1 Abstract— Artificial light-at-night (ALAN), emitted from the ground and visible from space, marks human presence on Earth. Since the launch of the Suomi National Polar Partnership satellite with the Visible Infrared Imaging Radiometer Suite Day/Night Band (VIIRS/DNB) onboard, global nighttime images have significantly improved; however, they remained panchromatic. Although multispectral images are also available, they are either commercial or free of charge, but sporadic. In this paper, we use several machine learning techniques, such as linear, kernel, random forest regressions, and elastic map approach, to transform panchromatic VIIRS/DBN into Red Green Blue (RGB) images. To validate the proposed approach, we analyze RGB images for eight urban areas worldwide. We link RGB values, obtained from ISS photographs, to panchromatic ALAN intensities, their pixel-wise differences, and several land-use type proxies. Each dataset is used for model training, while other datasets are used for the model validation. The analysis shows that model-estimated RGB images demonstrate a high degree of correspondence with the original RGB images from the ISS database. Yet, estimates, based on linear, kernel and random forest regressions, provide better correlations, contrast similarity and lower WMSEs levels, while RGB images, generated using elastic map approach, provide higher consistency of predictions. Index Terms—Artificial Light-at-Night (ALAN), Day-Night Band of the Visible Infrared Imaging Radiometer Suite (VIIRS/DNB), elastic map approach, International Space Station (ISS), multiple linear regression, non-linear kernel regression, panchromatic nighttime imagery, RGB nighttime imagery, validation. This paper was submitted for review on September, 3, 2020. Work of N. Rybnikova was supported by the Council for Higher Education of Israel. Work of N. Rybnikova, E. M. Mirkes, and A. N. Gorban was supported by the University of Leicester. Work of A. Zinovyev was supported by Agence Nationale de la Recherche in the program Investissements d’Avenir (Project No. ANR-19-P3IA-0001; PRAIRIE 3IA Institute). Work of E. M. Mirkes, A. Zinovyev, and A. N. Gorban was supported by the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2020-808). N. Rybnikova is with Dept. of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom; Dept. of Natural Resources and Environmental Management, and Dept. of Geography and Environmental Studies, University of Haifa, Haifa 3498838, Israel (e-mail: [email protected]). B. A. Portnov is with Dept. of Natural Resources and Environmental Management, University of Haifa, Haifa 3498838, Israel (e-mail: [email protected]). I. INTRODUCTION RTIFICIAL Light-at-Night (ALAN), emitted from streetlights, residential areas, places of entertainment, industrial zones, and captured by satellites' nighttime sensors, has been used in previous studies for remote identification of different Earth phenomena, such as stellar visibility [1]–[3]; ecosystem events [4], [5]; monitoring urban development and population concentrations [6]–[11]; assessing the economic performance of countries and regions [12]–[17], and in health geography research [18]–[20]. Compared to traditional techniques, which national statistical offices use to monitor the concentrations of human activities (such as, e.g., monitoring the level of urbanization, production density, etc.), using ALAN as a remote sensing tool has several advantages (see [21] for a recent review). First and foremost, satellite-generated ALAN data are available seamlessly all over the world, providing researchers and decision-makers with an opportunity to generate data even for countries and regions with extremely poor reporting behavior. Second, ALAN data are mutually comparable for different geographic regions, which minimizes the problem of comparability between socio- economic activity estimates, potentially originating from differences in national reporting procedures. Third, data on remotely sensed ALAN intensities are now available worldwide on a daily basis [22], which enables researchers and public decision-makers to obtain prompt estimates of ongoing changes in the geographic spread of different human activities and their temporal dynamics. The latter is especially important for E. M. Mirkes is with Dept. of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom; Lobachevsky University, Nizhny Novgorod 603105, Russia (e-mail: [email protected]). A. Zinovyev is with Institut Curie, PSL Research University, Paris 75248, France; Institut National de la Santé et de la Recherche Médicale, U900, Paris 75013, France; MINES ParisTech, CBIO-Centre for Computational Biology, PSL Research University, Paris 77305, France; Lobachevsky University, Nizhny Novgorod 603105, Russia (e-mail: [email protected]). A. Brook is with Dept. of Geography and Environmental Studies, University of Haifa, Haifa 3498838, Israel (e-mail: [email protected]). A. N. Gorban is with Dept. of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom; Lobachevsky University, Nizhny Novgorod 603105, Russia (e-mail: [email protected]). Coloring Panchromatic Nighttime Satellite Images: Comparing the Performance of Several Machine Learning Methods Nataliya Rybnikova, Boris A. Portnov, Evgeny M. Mirkes, Andrei Zinovyev, Anna Brook, and Alexander N. Gorban A
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1
Abstract— Artificial light-at-night (ALAN), emitted from the
ground and visible from space, marks human presence on Earth.
