Classifying Pan-STARRS sources with unsupervised and supervised learning

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Learning Goals

In this tutorial, you will see an example of using models to classify sources extracted from astronomical data. By the end of this tutorial you will have working examples of how to apply principal component analysis (PCA), t-distributed stochastic neighbor embedding (tSNE), k-means clustering (unsupervised learning) and stochastic gradient descent (SGD) classification (supervised learning).

Introduction

Machine learning which can be applied in both supervised and unsupervised contexts for classification. In this notebook, we will walk through the basic steps of reducing the dimensionality of astronomical source catalogs with PCA and tSNE and classifying the sources in unsupervised and supervised formats.

1. Download and import the data

2. Perform data cleaning steps

3. Reduce dimensionality with PCA and tSNE

4. Perform unsupervised clustering with k-means

5. Perform supervised classification with SGD

6. Assess the success of the model with a confusion matrix

Here we will classify sources extracted from multi-wavelength photometry from the Pan-STARRS survey, and compare with previous classifications from a convolutional neural network analysis by the PS1-STRM team.

Imports

This notebook uses the following:

• numpy to handle array functions

• astropy for accessing FITS files

• matplotlib.pyplot for plotting data

• sklearn for models and performance metrics

• itertools for generating combinations

• scipy for statistics

If you do not have these packages installed, you can install them using pip or conda.

# arrays
import numpy as np

# fits
from astropy.io import fits
from astropy.utils.data import download_file
from astropy.table import Table

# Plotting
import matplotlib.pyplot as plt

# sklearn for performance metrics

# sklearn 
from sklearn.preprocessing import LabelEncoder
from sklearn.model_selection import train_test_split
from sklearn.cluster import KMeans
from sklearn.manifold import TSNE
from sklearn.decomposition import PCA
from sklearn.linear_model import SGDClassifier
from sklearn.metrics import confusion_matrix
from sklearn import metrics

# iterative combinations
from itertools import combinations

# statistics 
import scipy.stats as st

# from IPython import get_ipython
# get_ipython().run_line_magic('matplotlib', 'notebook')

# set random seed for reproducibility 
np.random.seed(42)

1. Download the data

For the following exercises, we will use data from the Pan-STARRS1 (PS1) catalog, which includes wide-area imaging in five wavelength bands, g, r, i, z and y.

Using convolutional neural networks (CNNs) trained on spectroscopic surveys, the Pan-STARRS1 Source Types and Redshifts with Machine Learning (PS1-STRM) (Beck et al. 2020) team classified (“star”, “galaxy”, “QSO” and “unsure”) and regressed redshift information for the 2,902,054,648 discree sources in the PS1 3\(\pi\) DR1 catalog. This volume of data is far too large to analyze in a short notebook example. Therefore, we extracted a subset of PS1-STRM and cross-matched it with the PS1 catalog (see Appendix for details on how to obtain this subset from MAST).

This subset of PS1 will be used to test whether simple clustering algorithms can reproduce the classification results of PS1-STRM. The dataset consists of 100,000 sources, randomly selected to have roughly equal representation in the four PS1-STRM classes.

First, load the data into an astropy table:

%%time
file_url = 'https://archive.stsci.edu/hlsps/hellouniverse/hellouniverse_ps1strm_subset.fits'
tab = Table.read(download_file(file_url, cache=True))

CPU times: user 617 ms, sys: 343 ms, total: 960 ms
Wall time: 2.54 s

Inspect the contents of the table:

