Testing Convolutional Neural Networks for finding strong gravitational lenses in KiDS

Convolutional Neural Networks (ConvNets) are one of the most promising methods for identifying strong gravitational lens candidates in survey data. We present two ConvNet lens-finders that we have trained with a dataset composed of real galaxies from the Kilo Degree Survey (KiDS) and simulated lensed sources. One ConvNet is trained with single r-band galaxy images, hence basing the classification mostly on the morphology. While the other ConvNet is trained on g-r-i composite images, relying mostly on colours and morphology. We have tested the ConvNet lens-finders on a sample of 21 789 luminous red galaxies (LRGs) selected from KiDS and we have analysed and compared the results with our previous ConvNet lens-finder on the same sample. The new lens-finders achieve a higher accuracy and completeness in identifying gravitational lens candidates, especially the single-band ConvNet. Our analysis indicates that this is mainly due to improved simulations of the lensed sources. In particular, the single-band ConvNet can select a sample of lens candidates with similar to 40 per cent purity, retrieving three out of four of the confirmed gravitational lenses in the LRG sample. With this particular setup and limited human intervention, it will be possible to retrieve, in future surveys such as Euclid, a sample of lenses exceeding in size the total number of currently known gravitational lenses.

[1]  Jose Luis. Sersic,et al.  Atlas de Galaxias Australes , 1968 .

[2]  C. Alcock.  Gravitational lenses , 1982, Nature.

[3]  C. Kochanek.  The Flat-Spectrum Radio Luminosity Function, Gravitational Lensing, Galaxy Ellipticities, and Cosmology , 1996, astro-ph/9611231.

[4]  L. Moscardini,et al.  Measuring and modelling the redshift evolution of clustering: the Hubble Deep Field North , 1999, astro-ph/9902290.

[5]  K. Chae.  The Cosmic Lens All‐Sky Survey: statistical strong lensing, cosmological parameters, and global properties of galaxy populations , 2002, astro-ph/0211244.

[6]  T. Treu,et al.  The Structure and Dynamics of Luminous and Dark Matter in the Early-Type Lens Galaxy of 0047–281 at z = 0.485 , 2002, astro-ph/0205281.

[7]  T. Treu,et al.  The Internal Structure and Formation of Early-Type Galaxies: The Gravitational Lens System MG 2016+112 at z = 1.004 , 2002, astro-ph/0202342.

[8]  Neil A. Dodgson,et al.  Proceedings Ninth IEEE International Conference on Computer Vision , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[9]  Kunihiko Fukushima,et al.  Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position , 1980, Biological Cybernetics.

[10]  P. Murdin.  MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY , 2005 .

[11]  B. Flaugher.  The Dark Energy Survey , 2005 .

[12]  The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples , 2005, astro-ph/0507454.

[13]  A. Bolton,et al.  The Sloan Lens ACS Survey. III. The Structure and Formation of Early-Type Galaxies and Their Evolution since z ≈ 1 , 2006, astro-ph/0601628.

[14]  Peter Schneider,et al.  Gravitational Lensing: Strong, Weak and Micro , 2006 .

[15]  The image separation distribution of strong lenses: halo versus subhalo populations , 2005, astro-ph/0508528.

[16]  Automated detection of gravitational arcs , 2006, astro-ph/0606757.

[17]  J. Rhodes,et al.  The Sloan Lens ACS Survey. IV. The Mass Density Profile of Early-Type Galaxies out to 100 Effective Radii , 2007, astro-ph/0701589.

[18]  P. Hall,et al.  A Systematic Search for High Surface Brightness Giant Arcs in a Sloan Digital Sky Survey Cluster Sample , 2007, astro-ph/0701383.

[19]  Strong lensing statistics in large, z 0.2 surveys: bias in the lens galaxy population , 2006, astro-ph/0607032.

[20]  C. Kochanek,et al.  The Baryon Fractions and Mass-to-Light Ratios of Early-Type Galaxies , 2007, 0705.3647.

[21]  Jeffrey M. Kubo,et al.  A method to search for strong galaxy-galaxy lenses in optical imaging surveys , 2007, 0712.3063.

[22]  C. Fassnacht,et al.  Probing a massive radio galaxy with gravitational lensing , 2007, 0712.1145.

[23]  O. Wucknitz,et al.  A gravitationally lensed water maser in the early Universe , 2008, Nature.