Since the launch of the Suomi National Polar Partnership satellite
with the Visible Infrared Imaging Radiometer Suite Day/Night
Band (VIIRS/DNB) onboard, global nighttime images have
significantly improved; however, they remained panchromatic.
Although multispectral images are also available, they are either
commercial or free of charge, but sporadic. In this paper, we use
several machine learning techniques, such as linear, kernel,
random forest regressions, and elastic map approach, to transform
panchromatic VIIRS/DBN into Red Green Blue (RGB) images. To
validate the proposed approach, we analyze RGB images for eight
urban areas worldwide. We link RGB values, obtained from ISS
photographs, to panchromatic ALAN intensities, their pixel-wise
differences, and several land-use type proxies. Each dataset is used
for model training, while other datasets are used for the model
validation. The analysis shows that model-estimated RGB images
demonstrate a high degree of correspondence with the original
RGB images from the ISS database. Yet, estimates, based on
linear, kernel and random forest regressions, provide better
correlations, contrast similarity and lower WMSEs levels, while
RGB images, generated using elastic map approach, provide
higher consistency of predictions.
Index Terms—Artificial Light-at-Night (ALAN), Day-Night
Band of the Visible Infrared Imaging Radiometer Suite
(VIIRS/DNB), elastic map approach, International Space Station
(ISS), multiple linear regression, non-linear kernel regression,
[69] P. A. N. Gorban and D. A. Y. Zinovyev, “Visualization of Data by Method of Elastic Maps and Its Applications in Genomics,
Economics and Sociology,” 2001.
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FIGURES AND TABLES
(a) (b)
(c) (d)
Fig. 1. Satellite images of the Haifa metropolitan area: (a) day-time image ([40]), (b) ~10-meter resolution RGB image with the range of values of 0-255 dn for each band;
(c) ~750-meter resolution panchromatic image with the values in the range of 1-293 nW/cm2/sr, and (d) ~30-meter resolution HBASE image with the values in the 0-100 % range.
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Fig. 2. Energies of elastic map (principal manifold approximation). The principal manifold is represented by a regular grid of nodes (large black
circles) connected by attractive springs (shown by thick zigzag lines and
representing the stretching energy). In addition, the triples of nodes in the grid are assigned the bending energy (not represented here). The data points shown
by small circles are assigned to the closest node of the grid similarly to the k-
means clustering. Then the data approximation term (Mean Squared Error) can be represented as the total elastic energy of springs connecting the data
points and the grid nodes (thin zigzag lines here).
(Source: [69])
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R = 0.86; WMSE = 0.56
R = 0.89; WMSE = 0.37
R = 0.85; WMSE = 0.09
C_sim = 0.96
R = 0.88; WMSE = 0.39
R = 0.91; WMSE = 0.25
R = 0.87; WMSE = 0.07
C_sim = 0.98
R = 0.96; WMSE = 0.14
R = 0.96; WMSE = 0.11
R = 0.95; WMSE = 0.03
C_sim = 0.99
R = 0.87; WMSE = 0.37
R = 0.90; WMSE = 0.28
R = 0.81; WMSE = 0.08
C_sim = 0.98
Fig. 3. Haifa metropolitan area (Israel): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-provided,
resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under the 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted mean
squared error of the red, green, and blue lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city area correspond to outliers.
(a) (b) (c) (d)
(e) (f) (g) (h)
(i) (j) (k) (l)
(m) (n) (o) (p)
(q) (r) (s) (t)
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(a) (b) (c)
(d) (e) (f) Fig. 4. Mutual comparison of linear, kernel, random forest, and elastic map models for the training (top row) and testing (bottom row) datasets, in terms of averaged Pearson correlation coefficients ((a) & (d)), WMSE ((b) & (e)), and contrast similarity ((c) & (f))
Notes: In case of Pearson’s correlation ((a) & (d)) and contrast similarity ((c) & (f)), greater means better; In case of WMSE ((b) & (e)), lower means better.