tab

Table length=100000

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GALAXY	0.79322743	0.17576069	0.031011794	0.677324831485748	0.244630052392452	200422297094590056	3938806000009635	356366321560210	0.575081246509292	82	3938806	3	11	3	3	3	3	3	3	8.17628972527018e-07	3.74233991351502e-07	0.40489798784256	24.1187000274658	0.496948003768921	5.00710984852049e-06	1.24618998142978e-06	0.67280501127243	22.1511001586914	0.270224004983902	3.95864981328486e-06	1.42314002005151e-06	3.85121989250183	22.4062004089355	0.390323996543884	3.49881997863122e-06	2.18756008507626e-06	2.41187990468461e-06	0.950509011745453	22.5403003692627	0.678834021091461	5.06859987581265e-06	3.4214899642393e-06	3.48208004652406e-06	0.973330020904541	22.1378002166748	0.732910990715027	1.08306003312464e-05	5.31427986061317e-06	1.09177999547683e-05	0.895157992839813	21.3134002685547	0.532739996910095	16416	-0.288262009620667	0.666837990283966	20	5	5	4	5	5	5	2.28841008720337e-06	4.94957021146547e-07	0.621154010295868	23.00119972229	0.234832003712654	1.48455001180992e-06	1.75465004303987e-06	1.99085998535156	23.4710998535156	1.28328001499176	1.43893998938438e-06	9.47149999319663e-07	1.29446995258331	23.5049991607666	0.714663028717041	1.53025996496581e-06	3.01931004287326e-06	3.98289012082387e-06	0.974824011325836	23.4381999969482	2.14223003387451	2.26742002951141e-07	4.73025011160644e-06	8.51312961458461e-06	1.00258994102478	25.5111999511719	22.6504993438721	1.50988000768848e-06	7.55585006118054e-06	2.22758008021628e-05	0.989441990852356	23.4526996612549	5.43330001831055	16416	-0.291516005992889	-0.154441997408867	21	4	3	2	4	4	4	4.22301991420682e-06	3.56664008904772e-06	2.94200992584229	22.3360004425049	0.916980981826782	3.25818982673809e-05	7.89663044997724e-06	8.36746978759766	20.1175994873047	0.263141989707947	3.79405992134707e-06	4.58911017631181e-06	3.91392993927002	22.452299118042	1.31324994564056	7.41933990866528e-06	4.96676011607633e-06	1.21336997835897e-05	0.974824011325836	21.7241992950439	0.726828992366791	2.46378003794234e-05	7.80076970841037e-06	2.75856000371277e-05	1.00258994102478	20.4211006164551	0.343764007091522	4.33729983342346e-05	1.24948001030134e-05	5.4813801398268e-05	1.0008499622345	19.806999206543	0.312775999307632	16416	-0.154929995536804	-0.0871376022696495	14	2	2	2	2	2	2	5.82117024805484e-07	1.14639999537758e-06	0.178731992840767	24.4874992370605	2.13821005821228	1.93905998457922e-05	7.16155000191065e-07	0.00504788989201188	20.6811008453369	0.0401000007987022	1.10721002783976e-05	8.7896302147783e-07	0.105062000453472	21.2894992828369	0.0861919969320297	1.14140002551721e-05	6.66261985315941e-06	1.57299000420608e-05	0.974824011325836	21.2565002441406	0.633772015571594	1.45024996527354e-05	1.04852997537819e-05	8.36017989058746e-06	1.00258994102478	20.9965000152588	0.784990012645721	-1.192780018755e-05	1.66262998391176e-05	4.1579198295949e-05	0.984950006008148	-999.0	-999.0	16416	-18.0902004241943	37.8647003173828	16	6	5	5	6	6	6	1.9562799934647e-05	7.69366033637198e-06	4.8617000579834	20.6714992523193	0.426997989416122	3.01298005069839e-05	1.92253992281621e-05	7.78587007522583	20.202600479126	0.692794024944305	3.36242010234855e-05	1.31585002236534e-05	7.80966997146606	20.0834007263184	0.424892991781235	7.31550971977413e-05	2.25443000090308e-05	7.86886012065224e-05	0.972981989383698	19.2395000457764	0.334592998027802	0.000154919995111413	3.54039002559148e-05	0.000208625002414919	1.00074005126953	18.4248008728027	0.248123005032539	0.000387306994525716	5.67091010452714e-05	0.000479506998090073	0.99806797504425	17.4298992156982	0.15897199511528	115000	0.333539992570877	-0.605168998241425
GALAXY	0.99721175	5.262087e-05	0.0027355852	0.0950550884008408	0.00796880137784138	200422302783812138	3939368000000719	356370616426218	0.987247876811072	166	3939368	3	25	7	11	6	11	11	11	0.000121566001325846	1.78244999915478e-06	8.42679023742676	18.6879997253418	0.0159189999103546	0.000235662999330089	3.28704004459723e-06	6.38078022003174	17.9692993164063	0.0151439998298883	0.000201386006665416	7.26288021724031e-07	1.5615199804306	18.1399993896484	0.00391600001603365	0.000179074995685369	3.05216008200659e-06	2.07353004952893e-05	0.973617970943451	18.2674999237061	0.0185049995779991	0.000223270006245002	4.49162007498671e-06	1.29454001580598e-05	0.999734997749329	18.0279998779297	0.021841999143362	0.000251040008151904	6.82997006151709e-06	1.96618002519244e-05	0.981078028678894	17.9006996154785	0.0295390002429485	16892216	0.0159204006195068	0.0417909994721413	40	7	11	7	12	12	12	0.000235137005802244	3.32867989527585e-06	8.34934997558594	17.9717998504639	0.01537000015378	0.000511545978952199	4.84365000374964e-06	2.97360992431641	17.1278991699219	0.0102800000458956	0.000409947009757161	2.08799997380993e-06	6.68710994720459	17.368200302124	0.00553000019863248	0.000386250991141424	6.18750982539495e-06	3.45266016665846e-05	0.974824011325836	17.4328994750977	0.0173930004239082	0.000483545998577029	9.44254043133697e-06	1.7562300854479e-05	0.998355984687805	17.1889991760254	0.0212019998580217	0.000553885998670012	1.49208999573602e-05	2.56868006545119e-05	0.998127996921539	17.0415000915527	0.0292479991912842	16892216	0.0211217999458313	0.0374512001872063	42	10	17	12	18	18	18	0.000350957008777186	5.16001000505639e-06	21.4904003143311	17.5368995666504	0.0159629993140697	0.000766294018831104	5.63628009331296e-06	4.80072021484375	16.6891002655029	0.00798599980771542	0.000614051998127252	6.32956016488606e-06	46.8216018676758	16.9295997619629	