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\begin{document}

\title{Unnamed Article}



\author[1]{Sahraoui}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\sloppy


\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/esahubble/esahubble}
\caption{{Couldn't find a caption, edit here to supply one.
{\label{div-597167}}%
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\textbackslash{}contentslabel

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}\textbackslash{}AddToShipoutPicture*Rapportd'activit\selectlanguage{ngerman}é\\
Lyc\selectlanguage{ngerman}éeeJeanRostandetTchackMohamed-AliSahraouiRapportd'Activité,LycéeJeanRostand,Roubaix.\\
github.com/LaurethTeX/Clustering\\
ThisresearchwasdoneunderthesupervisionofDr.PaulineBarmbywiththefinancialsupportoftheMITACSGlobalinkResearchInternshipAwardwithinatotalof12weeks,fromJune16thtoSeptember5thof2014.\\
Septembre2018\textbackslash{}chapterimagehead1.png

Contents: Introduction \textbackslash{}chapterimage

head2.png

Introduction

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\section*{Motivation}\label{motivation}

WhenIappliedforthesummerresearchinternship,thetitleoftheprojectwas\emph{Themanycoloursofnearbygalaxies}anthedescriptionwas

\begin{quote}
Thedifferentpopulationsofstarsinagalaxycarrytherecordofitspaststarformationhistory,andalsoaffectitsfuture.TheprojectinvolvesanalyzingHubbleSpaceTelescopesimagesofnearbygalaxiesofdifferenttypes.Bymeasuringthebrightnessandcoloursofmillionsofstars,wecanunderstandtheagesandcompositionsofthestars,andlearnhowthegalaxyformedstarsinthepast.Theradiationemittedbystarsaffectsthegasinagalaxy,andthushowitwillformstarsinthefuture.Wewillusemulti-colourimagesofgalaxiestogainnewinsightsintoboththeirpastandfuture.\\
\end{quote}

So,asanengineerwithoutanyastrophysicsbackgroundIthougthIwouldbedoingimageprocessingappliedtoastronomyandIendedupdoingsomuchmore,buthey!Youneverknowwhatyouwillendupdoing.BeforecommingtoCanada,PaulineandIexchangedsomeemailswhereshesharedmesomeinterestingpapers,webpagesandanastronomyonlinecoursewhichlaterIdidtake,mainlytheinformationwasaboutageneralintroductiontoastronomyandhowastronomyimagesare,yes,astronomyimagesarecompletelydifferentasanyother\emph{normal}images,theyaremadeofpurelysciencedataandeveryimagehasvaluableknowledgeyoucanlearnfrom,andheyyouwillforgetsoonaboutpixelsandstarttalkingaboutskycoordinates.So,inafewwordsIhadnoideaofwhatIwasgoingtodo(still),IrealizedIdidn'thaveanyidea,andtheonlythingIundestoodwashowCCDdetectorswork.Ididn'tknowIhadaresearchadventureawaitingforme.

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\section*{Objective}\label{objective}

AfterIarrivedandhadmyfirstmeetingwithPauline,sheexplainedmeageneralideaofwhatshewantedandsharedmesomemorepapers(aboutmulti-wavelenghtstudies),Ireadtheinformationandcameupwiththeobjective.

\begin{itemize}
\tightlist
\item
  Findoutamethodtotransformdatafromahighdimensionaldataset(FITScubeoranyotherdataarrangement)toalowdimensionalunderstandableinformation(graphs,clusters).
\end{itemize}

Thismeansthatfrommultipleimageswithdifferentwavelengthsofthesametargetapplyanalgorithmtofindthehiddenpatternsthatliehiddenbetweenthem.



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\section*{Firstideas}\label{firstideas}

So,nowhereyouhaveyourfirstastronomypicture,11ForexamplepurposestheimageselectedisapictureofM83throughaWideH-alphaand{[}NII{]}filter.whatdoyousee?,itisamonochromeimage,withdifferentlevelsofbrightness,slightlybig(8500x5000),itlookslikealotofstarsmakingaspiral.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/ha-gray-conv-crp/ha-gray-conv-crp}
\caption{{\textbackslash{}contentslabel
{\label{div-502827}}%
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\end{center}
\end{figure}

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Howcanwelearnsomethingaboutthisimage,quantize,getusefulinformation?InthenextsubsectionsIwillexplainthefirstideas.

\subsection*{Superpixelsegmentation}\label{superpixelsegmentation}

Themainconceptofthisistocutanimageintobiggerneighborhoodsections,sofromanimagethathas\(425x10^{5}\)pixelswecangetmaybelessthan500superpixels,andthenanalyseseparatelythoselittlesectionsandidentifywhatkindofintersellarobjectsarethey,lookatimage{\ref{fig:super}}itisaself-explanatoryexampleofhowasuperpixelalgorithmworks.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/combo/combo}
\caption{{\textbackslash{}contentslabel
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\end{figure}\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/fig-PCA/fig-PCA}
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\end{figure}



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\section*{Hypothesis}\label{hypothesis}