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(a)
(b)
(c) Fig. 5. Changes in the models’ performance (Δr), attributed to the exclusion of particular variables from the set of predictors, estimated separately for different model types (Study dataset: all metropolitan areas under analysis; N. of pixels/obs. = 33,846); the models are estimated separately
for the Red (a), Green (b), and Blue (c) spectra)
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TABLE I Mutual comparison of linear, kernel, random forest, and elastic map models in terms of estimate consistency for training and testing datasets
Model type
Model performance measure
Pearson
correlation coefficient WMSE
Contrast
similarity R G B R G B RGB
Linear regression 0.938 0.979 0.880 0.124 0.147 0.096 0.541
The results of the best-performing model are reported with: 1a α=0.0001; 1b α=0.05; 1c α=0.00001; 1d α=0.001.
The grey cell backgrounds mark the best-performed model for specific measures.
TABLE II
The association between ALAN intensities in different RGB bands and predictors from the VIIRS and HBASE datasets (Study area – all geographical sites together (N. of pixels/obs. = 33,846); method
– ordinary least square regression (OLS); dependent variables – ALAN intensities in different parts of the RGB spectra) and significance of differences in the regression coefficients
R2 0.67 0.70 0.57 F = (3487.79)*** F = (5540.62)*** F = (7074.78)***
B = unstandardized regression coefficients; t = t-statistics; VIF = variance of inflation; *, ** and *** indicate correspondingly 0.1, 0.05 and 0.01 significance levels
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Nataliya Rybnikova was born in Lugansk, Ukraine, in 1981. She received her M.S. and Ph.D.
degrees in economics from the Volodymyr Dahl Eastern Ukrainian National University, Ukraine,
in 2004 and 2011. She received her second Ph.D. degree in remote sensing from the University
of Haifa, Israel, in 2018.
From 2005 to 2010, she was a Researcher with the Cadastre of Natural Resources Laboratory,
Ukraine. From 2011 to 2013, she was a Lecturer with the Dept. of Economics, Volodymyr Dahl
Eastern-Ukrainian National University, Ukraine. From 2018 to 2019, she was a Postdoctoral
Fellow with the Remote Sensing Laboratory, University of Haifa, Israel. Since 2019, she is a
Postdoctoral Fellow with the Dept. of Mathematics, University of Leicester, UK, and School of
Environmental Studies, University of Haifa, Israel. She is the author of more than 30 articles and book chapters. Her
research interests include processing and using artificial night-time light imagery as a proxy for human presence on
Earth.
Dr. Rybnikova is a member of the European Regional Science Association and the International Society for
Photogrammetry and Remote Sensing. She was a recipient of the Israeli Ministry of Science, Technology and Space
the Ilan Ramon Scholarship from 2015 to 2018; of the Israeli Regional Science Association Best Young Scientist’s
Paper Prize in 2018. Since 2019, she is a recipient of the Council for Higher Education of Israel Postdoctoral
Excellence Scholarship.
Boris A. Portnov was born in Odessa, former USSR. He received the M.A. degree in Architecture
from the Poltava Civil Engineering Institute, Ukraine, in 1982; the Ph.D. degree in Urban
Planning from the Central Scientific & Project Institute of Town-Building, Moscow, Russia, in
1987, and D.Sc. (2nd Russian Doctoral Degree) in urban planning from the Moscow Architectural
Institute, Russia, in 1994.
From 1988 to 1995, he served as a Senior Lecturer, an Associate Professor, and a Full Professor
in the Dept. of Architecture and Urban Planning, Krasnoyarsk Civil Engineering Institute –
Siberian Federal University, USSR. From 1995 to 2002, he was a Senior Researcher, and then a
Research Professor in the Dept. of Man in the Desert, Ben-Gurion University of the Negev, Israel.
Since 2002, he was a Senior Research Fellow, an Associate Professor, and, in 2012, he was
appointed a Full Professor in the Dept. of Natural Resources and Environmental Management, University of Haifa,
Israel. Prof. Portnov authored or edited seven books, and more than 180 articles and book chapters. He is a member
of the editorial board of several journals. His research interests include geographic information systems, urban
planning, population geography, and real estate valuation and management.