0.0111919995397329	0.000587219023145735	7.14992984285345e-06	3.34785981976893e-05	0.969789028167725	16.978099822998	0.0132200000807643	0.000717920018360019	1.08357999124564e-05	2.48866999754682e-05	0.998175978660584	16.7598991394043	0.0163870006799698	0.000801234971731901	1.69997001648881e-05	4.36543014075141e-05	0.997907996177673	16.6406993865967	0.0230359993875027	16892216	-0.00922395009547472	0.0406208001077175	28	4	6	4	6	6	6	0.000475412991363555	9.48391971178353e-06	17.317699432373	17.2073993682861	0.0216589998453856	0.000973592977970839	1.26612003441551e-05	6.6236400604248	16.4291000366211	0.0141200004145503	0.000796727021224797	4.80060998597764e-06	4.80774021148682	16.6467990875244	0.00654199998825789	0.000760954979341477	7.36334004614037e-06	2.99966995953582e-05	0.954192996025085	16.6966991424561	0.0105060003697872	0.000928746012505144	1.08648000605172e-05	3.67499997082632e-05	0.986728012561798	16.4803009033203	0.0127010000869632	0.00103086000308394	1.65917008416727e-05	4.93838997499552e-05	0.970034003257751	16.3670997619629	0.0174749996513128	16892216	-0.00811044033616781	0.0493528991937637	31	9	10	7	10	10	10	0.000561578024644405	2.41697998717427e-05	43.9789009094238	17.0265007019043	0.0467289984226227	0.00106373999733478	1.3959799616714e-05	4.37357997894287	16.3330001831055	0.0142480004578829	0.0010175199713558	1.68798997037811e-05	12.4666996002197	16.3812007904053	0.0180120002478361	0.000858751009218395	1.84038999577751e-05	8.82847016328014e-05	0.968414008617401	16.5653991699219	0.02326799929142	0.0010701100109145	2.80862004728988e-05	7.58941969252191e-05	0.993997991085052	16.3264999389648	0.0284960009157658	0.00119692995212972	4.44299985247198e-05	0.00011120500130346	0.997600972652435	16.2049007415771	0.040302000939846	16892216	0.0158769004046917	0.0384196005761623
QSO	0.03287622	0.04926253	0.9178612	-999.0	-999.0	200422337243332337	3940032000001091	356374911398983	0.25860480522607	122	3940032	3	17	8	8	5	8	8	8	1.30348998936825e-05	6.93898982717656e-07	2.62853002548218	21.1123008728027	0.0577979981899261	1.40196998472675e-05	1.63945003350818e-06	6.80090999603271	21.0331993103027	0.126965001225472	1.42026001412887e-05	1.7163999928016e-06	9.42453002929688	21.019100189209	0.131211996078491	1.46319998748368e-05	2.77671006188029e-06	8.50950982567156e-06	0.962665975093842	20.9867992401123	0.206039994955063	2.05792002816452e-05	4.35238007412408e-06	1.35126001623576e-05	0.993234992027283	20.6165008544922	0.229626998305321	2.78709994745441e-05	6.95724020260968e-06	1.44217001434299e-05	0.98598301410675	20.2872009277344	0.271025002002716	115000	-0.0423665009438992	0.0733482986688614	31	18	18	17	18	18	18	1.42095996125136e-05	5.00810017456388e-07	1.89259004592896	21.0186004638672	0.0382659994065762	1.47738001032849e-05	1.24640996546077e-06	2.62898993492126	20.9762992858887	0.0916000008583069	1.48862000060035e-05	1.14316003418935e-06	7.76796007156372	20.9680995941162	0.0833770036697388	1.47625996760326e-05	3.77555011255026e-06	5.98887982050655e-06	0.974824011325836	20.9771995544434	0.2776780128479	1.57538997882511e-05	5.90916988585377e-06	1.07875002868241e-05	1.00258994102478	20.9066009521484	0.407251000404358	1.95171996892896e-05	9.46578984439839e-06	3.40115002472885e-05	1.00093996524811	20.673999786377	0.526579976081848	115000	0.0264203008264303	-0.111978001892567	36	14	14	13	14	14	14	1.70755993167404e-05	4.39030998222734e-07	0.790808975696564	20.8190994262695	0.0279150009155273	1.47932996696909e-05	6.27519000317989e-07	0.970220029354095	20.9748992919922	0.0460559986531734	1.55423003889155e-05	1.07388996184454e-06	4.97104978561401	20.9213008880615	0.0750190019607544	1.57094000314828e-05	4.61450008515385e-06	5.3736998779641e-06	0.974824011325836	20.9097003936768	0.318924993276596	1.77919991983799e-05	7.22223012417089e-06	1.0368100447522e-05	1.00021994113922	20.7744998931885	0.44072899222374	2.18110999412602e-05	1.1513599929458e-05	4.0244198316941e-05	0.983896970748901	20.5534000396729	0.573132991790771	115000	0.0628589987754822	0.11183799803257	21	15	15	13	15	15	15	1.5854700905038e-05	1.09003997295076e-06	1.44456994533539	20.8997001647949	0.0746470019221306	1.37112001539208e-05	1.30018997879233e-06	1.04270994663239	21.0573997497559	0.102957002818584	1.89194997801678e-05	1.89421996310557e-06	4.99010992050171	20.707799911499	0.108704000711441	1.52269003592664e-05	7.98933979240246e-06	1.22333003673702e-05	0.969814002513886	20.9435005187988	0.569669008255005	2.85736005025683e-05	1.25254000522546e-05	3.01456002489431e-05	0.995999991893768	20.2602005004883	0.475937992334366	6.44745014142245e-05	2.00654994841898e-05	7.31866966816597e-05	0.995048999786377	19.3766002655029	0.33789798617363	115000	-0.607792019844055	0.0594804994761944	17	9	9	8	9	9	9	2.76549999398412e-05	4.58896010968601e-06	1.78558003902435	20.2956008911133	0.180161997675896	2.33826995099662e-05	4.44785018771654e-06	0.97408801317215	20.4778003692627	0.206529006361961	2.70261007244699e-05	2.90734010377491e-06	0.612289011478424	20.3206005096436	0.116798996925354	3.22277992381714e-05	1.79978997039143e-05	2.07067005248973e-05	0.974824011325836	20.1294994354248	0.606338977813721	7.04771009623073e-05	2.82410001091193e-05	4.55566005257424e-05	1.00258994102478	19.279899597168	0.435066998004913	0.000114845999632962	4.49924009444658e-05	0.000127330000395887	0.986647009849548	18.7497997283936	0.42535001039505	114720	0.363135010004044	-0.21280300617218