OurdatalooksliketheimagesonFig.{\ref{fig:cubes}},anditcointainsdatafromlet'ssayadeterminedgalaxyatdifferentwavelengths,ifweassumethatthegalaxycontainsvariousregionsthatrelatetointerstellarobjectsthatcantell,howstarsareformed,where,howstarsdie,wherewasastar,andothermysteries,Iguesswecanassumethatthosecertainregionscanbeidentifiedbecausetheysharesimilarcharacteristics,theideasistofindhowagalaxyismadefrom,itscontents,applytheconceptofthesuperpixelideain3Dsuperpixels.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/nphoton/nphoton}
\caption{{\textbackslash{}contentslabel
{\label{div-959338}}%
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\end{center}
\end{figure}

Take the time to think about this, how the data looks like in 3D, how a star looks like in the datacube, imagine it, this is where ideas of how to tackle this problem come from.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/nine/nine}
\caption{{\textbackslash{}contentslabel
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\end{center}
\end{figure}

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\subsection*{Topicsyoushouldreview}\label{topicsyoushouldreview}

Thiswillrequerealotofwork,butheyitwillbeworthyandfun!

\begin{itemize}
\tightlist
\item
  Astroinformaticsandcomputerscience
\item
  Dataminig
\item
  MachineLearning
\item
  BigDataAnalysis
\item
  NeuralNetworks
\item
  VisualizationResources
\item
  StatisticsandImageProcessing
\item
  ProbabilityDensityFunction
\item
  PointSpreadFunction
\item
  Fullwidthathalfmaximum
\item
  Convolution
\item
  Interstellarmediumandstarformation
\item
  HIIregions
\item
  PlanetaryNebulae
\item
  SupernovaRemnants
\item
  MolecularGas
\item
  AllkindsofNebulae(e.g.dark,refletion)
\item
  AGN's(ActiveGalacticNucleus)
\item
  Astrophysics
\item
  Units(light-years,parsecs)
\item
  Worldcoordinatesystem
\item
  Light
\item
  Telescopes
\item
  StarsandStellarEvolution
\item
  Distance,Brightness,Luminosity
\item
  Galaxies
\end{itemize}

TheGitHubpagewillcertainlyhelpyoutounderstandwhyyouneedtolearnaboutthat,andwheretofindarticles,wepagesandbooks.

\subsection*{Downloading}\label{downloading}

First,let'sequipourselveswiththebasicsoftwareyouwillneedinordertostartthenyoumayprobablyfindothercoolprogramsandlateryouwillinstallthem.Thereisalsothepossibilitythatyourassignedcomputerwillhavetheminstalledalreadybuthereisabriefdescriptionofwhatyoucandowiththem,mostofthemareeasytouse.

ItisaprogramthatvisualizesastronomyimagesinFITSformat(don'tworryifyourecognizethisformat,itwillbeexplainedlater),whereyoucaneasilymanipulatethem,readtheirheaders,compare,lookatregions,seetheircharacteristics,makegraphs,evenmovies.Well,dependingonwhatyouneedtouselateryouwillbefindingallthefunctions,thebestwayistoclickeverywhereandfindoutwhathappens,alsoyoucanasktoyourastronomycolleaguestheywilltellyoualltheperks,orifyoulikelearningbyyourselforyouneedsometingspecificcheckthedocumentationwebpage.Itisfailyeasytoinstall,justfollowtheinstructions.