Prof. Portnov was a recipient of the Ukraine State Committee of Town-Building Honor Diploma, Ukraine, in 1986;
All-Union Architectural Competition 2nd Award, Russia, in 1989; Gelsenkirchen Municipality Redesigning of
Gelsenkirchen Industrial district Summer School Award, Germany, in 1993; Russian Ministry of Higher Education,
Increasing Land Use Effectiveness under Transition to a Market-Oriented Society Federal Text-Book Writing Award,
Russia, in 1994; Deichmann Scholarship in Desert Studies in 1999-2001; 2000 PLEA Conference on 'Architecture
and City Environment’ Best Paper Award, UK, in 2000; Israel Central Bureau of Statistics, Award for Monograph
Writing in 1998-2001; Gilladi Scholarship in 2001-2003; Sheikh Zayed Prize in Environmental Studies in 2006;
Excellent Thesis Supervisor Award, Israel, in 2006; Ministry of Foreign Affairs, Republic of China - Taiwan Research
Fellowship in 2011; the 1st International Conference on Sustainable Lighting and Light Pollution Best Paper Award,
South Korea, in 2014. He is a member of Professional Union of Russian Architects, European Network for Housing
Research, Association of Computer-Aided Design in Architecture, Israel Regional Science Association, Professional
Union of Israeli Architects and Engineers, Association of Israeli Geographers, International Geographical Union,
American Real Estate Society, and Network on European Communications and Transport Activities Research.
Evgeny M. Mirkes was born in Krasnoyarsk, Russia, in 1964. He received the M.S., Ph.D., and
D.Sc. (2nd Russian Doctoral Degree) degrees in mathematics from the Krasnoyarsk State
University, Russia, in 1985, 1990, and 2001, correspondingly.
From 2002 to 2012 he was a Professor with Dept. of Computer Science, Siberian Federal
University, Russia. From 1993 to 2002 he was a Lecturer with Dept. of Computer Science,
Krasnoyarsk State University, Russia. Since 2012, he is a Researcher with the School of
Mathematics and Actuarial Science, University of Leicester, UK. He was a supervisor of 6 Ph.D.
theses. He is the author of 6 books, more than 80 articles and book chapters. His research interests
include biomathematics, data mining and software engineering, neural network and artificial
intelligence.
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Andrei Zinovyev was born in Krasnoyarsk, Russia, in 1974. He received the M.S. degree in
physics from Krasnoyarsk State University, Russia, in 1997 and Ph.D. degree in computer science
from Institute of Computational Modeling of Russian Academy of Science in 2001.
From 2001 to 2004, he was a Postdoctoral Fellow at the Institut des Hautes Etudes Scientifiques,
France. Since 2005, he is a Senior Researcher and the Leader of the Computational Systems
Biology of Cancer group at Institut Curie, France. Since 2019, he is an Interdisciplinary Chair
with the Paris Artificial Intelligence Research Institute, France. He is the author of three books,
more than 120 articles and book chapters. His research interests include application of machine
learning to biological and healthcare problems, learning latent spaces and structures in big data point clouds, cancer
systems biology, modeling and dimension reduction in complex systems.
Dr. Zinovyev was a recipient of Student Soros Prize in 1994 and 1995 and the Agilent Thought Leader Award in
2014 as a part of the group.
Anna Brook Anna Brook was born in Tbilisi, Georgia, in 1981. She received her Ph.D. degree in
remote sensing and spectroscopy from Tel-Aviv University, Israel, in 2010.
From 2011 to 2013, she was a Researcher with the CISS Department at the Royal Military
Academy of Belgium. Since 2014, she is a Lecturer with Dept. of geography and environmental
studies, the University of Haifa, Israel. She is the author of 3 books, more than 50 articles, and
book chapters. Her research interests include the development and implementation of advanced
remote sensing methods and techniques for environment and ecological studies emphasizing the
importance of multi-source data fusion.
Dr. Brook was a recipient of the Dean’s Excellence Award, Tel-Aviv University, Israel, in 2003;
the Federal Ministry of Education and Research Excellence Scholarship of “Young Scientists Exchange Program”,
Germany, in 2008; the Rector’s Excellence Scholarship, Tel-Aviv, Israel, in 2009. She is a member of the IEEE
Women in Engineering (WIE), and the European Geosciences Union (EGU).