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QSO	0.13154528	0.048649073	0.8198056	-999.0	-999.0	215802945600502567	4014152000004343	361670606105105	0.589556147893477	76	4014152	3	11	7	7	5	7	7	7	6.3835700530035e-06	9.08780975805712e-07	0.771224975585938	21.8873996734619	0.154568001627922	6.07162019150564e-06	3.39877010446799e-06	4.93940019607544	21.9417991638184	0.607773005962372	1.07454998214962e-05	1.89864999811107e-06	3.904629945755	21.32200050354	0.191841006278992	6.6823899942392e-06	3.370100102984e-06	5.41632016393123e-06	0.97071897983551	21.8376998901367	0.547564029693604	7.61141018301714e-06	5.25808991369559e-06	1.3404000128503e-05	0.980018019676209	21.6963996887207	0.750043988227844	1.02794001577422e-05	8.42367990117054e-06	2.38649990933482e-05	0.960997998714447	21.3701000213623	0.889730989933014	16416	0.0200907997786999	-0.4706209897995	16	12	12	11	12	12	12	9.44018029258586e-06	1.00770000699413e-06	1.12676000595093	21.4626007080078	0.115897998213768	8.45168960950105e-06	1.80171002739371e-06	2.41034007072449	21.5827007293701	0.231453999876976	8.16857027530205e-06	3.74922001356026e-06	14.0581998825073	21.6196994781494	0.498331993818283	8.64694993651938e-06	5.17867010785267e-06	7.02287979947869e-06	0.974824011325836	21.5578994750977	0.650249004364014	5.96194013269269e-06	8.10993969935225e-06	1.55498000822263e-05	0.989114999771118	21.9615993499756	1.47690999507904	8.86395991983591e-06	1.2925500413985e-05	3.01395994029008e-05	0.952482998371124	21.5310001373291	1.58323001861572	114720	0.0723079964518547	-0.214270994067192	21	12	12	11	12	12	12	9.8328400781611e-06	8.45784995817667e-07	0.813528001308441	21.418399810791	0.0933910012245178	1.16440996862366e-05	1.76272999397042e-06	1.30164003372192	21.2348003387451	0.164361998438835	1.22946003102697e-05	3.37197002409084e-06	10.3430004119873	21.1758003234863	0.297778010368347	1.19093001558213e-05	6.94272011969588e-06	8.88861995917978e-06	0.96450799703598	21.2103996276855	0.632947981357574	1.06959996628575e-05	1.08023996290285e-05	2.9420800274238e-05	0.969403028488159	21.3269996643066	1.09653997421265	1.17311001304188e-05	1.71875999512849e-05	5.68737013963982e-05	0.948948979377747	21.2266998291016	1.59073996543884	114720	0.0825961008667946	0.19777500629425	11	1	1	1	0	0	0	1.55571997311199e-05	5.78718982069404e-06	-999.0	20.9202003479004	0.403889000415802	0.0	0.0	-999.0	-999.0	-999.0	5.97892994846916e-06	5.78718982069404e-06	-999.0	21.9584999084473	1.05092000961304	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0	17	5	5	5	5	5	5	1.89227994269459e-05	4.28774001193233e-06	0.39309498667717	20.7075996398926	0.246018007397652	5.02793009218294e-05	9.21065020520473e-06	0.478060007095337	19.6466007232666	0.198896005749702	4.25723992520943e-05	9.08127003640402e-06	2.51114988327026	19.8271999359131	0.231601998209953	4.74555017717648e-05	2.5511499188724e-05	1.42212002174347e-05	0.974824011325836	19.709400177002	0.583678007125854	5.15071005793288e-05	3.99558994104154e-05	5.12396982230712e-05	1.00258994102478	19.6203994750977	0.842244982719421	6.04583983658813e-05	6.40326979919337e-05	0.000174567001522519	0.99857097864151	19.4463996887207	1.14991998672485	16416	0.286370992660522	0.694639980792999
STAR	7.238483e-05	0.9999058	2.17957e-05	-999.0	-999.0	215811127390347511	4051687000001124	361662016136093	0.82680821961426	91	4051687	3	13	9	8	7	7	7	7	0.00016390900418628	1.84955001714116e-06	2.48726010322571	18.3635997772217	0.0122509999200702	0.000156263005919755	1.49028994655964e-06	1.43408000469208	18.4153995513916	0.0103550003841519	0.000164633005624637	1.71788997249678e-06	3.23148989677429	18.3588008880615	0.0113289998844266	0.000475439999718219	9.18216028367169e-06	0.00025128701236099	0.974824011325836	17.2073001861572	0.0209689997136593	0.000491953978780657	1.39173998832121e-05	0.000245712988544256	1.00258994102478	17.1702995300293	0.0307160001248121	0.000480307004181668	2.18654004129348e-05	0.00022173099569045	0.99211198091507	17.1963005065918	0.0494269989430904	115000	-0.0171202998608351	0.0308749992400408	21	11	12	11	7	7	7	0.000346271001035348	1.94811991605093e-06	3.14560008049011	17.5515003204346	0.00610799994319677	0.000319000013405457	2.73022010333079e-06	5.3051700592041	17.6406002044678	0.00929199997335672	0.000341487000696361	2.42511009673763e-06	5.69199991226196	17.5666007995605	0.00771000003442168	0.000341264996677637	7.16877002560068e-06	6.92497997079045e-05	0.974824011325836	17.5673007965088	0.0228070002049208	0.000372674985555932	1.09276998045971e-05	7.41655021556653e-05	0.985430002212524	17.471700668335	0.031835999339819	0.000370144000044093	1.64168995979708e-05	0.000109920001705177	0.924646973609924	17.4790992736816	0.0481549985706806	115000	0.005839420016855	0.0145984999835491	27	11	11	10	9	9	9	0.000480304006487131	1.91851995623438e-06	1.35175001621246	17.1963005065918	0.00433700019493699	0.000441409996710718	3.82177995561506e-06	7.24265003204346	17.2880001068115	0.00939999986439943	0.000480232993140817	5.29437011209666e-06	15.8977003097534	17.1963996887207	0.0119700003415346	0.000158238995936699	7.11469010639121e-06	0.000143821001984179	0.697040021419525	18.4018001556396	0.0488159991800785	0.000161417992785573	1.0920600288955e-05	0.000155817993800156	0.726608991622925	18.380199432373	0.0734549984335899	0.000151708998600952	1.76680005097296e-05	0.000166117999469861	0.745446026325226	18.4475002288818	0.12644399702549	115000	0.00475687021389604	0.00669485982507467	12	9	9	7	6	6	6	0.000571387994568795	2.38768006965984e-06	1.76490998268127	17.0076999664307	0.00453699985519052	0.000531048979610205	5.0977600949409e-06	2.69152998924255	