http://ds9.si.edu/site/Download.html

http://ds9.si.edu/site/Documentation.html

Thepicturebelowshows(Fig.{\ref{fig:screen}}somethingcoolyoucandoinDS9.\selectlanguage{english}
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Themost\emph{limitless}anduserfiendlywaytodevelopprogramsinAstronomyisusingPython,therearemanypackages,modules,functionsnowavailabletohelpyouinalmostanything.Me,asanundergradengineerI'musedtoprogramonanuserinterfaceandnotdirectlyinaterminal.So,hereIwillexplainyoumyownwayofdoingthings.ImakemyprogramsontheCanopyeditor,itshowswhenandwhereyouhaveprogramingerrorandwarnings,andtheinterfaceiseasytolearn,nowtorun,Iopenaterminal,gotothedirectorywheremyprogramis,typeipythonwaitandthentyperunmyProgram.py,andwaitfortheresult.Nowtherearealotoffancierwaystoworkwith\emph{Python},youcanprogramandtestdirectlyusing\emph{IPythonNotebook}onawebbrosweroryoucanjustgofortheterminal,use\emph{nano}or\emph{vi}orthetexteditoryoulikeandthenrunitbytypingpythonmyProgram.py.Atthispointisuptoyou,butheyherearesomelinkstostartandthepackages/modulesyoushouldinstall.
PyCharm,itadevelopmentenvironment,justlikeCodeBlocksorNetBeanshttp://www.jetbrains.com/pycharm/
Spyder,actuallythisistheinterfacethatcomeswiththePythondiscritutionAnaconda,youwillgetthePythondistricutionandtheintrerface.https://store.continuum.io/cshop/anaconda/
Canopy,thisistheoneImentionedbefore,itsupereasytouseandyoucaninstallpackageswithoneclick.https://www.enthought.com/products/canopy/\\
InPython,modulesarelikethelibrariesinC,therefore,tousemath,astronomyandcomputersciencetoolsyouneedtoinstallthem.Tolearnwhetheryoualreadyhaveamoduleinstalledornot,typeon\emph{iPython}importandreaModule,iftheoutputresultissomethinglikeImportError:NomodulenamedandreaModule,youdefinitelydon'thaveitinstalled.Thestrategyheretoinstallpackagesitfairlyeasy,findtheirwebsite,gotothedownloadsectionandfollowtheinstructions,almostallthepackagesareavailableonthePythonPackaingIndexandmaybeinstalledbyrunning:
pip install pyfits
Tolearnhowtousethemcheckthedocumentationpage,usermanualsortheirAPI's,ifyouhaveexperienceonobjectorientedprogramingitwillbelikerunninganewbikeandifyoudon't,don'tworrytoomuch,Pythonwasdesignedtobeeasytoprogram,justlearntherulesofthegame.
Astropy,thispackageisthe\emph{musthave}ofeveryastronomer,containstoolstohandlecoordinatesystems,units,convolution..wellisbetterifyoutakealookatthewebpage.http://www.astropy.org/
Numpy,thispackagecontainsthemathmagicfunctions,linearalgebratoolsandthearraymanagementvariables,makesureyoulearnallabout\emph{Numpyarrays}youwillworkwiththemallthetime.http://www.numpy.org/
SciPy,wellthispackageisthebaseofallscikitmoduleswhichcontainthefunctionsyouwilluseinimageprocessingandmachinelearning.http://www.scipy.org/
ScikitImage,containsimageprocessingtools,itisthe\emph{OpenCV}for\emph{Python}http://scikit-image.org/
ScikitLearn,containsdataminingalgorithms,prettymuchcontainseverythingthatyouwilleverneed.http://scikit-learn.org/
Matplotlib,thispackageisprobablyoneofthemostpowerfultoolsvisualizedata,youcandrawalmostanythingyouwantandexaclyhowyouwantit.AnexampleofthataretheimagesoftheAstroMLbook,youcanaccesstotheimagelibrarycodeandlearnhowtheyaremade,thisisthewebsitehttp://www.astroml.org/book\_figures/index.html.11Statistics,DataMining,andMachineLearninginAstronomybook,itwasmentionedbefore.Youcandownloadthepackageherehttp://matplotlib.org/.
PyFITS,inthispackageyouwillfindtoolstomanipulateFITSfiles,createnewones,createimagecubes,tables,anddoallkindsofthingswiththeirheaders.Certainlythispackageismorethanuseful.http://www.stsci.edu/institute/software\_hardware/pyfits
InthepathofresearchingI'mcertainyouwillfindmoreandnewpackagesandbythemyouwillbepreparedtoinstallanything.
Thisisatoolkitforassemblingastronomicalimagesintomosaics,butithasmorefunctionsthatyoumayneedinthefuturetoprepareyourdatabeforeprocessingit.TherearetwowaysofinstallingandIwouldsaythatisbettertohavethemboth.Oneistoinstallthetoolkitandanytimeyouneedit,yourunthecommandsontheterminal,theotheroneistoinstalla\emph{Python}moduleanduseitjustlikeanyothermodule.Toinstallmontageforterminal,downloadthelastestversioninthiswebsitehttp://montage.ipac.caltech.edu/docs/download.html,\textbf{readtheREADMEfile}orgotothiswebsitehttp://montage.ipac.caltech.edu/docs/build.htmlandfollowthesteps,nowifyoudon'thaveanyprobleminstallingit,youcantrytestingitwithanexampleprogramfoundonthiswebsitehttp://montage.ipac.caltech.edu/docs/pleiades\_tutorial.html,incaseyouarehavingtroubleandyourcomputerisaMAC,insteadofdoingstepfive(\emph{IfyouwanttobeabletoruntheMontageexecutablesfromanydirectory}),trythis:
Openafilecalled.profilelocatedinyouruserfolder.(e.g./Users/Laureth) \$
vi .profile Includeinthefilethefollowing export
PATH=/Applications/Montage\_v3.3/bin:\$PATH
Inthislink(https://github.com/LaurethTeX/Clustering/blob/master/Tools.md\#the-profile-file)youwillfindanexampleofhowthisfileshouldlook.Afteryoumodifyit,makesurethatyousaveitandtypein/Users/Laureth,
\$ source .profile
Thentrytestingthe\emph{Montage}commands,andI'msurethatitwillmagicallywork,justrememberthatanytimeyouuseanycommand,typesource.profile.\\
Nowtheotherwaytoinstall,impliesonlytoinstalla\emph{Python}modulebutthismodulecontainslessfunctionsthattheterminalapplication,inanycasecheckthewebsitehttp://www.astropy.org/montage-wrapper/,thereyouwillfindallthedocumentationyoumayneedandtheinstructionstoinstallit(\emph{Spoilers}pipinstallmontage-wrapper).\\
Anyquestionsyoumayhaveandhowtoinstall,hereismyGitHubpageforsoftwaretoolshttps://github.com/LaurethTeX/Clustering/blob/master/Tools.md\textbackslash{}chapterimageboat.png

Understandyourdata

Beforecontinuing,firstandmostimportantlyyoumustselectthe\emph{raw}datayouaregoingtoprocessandlaterafteryouaquireexperiencewithanspecificdatasettheideaistoexpandthealgorithmstoanykindofdataset.Theimportantthingsaretolearnhowtoinputthedatacorrectly,establishtheright\emph{learningparamenters}intheselectedalgorithmandfindthebestwaytovisualizeyourresultsandinterpretthemcorrectly.Nowlet'sstartwithbasicconceptsthatvaryfromanengineeringtoanastronomerpointofview.