Alexander N. Gorban (PhD, ScD, Professor) has held a Personal Chair in applied mathematics
at the University of Leicester since 2004. He worked for Russian Academy of Sciences, Siberian
Branch (Krasnoyarsk, Russia), and ETH Zurich (Switzerland), was a visiting Professor and
Research Scholar at Clay Mathematics Institute (Cambridge, MA), IHES (Bures-sur-Yvette, Île
de France), Courant Institute of Mathematical Sciences (New York), and Isaac Newton Institute
for Mathematical Sciences (Cambridge, UK). His main research interests are machine learning,
data mining and model reduction problems, dynamics of systems of physical, chemical and
biological kinetics, and biomathematics. He has been accorded the title of Pioneer of Russian
Neuroinformatics (2017) for his extraordinary contribution into theory and applications of artificial neural networks,
received Lifetime Achievement Award (MaCKIE-2015) in recognition of outstanding contributions to the research
field of (bio)chemical kinetics, and was awarded by Prigogine medal (2003) for achievements in non-equilibrium
thermodynamics and physical kinetics.
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APPENDIXES
Box 1: Outliers Analysis Procedure Outliers analysis was performed separately for each geographic site dataset. Proceeding from each variable distribution, we defined a cut-off
separating 1% of points as variable outlier. An observation was considered to be an outlier if either:
(i) It was beyond the cut-off point at the scale of at least one of the ‘predictors’ while being within the ‘usual’ interval at the scale of each of dependent variables (We should emphasize that here and hereinafter the notes ‘dependent variable’, as well as ‘independent variable’,
or ‘predictor’, when applied to elastic map approach, are used figuratively. Elastic map is set of points, connected via edges and ribs,
aimed at approximating points dataset in N-dimensional coordinate system, where N is number of input variables, no matter which of them is implied to be dependent variable.);
(ii) It was beyond the cut-off point at the scale of at least one of the dependent variables while being ‘normal’ at the scale of each independent
variable; (iii) It was beyond opposite cut-off points (that is, upper/lower or lower/upper) at the scale of predictor and dependent variable under their
positive bivariate association;
(iv) It was beyond same-range cut-off points (that is, upper/upper or lower/lower) at the scale of predictor and dependent variable under their negative bivariate association.
Thus, the percentage of excluded outlying observations varied from 2.92% for the Atlanta dataset to 3.90% for the Beijing dataset (see Table A1).
Fig. A1. Relative response of VIIRS/DNB sensor and Nikon D3 DSLR camera from the ISS
(Source: Built from data obtained upon request from A. Sánchez de Miguel.)
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FVU = 4.04%
FVU = 4.65%
FVU = 6.48%
(a) (b) (c)
FVU = 8.61%
FVU = 10.46%
FVU = 11.21%
(d) (e) (f)
FVU = 12.48%
FVU = 12.78%
FVU = 13.04%
(g) (h) (i) Fig. A2. Examples of elastic maps (depicted by red grid) built for the Haifa's blue light containing dataset (marked by blue dots) using varying bending regimes (see text for explanations): (a) 0.00001; (b) 0.0001; (c) 0.001; (d) 0.01; (e)
0.05; (f) 0.1; (g) 0.3; (h) 0.5, and (i) 1.
Notes: The first three principal components (PC1, PC2, and PC3) are used as coordinates for the elastic maps' visualization. Fraction of total (by all six coordinates of the parameter space) variance unexplained (FVU) by elastic maps built under varying bending regimes are reported
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Panel (a): ISS-provided resampled to the spatial resolution of VIIRS imagery (see explanation at p.7)
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R = 0.81; WMSE = 15.57
R = 0.80; WMSE = 9.62
R = 0.73; WMSE = 1.80
C_sim = 0.93
Panel (b): Outputs of linear multiple regressions (see explanation at p.7)
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R = 0.81; WMSE = 10.64
R = 0.78; WMSE = 9.11
R = 0.69; WMSE = 2.53
C_sim = 0.95
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.7)
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R = 0.78; WMSE =8.55
R = 0.78; WMSE =7.09
R = 0.73; WMSE =2.59
C_sim = 0.94
Panel (d): Outputs of random forest regressions (see explanation at p.7)
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R = 0.76; WMSE = 12.39
R = 0.76; WMSE = 11.16
R = 0.70; WMSE = 3.30
C_sim = 0.95
Panel (e): Outputs of elastic map models
Fig. A3. Atlanta metropolitan area (the US): Red, Green, Blue bands, and RGB images, provided by ISS and resampled to the spatial resolution of VIIRS imagery
(panel (a)), and outputs of four models trained on Haifa datasets: linear multiple regressions (panel (b)), non-linear kernel regressions (panel (c)), random forest regressions (panel (d)), and elastic map models (panel (e)).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and
weighted mean squared error of the red, green, and blue lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White
points in the city area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.12)
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R = 0.79; WMSE = 3.31