17.0872001647949	0.0104219997301698	0.000568975985515863	4.49610979558202e-06	4.05645990371704	17.012300491333	0.00858000013977289	0.000267344003077596	8.0743102444103e-06	0.000260939996223897	0.82709002494812	17.8323993682861	0.0327909998595715	0.00027947299531661	1.19912001537159e-05	0.00028328801272437	0.821016013622284	17.784200668335	0.0465850010514259	0.000286216003587469	1.84942000487354e-05	0.000306222005747259	0.797819018363953	17.75830078125	0.0701560005545616	115000	-0.00171305995900184	-0.0218414999544621	18	5	5	4	5	5	5	0.000640467973425984	3.43222995979886e-06	0.737075984477997	16.8838005065918	0.00581800006330013	0.000547080999240279	9.0059002104681e-06	2.83067011833191	17.0548992156982	0.0178730003535748	0.000618058023974299	1.414360031049e-05	4.69218015670776	16.9225006103516	0.0248460005968809	0.000917459023185074	1.83488991751801e-05	0.000786132994107902	0.769690990447998	16.4936008453369	0.021714000031352	0.000945253006648272	2.81567008642014e-05	0.000821072026155889	0.793201982975006	16.4612007141113	0.0323409996926785	0.000940750003792346	4.43669014202897e-05	0.000819849024992436	0.765676975250244	16.4664001464844	0.05120500177145	115000	-0.00836171954870224	-0.0213687997311354
STAR	0.002416611	0.9943745	0.0032088761	-999.0	-999.0	215811516798300902	4051687000001929	361662016142264	0.554106026472623	91	4051687	3	13	7	8	8	4	4	4	0.00293629011139274	5.24629012943478e-06	2.82296991348267	15.2306003570557	0.00193999998737127	0.00285206991247833	9.53196013142588e-06	11.7985000610352	15.2622003555298	0.00362899992614985	0.00294223008677363	6.49583989797975e-06	4.17322015762329	15.2284002304077	0.0023970000911504	0.0105865001678467	1.5658299162169e-05	0.00593284005299211	0.974824011325836	13.8381996154785	0.00160600000526756	0.0111352996900678	1.97386998479487e-05	0.00614470010623336	1.00258994102478	13.7833003997803	0.00192499998956919	0.0113682998344302	2.74776994046988e-05	0.00622011022642255	1.00093996524811	13.7608003616333	0.00262399995699525	115000	-0.0109740998595953	0.0281805004924536	21	9	9	9	10	10	10	0.00627719005569816	1.64205994224176e-05	20.9612007141113	14.4056997299194	0.00283999997191131	0.00606695003807545	2.05320993700298e-05	52.3573989868164	14.4426002502441	0.0036740000359714	0.0063539301045239	1.71354004123714e-05	25.3841991424561	14.3924999237061	0.0029279999434948	0.00462277978658676	7.95551022747532e-06	0.00340139004401863	0.935920000076294	14.7377996444702	0.00186800002120435	0.00489648012444377	9.72831003309693e-06	0.00353271001949906	0.964704990386963	14.6753997802734	0.0021569998934865	0.00502035999670625	1.31400001919246e-05	0.00360525003634393	0.973052978515625	14.6482000350952	0.0028419999871403	115000	-0.016619399189949	0.0232295002788305	27	8	12	10	11	11	11	0.00902056973427534	2.00188005692326e-05	23.8878002166748	14.0120000839233	0.00240999995730817	0.00859041046351194	2.12155991903273e-05	71.7469024658203	14.0649995803833	0.00268099992536008	0.00906398985534906	1.74628003151156e-05	21.5533008575439	14.006799697876	0.00209200009703636	0.00499291997402906	1.08906997411395e-05	0.00237704999744892	0.974824011325836	14.6541996002197	0.00236800010316074	0.00534967007115483	1.42709995998302e-05	0.002452929969877	0.996459007263184	14.5791997909546	0.00289599993266165	0.00551712978631258	2.02751998585882e-05	0.00246808002702892	0.968106985092163	14.5458002090454	0.00399000011384487	115000	0.00262166000902653	-0.0167130995541811	12	2	2	2	1	1	1	0.0108497999608517	0.000176037996425293	184.255996704102	13.8114995956421	0.0176160000264645	0.0101589998230338	8.50395008455962e-05	53.4873008728027	13.8829002380371	0.00908899959176779	0.0108041996136308	2.00751001102617e-05	2.3910698890686	13.8161001205444	0.00201699999161065	0.00386289996095002	1.50424002640648e-05	-999.0	0.963771998882294	14.9328002929688	0.00422800006344914	0.00419188011437655	2.14941992453532e-05	-999.0	0.988731026649475	14.8439998626709	0.0055669997818768	0.00447783013805747	3.29583017446566e-05	-999.0	0.995552003383636	14.7723999023438	0.00799100007861853	115000	-0.0599368996918201	0.0977917984127998	18	9	11	11	7	7	7	0.0121812997385859	4.49330000265036e-05	18.9601993560791	13.6857995986938	0.00400499999523163	0.011455399915576	2.31220001296606e-05	4.17178010940552	13.7524995803833	0.00219099991954863	0.0120951998978853	2.84405996353598e-05	5.47292995452881	13.6934995651245	0.00255300011485815	0.0349926985800266	5.84699009777978e-05	0.0330867990851402	0.904088020324707	12.5401000976563	0.00181399995926768	0.0375524014234543	7.28414015611634e-05	0.0346142984926701	0.950052976608276	12.4635000228882	0.00210599997080863	0.0386836007237434	9.98139003058895e-05	0.0351576991379261	0.965413987636566	12.4312000274658	0.00280099990777671	115000	0.00154083000961691	0.028575399890542