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\section*{Whatisanimage?}\label{whatisanimage}

Asyoumayknow,animageisamatrixofnumbersthatcointainsthespecificbrightnesslevelthatcorrespondstoagivenpixel.Andfromtheretheconceptsevolvesandaddschannelsofcolouranddepth.Butfornow,let'sjustthinkaboutmonochromaticimages(onlyonechannel).InAstronomy,imagesareusuallyconsideredsetsofscientificdata,observations,thatcontaininformationaboutanspeficictargetintheskyseenthroughtanspecificfilterandthelevelsofbrightnesscorrespondtothebehaviouroftheopticalsensor(CCDcamera)inrelationwiththenumberofelectronsthathitaparticularpixelthroughanspecificwaveband.SomethingelsetoconsideristhattheskyisnotflatwiththisImeanthatthecelestialvaultislikeaspheresurroundingusthereforecartesiancoorditanesarenottheparamentersusedtoidentifypointsinspace,thereisanothersystemcalledWCS(WorldCoordinateSystem)henceaconversionbetweenpixelsandWCScoordinatesexists.Asyouarerealizingnowjustoneimagecancontaintonsofinformationrelatedtoit,nowimaginethatmultipliedforterabytesandterabytesofstars,galaxies,planets,nebulaeoranyobjectinspace.Fortunatelyinastronomythisissolvedusinganimageformatthatcointainstheimageanditsowninformation.

\subsection*{FITSfiles}\label{fitsfiles}

Thisformatisthestandarddataformatusedinastronomy,cancontainoneimage,multipleimages,tablesandheaderkeywordsprovidingdescriptiveinformationaboutthedata.Thewayitworksisthatthisformatcancontainatextfilewithkeywordsthatcomprisetheinformationabouttheobservationandamultidimensionalarraythatcouldbeatable,oranimage,oranarrayofimages(datacube).Thisfilescanbemanagedindiffetentways,withanimagepreviewuseDS9,forhandingthedatainaprogramusethe\emph{Python}package\emph{PyFITS}.

\subsection*{WFC3ERSM83DataProducts}\label{wfc3ersm83dataproducts}

TheselecteddatasettotestthedatamininglibrariesIfoundisaseriesofobservationsofM83at9differentwavelengths,theoriginalimagescanbefoundinthiswebpage,http://archive.stsci.edu/prepds/wfc3ers/m83datalist.html,thespecificinformationaboutthemcanbefoundinTable{\ref{tab:uno}}.ThisparticularimageswereobservedthroughHSTwiththeWFC3/UVIScamera.

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SummaryofObservations

{\label{tab:uno}}

Filter/Config.

Waveband/Central\(\lambda\)/Line

Obs.Date

Comment

F225W

UVfilter/235.9nm

26Aug2009

UVwide

F336W

UVfilter/335.5nm

26Aug2009

Str\(\ddot{o}\)mgren\(u\)

F373N

Narrow-BandFilter/373.0nm

19Aug2009

Includes{[}OII{]}

F438W

Wide-BandFilter/432.5nm

26Aug2009

\(B\),Johnson-Cousinsset

F487N

Narrow-BandFilter/487.1nm

25Aug2009

IncludesH\(\beta\)

F502N

Narrow-BandFilter/501.0nm

26Aug2009

Includes{[}OIII{]}

F657N

Narrow-BandFilter/656.7nm

25Aug2009

IncludesH\(\alpha\)+{[}NII{]}

F673N

Narrow-BandFilter/676.6nm

20Aug2009

Includes{[}SII{]}

F814W

Wide-BandFilter/802.4nm

26Aug2009

\(I\),Johnson-Cousinsset

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\section*{Preprocessingyourdata}\label{preprocessingyourdata}

Thissectioniswhereyouprepareyourdatatobeprocessed,youhavetomakesurethatallyourimageshavethesamegridsize,samespatialresolution,lesspossiblequantityofoutliersabdnoiseandsamecoordinatesystem.Now,whatarethosethings?Samegridsizemeansthatyourimagesmusthavethesamepixelsize,inthedatasetweareprocessingwedon'thavetoworryaboutthis,thepixelsizeis0.0396arcsec/pixel.Now,spatialresoultion,eachimagehasit'sownspatialresolutiondependingonthefilterthatwasusedtogettheobservation,thenumberthatyouwillbelookingforistheFWHMthatdescribesthePSFofeveryimage.WhenyouhavealltheFWHMforalltheimagesyoushouldchoosethelargestwhichcorrespondstothepoorestspatialresolutionandcreateaconvolutionkernelwith\emph{TinyTim}oruseagaussiankernelcalculatedwith\emph{Astropy}andconvolvealltheimageswiththatkernel.ThisexactlywhatIdid,ifyoulookatimage{\ref{img:conv}},youwillseethebeforeandafterconvolution.Intable{\ref{tab:dos}}youcanseehowIchosethenumberfortheFWHM.\selectlanguage{english}
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WFC3/UVISPSFFWHMinformationsfortheselecteddataset,asyoucanseethelargestnumberhereis0.083wichmeansthepoorestspatialresolution,thisisthenumberusedtocalculatetheconvolutionkernel,inordertoprecessthemallimagesmusthavethesamespatialresolution.

{\label{tab:dos}}

Filter/Config.