R = 0.85; WMSE = 3.60
R = 0.78; WMSE = 2.58
C_sim = 0.94
Panel (b): Outputs of linear multiple regressions (see explanation at p.12)
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R = 0.85; WMSE = 1.81
R = 0.85; WMSE = 3.89
R = 0.74; WMSE = 3.77
C_sim = 0.95
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.12)
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R = 0.86; WMSE = 1.02
R = 0.86; WMSE = 2.34
R = 0.72; WMSE =4.25
C_sim = 0.97
Panel (d): Outputs of random forest regressions (see explanation at p.12)
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R = 0.80; WMSE = 2.97
R = 0.79; WMSE = 6.14
R = 0.69; WMSE = 5.84
C_sim = 0.95
Panel (e): Outputs of elastic map models
Fig. A4. Beijing metropolitan area (China): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth
row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted mean squared error of the red, green, and blue
lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.17)
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R = 0.80; WMSE = 3.48
R = 0.86; WMSE = 2.52
R = 0.73; WMSE = 4.02
C_sim = 0.82
Panel (b): Outputs of linear multiple regressions (see explanation at p.17)
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R = 0.85; WMSE = 2.10
R = 0.87; WMSE = 2.20
R = 0.75; WMSE = 3.81
C_sim = 0.86
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.17)
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R = 0.86; WMSE = 1.37
R = 0.88; WMSE = 1.86
R = 0.76; WMSE = 4.17
C_sim = 0.90
Panel (d): Outputs of random forest regressions (see explanation at p.17)
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R = 0.85; WMSE = 1.63
R = 0.86; WMSE = 2.29
R = 0.74; WMSE = 4.78
C_sim = 0.91
Panel (e): Outputs of elastic map models
Fig. A5. Khabarovsk (Russia): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-
provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and
weighted mean squared error of the red, green, and blue lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White
points in the city area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.22)
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R = 0.83; WMSE = 2.00
R = 0.85; WMSE = 1.06
R = 0.77; WMSE = 0.23
C_sim = 0.98
Panel (b): Outputs of linear multiple regressions (see explanation at p.22)
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R = 0.85; WMSE = 1.32
R = 0.84; WMSE = 1.07
R = 0.79; WMSE = 0.29
C_sim = 0.99
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.22)
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R = 0.82; WMSE = 1.19
R = 0.82; WMSE = 0.88
R = 0.75; WMSE = 0.36
C_sim = 0.98
Panel (d): Outputs of random forest regressions (see explanation at p.22)
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R = 0.82; WMSE = 1.33
R = 0.81; WMSE = 1.09
R = 0.77; WMSE = 0.39
C_sim = 0.99
Panel (e): Outputs of elastic map models
Fig. A6. London metropolitan area (the UK): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth
row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted mean squared error of the red, green, and blue lights’
estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.27)
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R = 0.85; WMSE = 0.29
R = 0.85; WMSE = 0.27
R = 0.61; WMSE = 0.13
C_sim = 0.95
Panel (b): Outputs of linear multiple regressions (see explanation at p.27)
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R = 0.86; WMSE = 0.17
R = 0.87; WMSE = 0.17
R = 0.62; WMSE = 0.13
C_sim = 0.96
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.27)
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R = 0.86; WMSE = 0.14
R = 0.86; WMSE = 0.16
R = 0.64; WMSE = 0.14
C_sim = 0.97
Panel (d): Outputs of random forest regressions (see explanation at p.27)
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R = 0.83; WMSE = 0.20
R = 0.83; WMSE = 0.23
R = 0.60; WMSE = 0.16
C_sim = 0.95
Panel (e): Outputs of elastic map models
Fig. A7. Naples metropolitan area (Italy): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth
row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted mean squared error of the red, green, and blue lights’
estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.32)
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R = 0.84; WMSE = 2.35
R = 0.86; WMSE = 1.24
R = 0.80; WMSE = 0.24
C_sim = 0.97
Panel (b): Outputs of linear multiple regressions (see explanation at p.32)
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R = 0.87; WMSE = 1.20
R = 0.88; WMSE = 1.08
R = 0.77; WMSE = 0.37
C_sim = 0.98
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.32)
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R = 0.88; WMSE = 0.71
R = 0.88; WMSE = 0.66
R = 0.82; WMSE = 0.36
C_sim = 0.98
Panel (d): Outputs of random forest regressions (see explanation at p.32)
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R = 0.87; WMSE = 1.59
R = 0.86; WMSE = 1.51
R = 0.80; WMSE = 0.59
C_sim = 0.98
Panel (e): Outputs of elastic map models
Fig. A8. Nashville metropolitan area (the US): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth
column); ISS-provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted
mean squared error of the red, green, and blue lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city
area correspond to outliers.