[24]  A. Bolton,et al.  Accepted for publication in The Astrophysical Journal Preprint typeset using L ATEX style emulateapj v. 10/09/06 THE SLOAN LENS ACS SURVEY. V. THE FULL ACS STRONG-LENS SAMPLE 1 , 2022 .

[25]  A. Bolton,et al.  Two-dimensional kinematics of SLACS lenses - II. Combined lensing and dynamics analysis of early-type galaxies at z = 0.08-0.33 , 2009, 0904.3861.

[26]  L. Koopmans,et al.  Statistics of mass substructure from strong gravitational lensing: quantifying the mass fraction and mass function , 2009, 0903.4752.

[27]  Donald W. Sweeney,et al.  LSST Science Book, Version 2.0 , 2009, 0912.0201.

[28]  D. Thompson,et al.  COSMOS PHOTOMETRIC REDSHIFTS WITH 30-BANDS FOR 2-deg2 , 2008, 0809.2101.

[29]  P. Marshall,et al.  DISSECTING THE GRAVITATIONAL LENS B1608+656. II. PRECISION MEASUREMENTS OF THE HUBBLE CONSTANT, SPATIAL CURVATURE, AND THE DARK ENERGY EQUATION OF STATE , 2009, 0910.2773.

[30]  Cambridge,et al.  A Spatially Resolved Map of the Kinematics, Star-Formation and Stellar Mass Assembly in a Star-Forming Galaxy at z=4.9 , 2009, 0909.0111.

[31]  Santiago,et al.  GAUGING THE DARK MATTER FRACTION IN AN L* S0 GALAXY AT z = 0.47 THROUGH GRAVITATIONAL LENSING FROM DEEP HUBBLE SPACE TELESCOPE/ADVANCED CAMERA FOR SURVEYS IMAGING , 2008, 0809.4125.

[32]  A. Bolton,et al.  THE SLOAN LENS ACS SURVEY. X. STELLAR, DYNAMICAL, AND TOTAL MASS CORRELATIONS OF MASSIVE EARLY-TYPE GALAXIES , 2010, 1007.2880.

[33]  P. P. van der Werf,et al.  The Detection of a Population of Submillimeter-Bright, Strongly Lensed Galaxies , 2010, Science.

[34]  Ucsb,et al.  Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys , 2010, 1001.2037.

[35]  M. Biesiada,et al.  Cosmic equation of state from strong gravitational lensing systems , 2010, 1105.0946.

[36]  A. Bolton,et al.  THE INITIAL MASS FUNCTION OF EARLY-TYPE GALAXIES , 2010 .

[37]  V. Cardone,et al.  Dark matter scaling relations in intermediate z haloes , 2010, 1007.3673.

[38]  R. Bender,et al.  GOLDEN GRAVITATIONAL LENSING SYSTEMS FROM THE SLOAN LENS ACS SURVEY. I. SDSS J1538+5817: ONE LENS FOR TWO SOURCES, , 2009, 0912.0744.

[39]  K. Jahnke,et al.  GRAVITATIONAL LENS CANDIDATES IN THE E-CDFS , 2011, 1104.0931.

[40]  T. Treu,et al.  The X-Shooter Lens Survey - I. Dark-Matter Domination and a Salpeter-type IMF in a Massive Early-type Galaxy , 2011, 1103.4773.

[41]  U. Utah,et al.  Two-dimensional kinematics of SLACS lenses – III. Mass structure and dynamics of early-type lens galaxies beyond z ≃ 0.1 , 2011, 1102.2261.

[42]  S. Bamford,et al.  Galaxy and Mass Assembly (GAMA): survey diagnostics and core data release , 2010, 1009.0614.

[43]  P. Marshall,et al.  THE SL2S GALAXY-SCALE LENS SAMPLE. II. COSMIC EVOLUTION OF DARK AND LUMINOUS MASS IN EARLY-TYPE GALAXIES , 2010, 1008.3167.

[44]  J. Kneib,et al.  The CFHTLS-Strong Lensing Legacy Survey (SL2S): Investigating the group-scale lenses with the SARCS sample , 2011, 1109.1821.

[45]  Infn,et al.  TESTING THE DARK ENERGY WITH GRAVITATIONAL LENSING STATISTICS , 2012, 1206.4948.

[46]  A. Bolton,et al.  The SWELLS survey. III. Disfavouring "heavy" initial mass functions for spiral lens galaxies , 2012, 1201.1677.