Central\(\lambda\)

FWHM(arcsec)

F225W

235.9nm

\(\sim\)0.083

F336W

335.5nm

\(\sim\)0.075

F373N

373.0nm

\(\sim\)0.070

F438W

432.5nm

\(\sim\)0.070

F487N

487.1nm

\(\sim\)0.067

F502N

501.0nm

\(\sim\)0.067

F657N

656.7nm

\(\sim\)0.070

F673N

676.6nm

\(\sim\)0.070

F814W

802.4nm

\(\sim\)0.074

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Afterconvolingallthepicures,Istartedtodosometests,butIrealizedthatmaybearound30\%oftheimageswasmissinginformationand/ornoiseandtheresultsIwasgettingweremisleadbytheoutliers.Inclusteringalgorithmswemusthelpthealgorithm,makesurethatwhatweareinputingissomethingthatcanbeclustered,althoughsomeofthemare\emph{shielded}againstoutliers,makingourdatamoreaccesibleandeasyfortheneuralnetworkstointerpretwillhelpyoutogetbetterresults,asyoucanseeinimage{\ref{img:dos}}(openoneandexploreitinDS9)thereismissinginformationandnoise.InordertocorrectthisIdecidedtogowiththeeasiestwayIcouldthinkof,justcuttheimage.AndIdidselectedaprocessableareaexcludingallthemissinginformationandnoisyareas.\selectlanguage{english}
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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Thenextstepwastobuildthedatacube,atthispointyoucandecideifyouwanttoprocessyourimagesindendentlyorallofthem.Theidealhereistoinputalloftheminadatacube,sotheoutputclutersrelateinformationfromallthewavelenghtsandtheregionscoveredbythemcanbeinterpretedmoreeasily.Nowifyouchoosetocreateanimagecube(justappendtheimagearraysinoneFITSfile)itisposiblethatyouyimageshaveadifferentconversionbetweentheirworldcoordinatesystemtopixel,sohavetomakesureallofyourimagesareprojectedwithonlyoneconversion,thismeanthatyouhavetoreprojectthemtoacommonWCS.Well,whatIwrotebeforeitisabriefsummaryofwhatIdid,butI'msurethatyoucanfindabetterwaytodoyourowndatapre-processingbutherearesomethingsthatyoushouldconsider:

\begin{itemize}
\tightlist
\item
  Createamethondasgeneralaspossible,withinputparameterthatcanbeadaptedtoanykindofdata,thiswillsaveyoualotofworkinthefuture
\item
  Understandfirstyouralgorithm,howthedataisgoingtobeprocessedanddesignthebestwaytoinputyourdata
\item
  Accomodateyourdataaccordingtothetypeofattributesthatthealgorithmcanhandle
\item
  Considerthesizeofyourdataset,ifit'shugeyourprogrammayneverend
\item
  Findoutofyouralgorithmcanworkwithhighdimensionaldata(multi-wavelenght),becauseifnot,youwon'tbeabletoinputdatacubes
\item
  Findoutifyourselectedclusteringalgorithmsisabletofindclustersofirregularshapes,thiswillhelpyoutodevicethebestwaytoaccomodateyourpatterns
\item
  Handleoutliers,ifyouidentifythem,knowwheretheyare,trytoeliminatethemasmuchaspossible,wedon'twantthemmessingwithourclusters
\item
  IncasethatyoucomeupwithanartfulmathematicalmethodlikePCAtoreducedimensionality,makesurethatwhatyouinputcanlatermakesensewhenisclustered,becuaseyouwillbeworkinginanotherspace
\item
  Remeberthatthemostimportantgoalistofindhiddenknowledgetherefore,youmustknowyoutovisualizeandinterpretyourresults
\item
  Forthelet'scallit\emph{astronomyimageprocessing},makesurethatyourdataisscientificallyaprovedaskpeoplearoundyou.
\end{itemize}

ThissectionisexplainedatlenghtintheGitHubpage,thereyouwillfindmycodesandsomehelpfullinks,https://github.com/LaurethTeX/Clustering/blob/master/Preprocessing.md



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\section*{MethodsSelected}\label{methodsselected}

\subsection*{ESOM,EvolvingSelfOrganizingMaps}\label{esomevolvingselforganizingmaps}

The\emph{official}manualforthismethodcandefoundhere,http://dame.dsf.unina.it/documents/ESOM\_UserManual\_DAME-MAN-NA-0021-Rel1.2.pdf,thereyouwillfindafullexplanationofthemethod,themeaningofeveryvariableandthesupportedfiletypes.Hereismyownexplanationofhowthisparticularmethodworks,firstofall,canbeusedasanunsupervisedmachinelearningtechniqueoryoucanhelpthealgorithmtoidentifyregionsanmakeitasupervisedmachinelearnigtechnique,thistypeofclusteringfindsgroupsofpatternswithsimilaritiesandpreservesitstopology,startswithanullnetworkwithoutanynodesandthosearecretedincrementallywhenanewinputpatternispresented,theprototypenodesinthenetworkcompetewitheachotherandtheconnectionsofthewinnernodeareupdated.Themethodisdividedinthreestages,\emph{Train},\emph{Test}and\emph{Run}.ThefirststeptoexperimentwiththismethodisTrain.Here,theimportantvariablestoundertandanlookatare,thelearningrate,epsilonandthepruningfrequency.ItishighlyrecomendablethatyouchecktheDAMEWAREmanualforthisfunction,theretheywillexplainindetailthemeaningofeachonthementionedvariables.