QSO	0.0017456317	0.059080012	0.9391744	-999.0	-999.0	215811728488342412	4051687000002251	361662016144941	0.417286351711756	91	4051687	3	13	8	8	7	7	7	7	1.39362000481924e-05	6.02067018462549e-07	0.449014991521835	21.0396995544434	0.0469059981405735	1.54856006702175e-05	1.07812002170249e-06	2.00268006324768	20.925199508667	0.0755899995565414	1.38403001983534e-05	1.10649000362173e-06	1.59735000133514	21.0471992492676	0.0868009999394417	3.54955009242985e-05	1.10132996269385e-05	1.38492996484274e-05	0.974824011325836	20.0245990753174	0.33687698841095	4.8060501285363e-05	1.70582006830955e-05	3.01427007798338e-05	1.00258994102478	19.6956005096436	0.3853619992733	2.58416002907325e-05	2.69941992883105e-05	7.87734024925157e-05	0.998633027076721	20.3693008422852	1.13416004180908	115000	0.0244954992085695	0.151982992887497	21	10	10	9	4	4	4	1.94749991351273e-05	1.65723997724854e-06	1.97143995761871	20.676399230957	0.0923919975757599	1.45047997648362e-05	1.65059998380457e-06	2.42406010627747	20.9962997436523	0.12355399876833	1.82973999471869e-05	2.63425999946776e-06	7.17428016662598	20.7441005706787	0.156312003731728	3.12181982735638e-05	7.11102984496392e-06	3.30084985762369e-05	0.974824011325836	20.1639995574951	0.247315004467964	4.91216997033916e-05	1.09675002022414e-05	5.51291013834998e-05	0.975100994110107	19.6718997955322	0.242413997650146	9.95899972622283e-05	1.71872998180334e-05	0.000119465999887325	0.933194994926453	18.9044990539551	0.187377005815506	115000	-0.277254998683929	0.298283994197845	27	17	17	16	9	9	9	2.57368992606644e-05	8.11743007034238e-07	0.941026985645294	20.3736991882324	0.0342440009117126	2.40603003476281e-05	1.86726003903459e-06	1.70977997779846	20.4468002319336	0.0842610001564026	2.80276999546913e-05	2.40380995819578e-06	7.37856006622314	20.281099319458	0.0931190028786659	1.7004000255838e-05	5.87904014537344e-06	1.5891400835244e-05	0.866509974002838	20.8236999511719	0.375387996435165	1.92519000847824e-05	9.75085004029097e-06	3.46591987181455e-05	0.8923220038414	20.6888999938965	0.549911022186279	2.98357008432504e-05	2.09085992537439e-05	6.77209973218851e-05	0.898473024368286	20.2131996154785	0.760873019695282	115000	0.0810011997818947	-0.112810999155045	12	8	8	7	5	5	5	2.84801008092472e-05	2.11840006159036e-06	2.00382995605469	20.2637004852295	0.0807589963078499	2.32719994528452e-05	1.96103997041064e-06	1.34274995326996	20.4829998016357	0.0914909988641739	1.22120000014547e-05	6.51335994916735e-06	12.7267999649048	21.1830997467041	0.579086005687714	1.44565001392039e-05	7.89177011029096e-06	2.66497991106007e-05	0.974824011325836	20.9999008178711	0.592700004577637	2.25552994379541e-05	1.22682004075614e-05	4.95230997330509e-05	0.984849989414215	20.5168991088867	0.590550005435944	3.59797013516072e-05	1.93410996871535e-05	0.00011380499927327	0.956161022186279	20.0098991394043	0.583644986152649	115000	-0.169009998440742	0.15370200574398	18	8	8	8	7	7	7	4.41968004452065e-05	7.42100019124337e-06	3.42902994155884	19.786600112915	0.182303994894028	5.98178994550835e-05	1.18807001854293e-05	6.60586023330688	19.4580001831055	0.215643003582954	0.000111323002784047	2.04906991712051e-05	36.1575012207031	18.7835998535156	0.199845999479294	5.38837011845317e-05	1.87665991688846e-05	4.80554990645032e-05	0.835563004016876	19.5713996887207	0.378138989210129	7.24807978258468e-05	2.97114002023591e-05	9.76668015937321e-05	0.872829020023346	19.2495002746582	0.44506499171257	6.9341498601716e-05	4.8352998419432e-05	0.000142680000863038	0.890964984893799	19.2975997924805	0.757102012634277	16892216	-1.49083995819092	0.261462986469269
GALAXY	0.8302878	0.019351477	0.15036066	0.288313284516335	0.164239302982127	215833405070605911	4014152000005063	361670606105829	0.271554662167611	76	4014152	3	11	1	1	1	1	1	1	3.86058991352911e-06	2.46629997491254e-06	-999.0	22.4333992004395	0.69361400604248	2.6372299544164e-06	3.95944016418071e-06	-999.0	22.8472003936768	1.63007998466492	-2.68909002443252e-06	2.46629997491254e-06	-999.0	-999.0	-999.0	9.26298014292115e-07	2.82773999060737e-06	-999.0	0.974824011325836	23.9832000732422	3.31446003913879	3.92976005514356e-07	4.44087982032215e-06	-999.0	1.00258994102478	24.9141998291016	12.2694997787476	-1.55807003920927e-06	7.19116997061064e-06	-999.0	1.00093996524811	-999.0	-999.0	114720	-0.294117987155914	-1.25821995735168	16	2	2	2	2	2	2	4.61402987639303e-06	3.30875991494395e-06	1.95288002490997	22.2399005889893	0.778590023517609	9.33496994548477e-06	7.77034983912017e-06	3.2925500869751	21.4748001098633	0.903757989406586	1.18035995910759e-05	1.18197999654512e-06	0.248934999108315	21.2199993133545	0.108722999691963	6.88447016727878e-06	5.46557021152694e-06	3.27691009260889e-06	0.974824011325836	21.8054008483887	0.861965000629425	1.25652004498988e-05	8.5742703959113e-06	5.49826017959276e-06	1.00258994102478	21.152099609375	0.740884006023407	2.55922004726017e-05	1.37373999677948e-05	6.24594986220472e-06	1.00093996524811	20.3798007965088	0.582800984382629	16416	0.291177004575729	-0.182475000619888	21	4	3	3	4	4	4	9.33622959564673e-06	3.27619000017876e-06	2.37278008460999	21.4745998382568	0.380997002124786	6.86033990859869e-06	2.20622005144833e-05	7.88825988769531	21.8092002868652	3.49163007736206	1.06032002804568e-05	1.08144995465409e-05	18.917200088501	21.3365001678467	1.10738003253937	1.61633997777244e-05	7.20135994924931e-06	1.53573000716278e-05	0.974824011325836	20.8787002563477	0.483734011650085	2.81426000583451e-05	1.13184996735072e-05	3.6003599234391e-05	1.00213003158569	20.2766990661621	0.436666011810303	5.22709015058354e-05	1.81032992259134e-05	5.4209798690863e-05	0.996630012989044	19.6044006347656	0.376029014587402	16416	0.244028002023697	0.126539006829262	11	2	2	2	2	2	2	3.15475995193992e-06	6.39353004316945e-07	0.0518474988639355	22.6527004241943	0.220038995146751	1.3954099813418e-05	1.99983005586546e-05	3.64861989021301	21.0382995605469	1.55603003501892	8.73076987772947e-06	9.28065037442138e-06	11.773099899292	21.547399520874	1.15411996841431	5.85754014537088e-06	7.06409991835244e-06	1.99338992388221e-05	0.974824011325836	21.9808006286621	1.30938005447388	6.17665000390843e-06	1.10824003058951e-05	1.97358003788395e-05	1.00258994102478	21.9232006072998	1.94807994365692	-1.24956000036036e-06	1.77454003278399e-05	5.09126984979957e-05	1.00093996524811	-999.0	-999.0	16416	7.11289978027344	-42.7580986022949	17	2	2	2	2	2	2	1.5274299585144e-05	2.50867997237947e-05	4.8086199760437	20.9402008056641	1.78323996067047	3.2160500268219e-05	4.12349982070737e-06	0.0405201017856598	20.131799697876	0.139209002256393	3.91456014767755e-05	2.7916799808736e-05	5.98519992828369	19.918399810791	0.774294972419739	4.94275991513859e-05	2.56069997703889e-05	3.35568984155543e-05	0.944983005523682	19.6651000976563	0.5624880194664	4.86452008772176e-05	3.74521005142014e-05	1.26211000406329e-06	0.902332007884979	19.6825008392334	0.835913002490997	-4.17072988057043e-06	5.64184010727331e-05	9.16741992114112e-05	0.84747701883316	-999.0	-999.0	16416	-0.267080992460251	-0.198758006095886
