAEE GAEE-IVFm GAEE-VCA GAEE-IVFm-VCA
Mean 0.0236 0.0257 0.0197 0.0163 0.0194 0.0265 0.0268
Std 0.0000 0.0064 0.0107 0.0099 0.0097 0.0065 0.0059
p-value -5.2271 -7.2962 0.0000 3.8716 0.3603 -7.4272 -8.2866
Gain 28.7161 1.6376 0.7304 0.0000 -2.7595 8.3452 6.7899
Time 2.1929 7.8318 0.5106 8.9232 22.3329 8.7494 22.1761

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