\subsubsection*{ExpectedResults}\label{expectedresults}

ThisparticularmethodasImentionedbeforesupportsdatacubesandconsidersasanindependentpatternallthenumbersinthemulti-dimensionalarraythismeansthatourclustersaregroupsofpatternswithsimilarcharacteristics,thatcorrespondtovolumesofsimilarfluxesofelectronsinsidethedatacube.Theoutputfilesfromtheexperimentthatwillshowusourresultsare,

\begin{itemize}
\tightlist
\item
  \emph{E\_SOM\_TrainTestRun\_Results.txt}:Filethat,foreachpattern,reportsID,features,BMU,clusterandactivationofwinnernode
\item
  \emph{E\_SOM\_TrainTestRun\_Histogram.png}:Histogramofclustersfound
\item
  \emph{E\_SOM\_TrainTestRun\_U\_matrix.png}:U-Matriximage
\item
  \emph{E\_SOM\_TrainTestRun\_Clusters.txt}:Filethat,foreachclusters,reportslabel,numberofpatternassigned,percentageofassociationrespecttotalnumberofpatternanditscentroids.
\item
  \emph{E\_SOM\_Train\_Datacube\_image.zip}:Archivethatincludestheclusteredimagesofeachsliceofadatacube.11Ihavemydoubtswhetherthisfileisproducedornot,innoneofmytestwasproduced,youmightneedtocontactthedevelopersandaskaboutthis.
\end{itemize}

Thefilethatyouwillbelookingforwardtoseeisthelastone,thezipwhereyouwillbeabletoseetheslicesofthevolume,andhowthefinalconfigurationoftheclusterswasarranged.

\subsubsection*{Failedandstillrunningtests:Whatnotodoandwhatisstillrunning}\label{failedandstillrunningtestswhatnotodoandwhatisstillrunning}

ThefirsttestsIdidincludedallthecompletedatacube,includingtheareaswheredatawasmissing,theimageswereonlyreprojectedandconvolved.Thatwasbeforerealisingthatoutliersmigthaffecttheabilityofthealgorithmtoidentifytheclustersanddistractthemwithnoiseandmissingdata.So,thefirstthingyoumustNOTdo,istogetridoftheoutlierswhenyouaretrainingyournetwork,ifyouevergettohaveawelltrainednetworkthenitmightbeinterestingtolearnhowthenetworkinteractswithnoiseanoutliers,butfornowwewillhelpherabit.Intable{\ref{tab:ds9failed}}aretheinputparametersIusedtothefailedtestsappliedinthe\emph{raw}datacube,andintable{\ref{tab:ds9running}}aretheinputparametersusedonexperimetsthatarestilrunningsinceAugust7th,2014.(Iwonderiftheywilleverend)

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ThistabledescribesallthefailedexperimentsdoneintheworkspaceWFC3withthe\emph{raw}datacubeasaninput,usingtheESOMmethodintheDAMEplatformselectingthenumber3asthedatasettypeandwithoutusingapreviousconfigurationfile.

{\label{tab:ds9failed}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

Train2

1

1

0.3

0.001

5

Train3

1

1

0.7

10

100

Train4

1

1

0.95

1

10

Train5

1

1

0.99

0.1

10

Train6

1

1

0.01

0.01

1

Train7

1

1

0.5

0.7

5

Train8

1

1

0.5

0.5

7

Train11

1

1

0.25

0.00001

10

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ThistabledescribesalltheexperimentsdoneintheworkspaceWFC3thatarestillrunningsinceAugust7th,2014withthe\emph{raw}datacubeasaninput,usingtheESOMmethodintheDAMEplatformselectingthenumber3asthedatasettypeandwithoutusingapreviousconfigurationfile.

{\label{tab:ds9running}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

Train9

1

1

0.3

0.0001

5

Train10

1

1

0.99

0.0001

10

Train12

1

1

0.5

0.0001

5

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Hey,ifyouwerewonderingwhyIalwayschoosetonormilize,andoneastheinputnode,wellthenormalizationisduetothefactthatIknowthatthedatahas,accordingtoitsfilter,allkindsofrangesoffluxesoneverylayerwhichmeansthatthedistancesbetweenpatternsmightnotbecorrect,thisisatopicyoushouldlookinto.AndfortheinputnodeIchoose1becauseifIstartwithanyothernumbertheexperimentautomaticallyfails,andofcoursewedonotwantthat.AsIprogressedandsawtheresultsandthe\emph{logfiles}inallthefailedexperimentsIdecidetotrythealgorithmonindependentlayersandseeifIcouldgetsomething.ThereforeIselectedtheH\(\alpha\)convolvedobservation(halpha\_conv.fits)anddidsometestsonit,table{\ref{tab:hafailed}}showstheparametersIusedforthefailedexperimentsandtable{\ref{tab:harun}}showstheparamtersfothestillrunningexperiments.

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ThistabledescribesthefailedexperimentsdoneintheworkspaceWFC3forthe\emph{halpha\_conv.fits}file,usingtheESOMmethodforonelayerintheDAMEplatformselectingthenumber3asthedatasettypeandwithoutusingapreviousconfigurationfile.