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Panel (a): ISS-provided and resampled to the spatial resolution of VIIRS imagery (see explanation at p.37)
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R = 0.82; WMSE = 2.57
R = 0.87; WMSE = 2.54
R = 0.69; WMSE = 2.67
C_sim = 0.93
Panel (b): Outputs of linear multiple regressions (see explanation at p.37)
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R = 0.87; WMSE = 1.15
R = 0.85; WMSE = 3.43
R = 0.68; WMSE = 4.27
C_sim = 0.95
Panel (c): Outputs of non-linear kernel regressions (see explanation at p.37)
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R = 0.88; WMSE = 0.48
R = 0.87; WMSE = 1.33
R = 0.69; WMSE = 4.65
C_sim = 0.97
Panel (d): Outputs of random forest regressions (see explanation at p.37)
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R = 0.83; WMSE = 1.09
R = 0.82; WMSE = 2.80
R = 0.67; WMSE = 5.46
C_sim = 0.96
Panel (e): Outputs of elastic map models
Fig. A9. Tianjing metropolitan area (China): Red (the first column), Green (the second column), Blue (the third column)) bands, and RGB images (the fourth column); ISS-provided, resampled to the spatial resolution of VIIRS imagery (the first row), and outputs of four models trained on Haifa datasets: linear multiple regressions (the second row), non-linear kernel regressions (the third row), random forest regressions (the fourth
row), and elastic map models (the fifth row).
Notes: Output generated by elastic maps, built under 0.05 bending penalty, is reported. R and WMSE denote correspondingly for Pearson’s correlation and weighted mean squared error of the red, green, and blue
lights’ estimates, C_sim – for contrast similarity between restored and original RGB images. White points in the city area correspond to outliers.
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(a) Atlanta metropolitan area (the US)
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(b) Beijing metropolitan area (China)
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(c) Khabarovsk (Russia)
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(d) London metropolitan area (the UK)
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(e) Naples metropolitan area (Italy)
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(f) Nashville metropolitan area (the US)
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(g) Tianjing metropolitan area (China)
Fig. A10. Day-time satellite images for the cities under analysis (Source: Imagery basemaps provided by ArcGIS v.10.x software)
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(a) (b)
Fig. A11. The association between BC DKD rates and ALAN, estimated for different ALAN bands for the Haifa Bay metropolitan area (see text for explanations):
(a) the augmented random forest model with all explanatory variables included; (b) random forest model without HBASE-based predictors.
Notes: The BC DKD levels are estimated as the number of new cases per km2 divided by the population density in 100,000 persons per km2. The data are drawn
from [62]; the vertical axes feature values of the Pearson correlation coefficient between the BC DKD rate and ALAN emissions in different ALAN bands, estimated by the proposed modeling approach. The correlations are calculated for observations with BC DKD rates above a certain threshold. Overall
correlations correspond to zero BC DKD threshold and r=-3.40E-02 (B), r=-3.88E-02 (G), r=-3.69E-02 (R) and r=-1.1E-03 (Panchromatic) for the left panel
diagram and r=3.32E-02 (B), r=-2.47E-02 (G), r=-2.68E-02 (R) and r=-1.1E-03 (Panchromatic) for the right panel diagram.
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(a)
(b)
(c) Fig. A12. Changes in the models’ performance (Δr), attributed to the exclusion of different groups of variables from the set of predictors, estimated separately
for different model types (Study dataset: all metropolitan areas under analysis; N. of pixels/obs. = 33,846); the models are estimated separately for the Red (a), Green (b), and Blue (c) spectra)
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TABLE AI Datasets representation: Number of observations and numbers of contributing
points from middle-resolution HBASE layer and high-resolution RGB layer to