UNSURE	0.28027123	0.22520801	0.49452075	-999.0	-999.0	215840436920662798	4047197000001602	361657721171416	0.359974941574014	65	4047197	3	9	1	1	1	0	0	0	7.27905990061117e-06	4.03177000407595e-06	-999.0	21.7448997497559	0.601373970508575	-1.00794995887554e-05	7.39398001314839e-06	-999.0	-999.0	-999.0	-8.76314970810199e-06	4.03177000407595e-06	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0	16	9	9	9	7	7	7	9.22112030821154e-06	6.94690015734523e-07	0.652456998825073	21.4881000518799	0.0817959979176521	8.40578013594495e-06	1.15601994821191e-06	0.9269899725914	21.5886001586914	0.149316996335983	6.09694006925565e-06	1.30983994495182e-06	1.9789799451828	21.9372997283936	0.233255997300148	6.53719007459586e-06	5.32752983417595e-06	7.70636961533455e-06	0.835563004016876	21.8616008758545	0.884829998016357	1.2299399713811e-05	8.32944988360396e-06	2.23875995288836e-05	0.854611992835999	21.1753997802734	0.735288977622986	8.09972971183015e-06	1.31587003124878e-05	2.96220005111536e-05	0.831354975700378	21.6289005279541	1.76388001441956	114736	0.0121585000306368	0.0743812993168831	12	7	7	6	5	5	5	1.26739996630931e-05	8.6284097733369e-07	0.658354997634888	21.1427993774414	0.0739160031080246	1.02277999758371e-05	4.5613301153935e-06	4.58004999160767	21.3756008148193	0.484209001064301	8.52854009281145e-06	3.63840990758035e-06	8.33868980407715	21.5729007720947	0.463192999362946	1.90519995157956e-06	4.51689993496984e-06	6.70824010740034e-06	0.779859006404877	23.2001991271973	2.57407999038696	9.53884978116548e-07	7.01578983353102e-06	8.93257038114825e-06	0.781929016113281	23.9512996673584	7.98555994033813	4.23270012106514e-06	1.10091996248229e-05	2.26501997531159e-05	0.726213991641998	22.3334999084473	2.82398009300232	115000	-0.618142008781433	-0.89148998260498	11	6	6	6	3	3	3	9.84714006335707e-06	2.10852999771305e-06	1.62476003170013	21.4167995452881	0.232483997941017	6.46099988443893e-06	3.36594007421809e-06	1.9190000295639	21.8743000030518	0.565627992153168	8.01291025709361e-06	1.82755002242629e-06	2.03625011444092	21.6406002044678	0.247630000114441	1.48722001540591e-05	7.68868994782679e-06	2.43393005803227e-05	0.974824011325836	20.9691009521484	0.561307013034821	3.84023005608469e-05	1.19523001558264e-05	3.73770017176867e-05	1.00258994102478	19.9391994476318	0.337924003601074	3.19565988320392e-05	1.89742004295113e-05	5.90704985370394e-05	0.999026000499725	20.1387004852295	0.644653975963593	16416	0.128151997923851	-0.687596023082733	17	5	5	5	4	4	4	2.5744100639713e-05	1.01299001471489e-05	2.29470992088318	20.3733997344971	0.427219986915588	6.99551019351929e-05	2.19171997741796e-05	3.82873010635376	19.2880001068115	0.340164989233017	8.22540969238617e-05	3.01973996101879e-05	20.0414009094238	19.1121997833252	0.398597985506058	9.52573009271873e-06	1.56053993123351e-05	3.42821003869176e-05	0.73167097568512	21.4528007507324	1.77869999408722	-3.23164999826986e-06	2.60043998423498e-05	2.42458008870017e-05	0.7932950258255	-999.0	-999.0	-1.29725003716885e-05	4.51300984423142e-05	4.25590005761478e-05	0.85206001996994	-999.0	-999.0	16416	0.0738359987735748	-0.142980992794037
QSO	0.09862803	0.039303366	0.86206853	-999.0	-999.0	215881712479949329	4051687000002004	361662016142735	0.541622547005883	165	4051687	3	22	6	5	5	10	10	10	8.11224981589476e-06	9.21509979434632e-07	0.877155005931854	21.6271991729736	0.123333998024464	1.11348999780603e-05	2.3293100639421e-06	1.45432996749878	21.2833003997803	0.227125003933907	1.18485995699302e-05	2.12994996218185e-06	3.2334098815918	21.2159004211426	0.195175006985664	9.60530996962916e-06	5.60523994863615e-06	7.67563960835105e-06	0.798205971717834	21.4437999725342	0.633588016033173	1.49718998727622e-05	8.76851026987424e-06	1.34981000883272e-05	0.82591301202774	20.9619007110596	0.635877013206482	2.47737007157411e-05	1.38573996082414e-05	2.87519997073105e-05	0.829865992069244	20.4151000976563	0.607315003871918	16416	-0.0768020004034042	0.261451005935669	35	9	9	8	11	11	11	1.05848002931452e-05	1.176259956992e-06	1.10564005374908	21.338399887085	0.120655998587608	8.56712995300768e-06	1.2363200312393e-06	1.32876002788544	21.568000793457	0.156681999564171	1.02277999758371e-05	2.35526999858848e-06	5.46781015396118	21.3756008148193	0.250023007392883	7.76988963480107e-06	4.23976007368765e-06	5.88960983805009e-06	0.88620400428772	21.673999786377	0.592449009418488	4.15410977439024e-06	6.67229005557601e-06	1.35137997858692e-05	0.916655004024506	22.3539009094238	1.7438999414444	-9.03952968656085e-06	1.08429003375932e-05	2.26635002036346e-05	0.93471497297287	-999.0	-999.0	115000	-0.111308999359608	0.195879995822906	51	16	16	16	27	27	27	1.53561995830387e-05	1.08505003026949e-06	0.914686977863312	20.9344005584717	0.0767169967293739	1.41416003316408e-05	