{\label{tab:hafailed}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

TrainHa1

1

1

0.5

0.01

5

TrainHa2

1

1

0.5

0.001

5

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ThistabledescribesthestillrunningexperimentssinceAugust10th,2014intheworkspaceWFC3forthe\emph{halpha\_conv.fits}file,usingtheESOMmethodforonelayerintheDAMEplatformselectingthenumber3asthedatasettypeandwithoutusingapreviousconfigurationfile.

{\label{tab:harun}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

TrainHa3

1

1

0.5

0.0001

5

\textbackslash{}contentslabel

{[}\textbackslash{}thecontentslabel{]}1.25cm\textbf{ \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage\textbackslash{}contentslabel}{[}\textbackslash{}thecontentslabel{]}1.25cm
\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}MynextmentalstepwastorepeatthetestseliminatingasmanyoutliersIcouldreduce,myhypothesishereisthat,ifIelimantealltheareaswherethereismissingdataandnoise,theneuralnetworkswillbeconcentratedonlyinthepatternsI'minterestedinclusteringandmaybeidenfyinginterestingregionsthatcorrespondtosomeknowninterstellarobject.So,whatIdidwastotrytheESOMalgorithmwith,again,independentimages,thistimeIdecidedtoapplythesameexperimenttothreedifferentlayers,H\(\alpha\),UVwideand\(i\)-band.Intable{\ref{tab:threefail}}youcanseetheparametersofthefailedexperimentsandonfigure{\ref{img:fail3}}therearesomeoftheoutputhistograms.Also,intable{\ref{tab:threerun}}youcanseetheinputparametersofthestillrunningexperiments.

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Thisparameteswhereusedinthreedifferentworkspaces(\emph{halphaCrop,uvwidecrop,ibandcrop}),withtheirowninputfilethatcorrespondedtotheconvolvedandcroppedobservationofeachfilter(halpha\_conv\_crp.fits,uvwide\_conv\_crp.fits,iband\_conv\_crp.fits),alloftheexperimentshadnopreviousconfigurationfileandthedatasettypewas3andallfailed.

{\label{tab:threefail}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

Train1

1

1

0.5

0.001

50

Train2

1

1

0.5

0.01

50

Train3

1

1

0.5

0.1

100

Train4

1

1

0.5

0.001

100\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Histogram-halpha1/Histogram-halpha1}
\caption{{\textbackslash{}contentslabel
{\label{div-988566}}%
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\end{center}
\end{figure}

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Thisparameteswhereusedinthreedifferentworkspaces(\emph{halphaCrop,uvwidecrop,ibandcrop}),withtheirowninputfilethatcorrespondedtotheconvolvedandcroppedobservationofeachfilter(halpha\_conv\_crp.fits,uvwide\_conv\_crp.fits,iband\_conv\_crp.fits),alloftheexperimentshadnopreviousconfigurationfileandthedatasettypewas3.TheexperimentsmentionedarestillrunningsinceAugust11th,2014.

{\label{tab:threerun}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

Train5

1

1

0.5

0.0001

100

Train6

1

1

0.99

0.0001

75

\textbackslash{}contentslabel

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Asyoucansee,IdiscoveredthatifIchooseanepsilonof0.0001theexperimentswillbestillrunning,andalloftheothervariablescanbevariatedlikethelearningrateandthepruningfrequency.

\subsubsection*{Thebigandsmallreprojecteddatacube}\label{thebigandsmallreprojecteddatacube}

AfterafewdaysofwaitinganxiouslyfortheexperimentstoendandnotgettinganynewresultsIdecidedtotesttheconvolved,croppedandreprojecteddatacubeincludingallthelayerswithafixatedprunningfrequencyof0.0001,hoppingthatthistimeIcouldgetsomeinterestingresults.TheinputparametersforthetwoexperimentsItestedcanbeseenintable{\ref{tab:cubeesom}}.

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Thisparameteswhereusedintwodifferentworkspaces(\emph{DataCube,RPDataCube}),thefirstexperimentisstillrunningsinceAugust12th,2014andthesecondfailed.TheinputfortheDataCubeworkspacecorrespondstoa9layerdatacubewithnoreprojectionandtheRPDataCubeinputisthesamedatacubebutreprojected.

{\label{tab:cubeesom}}

Name

Inputnodes

Normalizeddata

Learningrate

Epsilon

PruningFrequency

ESOMtrain1

1

1

0.5/0.75

0.0001

100

ESOMtrain2

9

1

0.75

0.001

100

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Asyoucansee,intheexperiment\emph{ESOMtrain2}Itriedtostarttheneuralnetworkwith9nodes(thinkinglogicallyashaving9layersinthedatacube)andimmediatlytheexperimentfailed,so\textbf{donottrytoinputanumberdifferentthanone.}Iwaited17daysfortheexperimentstofinish(Ididsomeotherstuffinthemeanwhile,mostofthetimelearningnewthings)butIdidnotgetanyresultssoIcameupwithadifferentstrategy,selectingsmalldatacubeswithalreadyidentifiedregionsbytheNEDdatabase.IselectedrandomlyaparticularHIIregionlocatedinRA204.26971,DEC-29.84933(Seefigure{\ref{img:h2region}})andcentereditina605x605pixelssample.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/small-ex/small-ex}
\caption{{\textbackslash{}contentslabel
{\label{div-970932}}%
}}
\end{center}
\end{figure}

\textbackslash{}contentslabel

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Thistime,mostoftheexperimentsgavemeimmediateresultsfailingorfinishing.Ontable{\ref{tab:small}},youcanseetheinputparametersandthestatusoftheexperimentsItestedwiththesmalldatacube.