[47]  C. Lintott,et al.  Galaxy Zoo 2: detailed morphological classifications for 304,122 galaxies from the Sloan Digital Sky Survey , 2013, 1308.3496.

[48]  S. Meyer,et al.  Dusty starburst galaxies in the early Universe as revealed by gravitational lensing , 2013, Nature.

[49]  P. Marshall,et al.  The preferentially magnified active nucleus in IRAS F10214+4724 - III. VLBI observations of the radio core , 2013, 1307.6566.

[50]  Cosmology,et al.  THE SL2S GALAXY-SCALE LENS SAMPLE. III. LENS MODELS, SURFACE PHOTOMETRY, AND STELLAR MASSES FOR THE FINAL SAMPLE , 2013, 1307.4764.

[51]  Haibo Yuan,et al.  Empirical extinction coefficients for the GALEX, SDSS, 2MASS and WISE passbands , 2013, 1301.1427.

[52]  Rob Fergus,et al.  Visualizing and Understanding Convolutional Networks , 2013, ECCV.

[53]  M. Auger,et al.  Cosmological constraints from the double source plane lens SDSSJ0946+1006 , 2014, 1403.5278.

[54]  Cosmology,et al.  THE SL2S GALAXY-SCALE LENS SAMPLE. V. DARK MATTER HALOS AND STELLAR IMF OF MASSIVE EARLY-TYPE GALAXIES OUT TO REDSHIFT 0.8 , 2014, 1410.1881.

[55]  P. Marshall,et al.  RingFinder: AUTOMATED DETECTION OF GALAXY-SCALE GRAVITATIONAL LENSES IN GROUND-BASED MULTI-FILTER IMAGING DATA , 2014, 1403.1041.

[56]  G. Meylan,et al.  A 7 deg2 survey for galaxy-scale gravitational lenses with the HST imaging archive , 2012, 1206.3412.

[57]  Pavel Hála,et al.  Spectral classification using convolutional neural networks , 2014, ArXiv.

[58]  P. Marshall,et al.  Chitah: STRONG-GRAVITATIONAL-LENS HUNTER IN IMAGING SURVEYS , 2014, 1411.5398.

[59]  T. Collett.  THE POPULATION OF GALAXY–GALAXY STRONG LENSES IN FORTHCOMING OPTICAL IMAGING SURVEYS , 2015, 1507.02657.

[60]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[61]  Edwin Valentijn,et al.  Gravitational lensing analysis of the Kilo-Degree Survey , 2015, 1507.00738.

[62]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[63]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[64]  R. Gavazzi,et al.  COSMOLOGY WITH STRONG-LENSING SYSTEMS , 2015, 1509.07649.

[65]  U. California,et al.  The stellar initial mass function of early-type galaxies from low to high stellar velocity dispersion: homogeneous analysis of atlas3D and Sloan Lens ACS galaxies , 2014, 1407.5633.

[66]  Sander Dieleman,et al.  Rotation-invariant convolutional neural networks for galaxy morphology prediction , 2015, ArXiv.

[67]  A. Fontana,et al.  THE GRISM LENS-AMPLIFIED SURVEY FROM SPACE (GLASS). I. SURVEY OVERVIEW AND FIRST DATA RELEASE , 2015, 1509.00475.

[68]  Michael S. Bernstein,et al.  ImageNet Large Scale Visual Recognition Challenge , 2014, International Journal of Computer Vision.

[69]  Michael S. Lew,et al.  Deep learning for visual understanding: A review , 2016, Neurocomputing.

[70]  C. Lintott,et al.  Space Warps II. New gravitational lens candidates from the CFHTLS discovered through citizen science , 2015, 1504.05587.

[71]  M. Biesiada,et al.  Limits on the power-law mass and luminosity density profiles of elliptical galaxies from gravitational lensing systems , 2016, 1604.05625.

[72]  R. Ivison,et al.  TheHerschel-ATLAS: a sample of 500 μm-selected lensed galaxies over 600 deg2 , 2016, Monthly Notices of the Royal Astronomical Society.

[73]  Edwin Simpson,et al.  Space Warps – I. Crowdsourcing the discovery of gravitational lenses , 2015, 1504.06148.

[74]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[75]  S. Cole,et al.  Constraints on the identity of the dark matter from strong gravitational lenses , 2015, 1512.06507.

[76]  Edward J. Kim,et al.  Star-galaxy Classification Using Deep Convolutional Neural Networks , 2016, ArXiv.

[77]  Laurence Perreault Levasseur,et al.  Measuring the power spectrum of dark matter substructure using strong gravitational lensing , 2014, 1403.2720.

[78]  Karl Glazebrook,et al.  Finding strong lenses in CFHTLS using convolutional neural networks , 2017, 1704.02744.

[79]  N. R. Napolitano,et al.  The third data release of the Kilo-Degree Survey and associated data products , 2017, 1703.02991.

[80]  G. Meylan,et al.  H0LiCOW – I. H0 Lenses in COSMOGRAIL's wellspring: program overview , 2016, 1607.00017.

[81]  J. Kneib,et al.  Extreme magnification of an individual star at redshift 1.5 by a galaxy-cluster lens , 2017, 1706.10279.

[82]  Gabriela Csurka,et al.  Domain Adaptation for Visual Applications: A Comprehensive Survey , 2017, ArXiv.

[83]  Laurence Perreault Levasseur,et al.  Fast automated analysis of strong gravitational lenses with convolutional neural networks , 2017, Nature.

[84]  Pablo A. Estévez,et al.  Deep-HiTS: Rotation Invariant Convolutional Neural Network for Transient Detection , 2017, ArXiv.

[85]  G. Meylan,et al.  H0LiCOW - V. New COSMOGRAIL time delays of HE 0435-1223: H0 to 3.8 per cent precision from strong lensing in a flat ΛCDM model , 2016, 1607.01790.

[86]  L. Koopmans,et al.  The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation , 2017, 1710.03075.

[87]  P. Schneider,et al.  KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing , 2016, 1606.05338.

[88]  Philip J. Tait,et al.  A new quadruple gravitational lens from the Hyper Suprime-Cam Survey: the puzzle of HSC J115252+004733 , 2016, 1608.06288.

[89]  A. Fontana,et al.  First Results from the KMOS Lens-Amplified Spectroscopic Survey (KLASS): Kinematics of Lensed Galaxies at Cosmic Noon , 2016, 1610.03075.

[90]  Rémi Flamary,et al.  Support vector machine classification of strong gravitational lenses , 2017, 1705.08949.

[91]  N. R. Napolitano,et al.  Finding strong gravitational lenses in the Kilo Degree Survey with Convolutional Neural Networks , 2017, 1702.07675.

[92]  Chenzhou Cui,et al.  Automated Spectral Classification of Galaxies using Machine Learning Approach on Alibaba Cloud AI platform (PAI) , 2018, 1801.04839.

[93]  Mauricio Solar,et al.  Astronomical data analysis software and systems , 2018, Astron. Comput..

[94]  M. Maturi,et al.  EasyCritics – I. Efficient detection of strongly lensing galaxy groups and clusters in wide-field surveys , 2017, Monthly Notices of the Royal Astronomical Society.

[95]  A. Agnello,et al.  KiDS-SQuaD: The KiDS Strongly lensed Quasar Detection project , 2018, Monthly Notices of the Royal Astronomical Society.

[96]  F. Bellagamba,et al.  SEAGLE – I. A pipeline for simulating and modelling strong lenses from cosmological hydrodynamic simulations , 2018, Monthly Notices of the Royal Astronomical Society.

[97]  A. Leauthaud,et al.  Evidence for radial variations in the stellar mass-to-light ratio of massive galaxies from weak and strong lensing , 2018, Monthly Notices of the Royal Astronomical Society.

[98]  E. Decenciere,et al.  Deep learning for galaxy surface brightness profile fitting , 2017, Monthly Notices of the Royal Astronomical Society.

[99]  B. Póczos,et al.  CMU DeepLens: deep learning for automatic image-based galaxy–galaxy strong lens finding , 2017, Monthly Notices of the Royal Astronomical Society.

[100]  Asantha Cooray,et al.  LensFlow: A Convolutional Neural Network in Search of Strong Gravitational Lenses , 2017, 1705.05857.

[101]  J. Kneib,et al.  Deep convolutional neural networks as strong gravitational lens detectors , 2017, 1705.07132.

[102]  M. Meneghetti,et al.  The strong gravitational lens finding challenge , 2018, Astronomy & Astrophysics.

[103]  R. Bouwens,et al.  RELICS: The Reionization Lensing Cluster Survey and the Brightest High-z Galaxies , 2017, The Astrophysical Journal.