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AllthementionedexperimendbelongtotheSmallDataCubeworkspace,have3asdatatypeandoneinputnode,nopreviousconfigurationfileandtheinputfileis\emph{rp\_small\_datacube.fits}.

{\label{tab:small}}

Name

Normalized

Learningrate

Epsilon

PruningFrequency

Status

ESOMtrain1

0

0.5

0.001

50

Running

Train2

1

0.5

0.0001

50

Ended

Train3

1

0.5

0.1

50

Ended

Train4

0

0.5

0.0001

50

Running

Train5

0

0.95

0.0001

100

Running

Train6

1

0.99

0.001

50

Ended

\textbackslash{}contentslabel

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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Inthiscasethreeoftheexperimentsendedandnoneodthemfailed(yet),hereIdetectedthattheoutputfilethatcontainsthedistributionsoftheclustersoneverylayerismissing,butwegotsomeinterestingresuts,inthenextfigures({\ref{img:smallended}},{\ref{img:matrixended}})youcanapreciatebetterwhatI'mtakingabout.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Small-train2/Small-train2}
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{\label{div-758688}}%
}}
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\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/matrix2-01/matrix2-01}
\caption{{\textbackslash{}contentslabel
{\label{div-270905}}%
}}
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\textbackslash{}thecontentspage{[}{]}\textbackslash{}contentslabel{[}\textbackslash{}thecontentslabel{]}1.25cm \textbackslash{}titlerule*{[}.5pc{]}. \textbackslash{}thecontentspage{[}{]}Thereisworktobedoneforthiscases,understandwhatisgoingonandinterpretcorrectlytheresults,butlastwegotsome.

\subsection*{CSOM}\label{csom}

Well,asImentionedbeforeIdidsometestsusingtheESOMmethodbutsinceIwasntgettinganyresultsIthougthoftestingthismethond,asalwaysIstronglyrecommendtoreadcarefullyitsmanual,http://dame.dsf.unina.it/documents/SOFM\_UserManual\_DAME-MAN-NA-0014-Rel1.1.pdfandfullyundesrtandwhatisgoingonbehindthecurtains.Inthemeanwhile,thisismyownexplanation.ThismethodusesFITSfiles,doesnotsupportdatacubes,specifficallyusesaneighborhoodfunctioninordertopreservethetopologicalpropertiesoftheinputspace,itisatypeofartificialnetworkandismainlyunsupervisedlearningandproducesalowdimensionaldiscretizedrepresentationoftheinputspaceofthetrainingsamples.Iinthiscaseyoucanchoosethenumberofclusters/neuronsinthefirstlayer(neuralnetwork),thediameter,numberoflayers(intheneuralnetwork),learningrateandvarianceoneachlayer.Hereyouhavemoreinputparameterstocontrol.

\subsubsection*{ExpectedResults}\label{expectedresults}

Wellinthiscase,sinceonlyFITSimagesareallowed,whatweexpecttofindareareasindeitfyingthedifferentobjectsintheinterstellarmedium.Theimportantresultsinthiscase,aregotinthe\emph{Run}and\emph{Test}steps,inthe\emph{Train}steponlythenetworkconfigurationisoutputted.Whatweareinterestedonseeinaretheplottedclusters.

\subsubsection*{Tests}\label{tests}

InthiscaseIdidsometestsontheCSOMworkspace,butnoneofthe,wheresuccesful,toomanyinputvariablestocontrolandtest.So,inthiscaseIwillleavethisparametersfreeforyoutotry.Idobelievethattismethodcouldbeveryusefulandifyoufindawaytoinputthedatacubeinadifferentconfigurationyouwillgetsomeinterestingresults,duetothefactthatinthismethodthepreservationofthetopologyisoneofthemainprinciples.

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\section*{Furtherwork}\label{furtherwork}

Well,finallywereachedthepointwhereImytimeinCanadafinishedandIthisresearchisstillonitsfirststages.IhavesomanyideasofhowtoexploretheclusteringtechniquesintheDAMEplatform,MatLab,Pythonandeverythingelsethatcanbetested.

\subsection*{Someinterestingideas}\label{someinterestingideas}

Fornow,Iwouldsaythatyourbestchancehere,istodeviceanefficientwaytoinputtheinformationcontainedinadatacubeasalistofpointswithvaluesandreduceitsdimensionalitybyrandomlychoosingthemoneverylayer.Ifyouareeverstuck,ornonewideascometoyourmind,donothesitatetocontactmeImighthaveanewinterestingideayoucantest.

\subsection*{Linksyoushouldcheckout}\label{linksyoushouldcheckout}

MostofthemarelistedintheusefulresoursessectionofTheCaltech-JPLSummerSchoolonBigDataAnalytics,thewebpagehttps://class.coursera.org/bigdataschool-001/wiki/Useful\_resources,youmayneedtocreateanaccountinCourseraandenrollinthecourse.AndtherestofthemarelocatedintheReferencessectiononmyGitHubpage,https://github.com/LaurethTeX/Clustering/blob/master/References.md.\emph{Wishyouallthebest,AndreaHidalgo}

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