2.12861004911247e-06	1.49040997028351	21.0237998962402	0.163426995277405	1.54857007146347e-05	2.39115001932078e-06	6.42195987701416	20.925199508667	0.167648002505302	1.21817001854652e-05	8.57854956848314e-06	1.35568998302915e-05	0.974824011325836	21.1858005523682	0.764591991901398	9.58450982579961e-06	1.34641004478908e-05	3.13232012558728e-05	1.00258994102478	21.4461002349854	1.52522003650665	1.4647799616796e-05	2.16079006349901e-05	5.98750011704396e-05	1.00093996524811	20.9855995178223	1.60163998603821	115000	-0.0814921036362648	0.0316704995930195	22	5	5	4	8	8	8	1.465589957661e-05	2.9169900699344e-06	1.47581994533539	20.9850006103516	0.216095998883247	1.88320991583169e-05	8.71151041792473e-06	4.05038022994995	20.7127990722656	0.502249002456665	1.43849001688068e-05	3.43710007655318e-06	2.99870991706848	21.0053005218506	0.25942400097847	1.41025002449169e-05	2.18333007069305e-05	1.54823992488673e-05	0.892207026481628	21.0268001556396	1.68092000484467	1.06140996649629e-05	3.60369995178189e-05	2.4984899937408e-05	0.901408016681671	21.3353996276855	3.68630003929138	-4.35647007179796e-06	5.31471014255658e-05	4.49266990472097e-05	0.822543978691101	-999.0	-999.0	16416	-0.5521320104599	-0.0992475971579552	35	8	8	8	14	14	14	2.46020008489722e-05	5.57478006157908e-06	0.877574980258942	20.4225997924805	0.246025994420052	1.50349997056765e-05	1.17564995889552e-05	3.08294010162354	20.9573001861572	0.848980009555817	1.51716003529145e-05	9.98128962237388e-06	3.20192003250122	20.9475002288818	0.714295983314514	4.83426010760013e-05	3.07996997435112e-05	4.74865992146079e-05	0.971350014209747	19.6891994476318	0.691736996173859	5.90372983424459e-05	4.795740096597e-05	6.91995010129176e-05	0.977707982063293	19.4722003936768	0.881968975067139	0.00011195799743291	7.64095966587774e-05	0.000176410001586191	0.945261001586914	18.7773990631104	0.74099999666214	16416	-0.045101098716259	-0.431942999362946
UNSURE	0.6745695	0.14276634	0.18266417	-999.0	-999.0	215900249688286907	4047197000005516	361657721201206	0.147580708514509	65	4047197	3	9	3	3	2	3	3	3	1.51493004523218e-05	4.95319000037853e-06	6.4297399520874	20.9491004943848	0.354988992214203	2.943649997178e-05	7.76458000473212e-06	5.68076992034912	20.2278003692627	0.286388009786606	3.91899993701372e-05	3.86205010727281e-06	3.17767000198364	19.9171009063721	0.10699599981308	2.20435003939201e-06	5.44901013199706e-06	6.12518988418742e-06	0.649882972240448	23.0419006347656	2.68387007713318	1.01012001323397e-05	8.63405966811115e-06	1.50640998981544e-05	0.668394029140472	21.3890991210938	0.928043007850647	1.60878994392988e-06	1.38121004056302e-05	7.22538015907048e-06	0.663941025733948	23.3838005065918	9.32147026062012	114720	-0.147054001688957	0.29660901427269	16	2	2	2	1	1	1	5.58750980417244e-06	1.45291005537729e-06	0.309208005666733	22.0319995880127	0.282321989536285	6.91350987835904e-06	1.18014997951832e-06	0.0584188997745514	21.8008003234863	0.185337007045746	8.38016967463773e-06	2.82413998320408e-06	1.16851997375488	21.5918998718262	0.365895003080368	1.56078003783477e-05	3.87806994694984e-06	-999.0	0.974824011325836	20.9167003631592	0.269773006439209	3.40842016157694e-05	6.07174979450065e-06	-999.0	1.00258994102478	20.0687007904053	0.193413004279137	5.20411012985278e-05	9.72794987319503e-06	-999.0	1.00093996524811	19.6091995239258	0.202954992651939	16416	-0.223605006933212	0.0433560982346535	12	2	2	2	0	0	0	1.58548004947079e-07	9.59414023782301e-07	0.0511070005595684	25.8997001647949	6.57004976272583	-9.09091977518983e-06	1.54137997014914e-05	2.7563099861145	-999.0	-999.0	-2.61436002801929e-06	1.6641199181322e-05	17.1615009307861	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0	11	2	2	2	1	1	1	8.55971029523062e-06	2.27674991037929e-06	0.395857989788055	21.5688991546631	0.288789004087448	3.28774003719445e-05	1.16049995995127e-05	0.924902975559235	20.1077995300293	0.38324099779129	1.20578997666598e-05	1.62866999744438e-05	20.4640998840332	21.1968994140625	1.46651005744934	2.89139006781625e-06	8.40868960949592e-06	-999.0	0.974824011325836	22.7472991943359	3.15752005577087	-1.16012997750659e-05	1.31780998344766e-05	-999.0	1.00258994102478	-999.0	-999.0	-5.71046002733056e-05	2.11340993701015e-05	-999.0	1.00021994113922	-999.0	-999.0	16416	-1.68329000473022	2.18952989578247	17	3	3	3	0	0	0	4.66938990939525e-06	2.45165006163006e-06	0.134582996368408	22.226900100708	0.57006299495697	2.50342000072123e-05	3.21715997415595e-05	4.1339898109436	20.4036998748779	1.39528000354767	-1.12397998464076e-07	3.05950015899725e-05	12.8643999099731	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0
UNSURE	0.11359814	0.28135583	0.60504603	-999.0	-999.0	215931594416049445	4051687000001756	361662016140877	0.647658265798966	91	4051687	3	13	3	2	2	0	0	0	7.60400007493445e-06	3.16770001518307e-06	7.98159980773926	21.6975002288818	0.452298998832703	2.72066008619731e-05	5.11840016770293e-06	3.93690991401672	20.3134002685547	0.204260006546974	2.55932991422014e-05	2.38907000493782e-06	2.95379996299744	20.3798007965088	0.101351000368595	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16892216	-999.0	-999.0	21	4	3	3	3	3	3	2.94491997010482e-06	2.17259002965875e-06	2.5904700756073	22.7273998260498	0.800993978977203	7.79929996497231e-06	4.82167979498627e-06	4.225830078125	21.669900894165	0.671223998069763	-4.16866987507092e-06	4.6334798753378e-06	4.69747018814087	-999.0	-999.0	3.5056700653513e-07	5.18850993103115e-06	1.27967996377265e-05	0.66093498468399	25.0380992889404	16.069299697876	-1.61246998686693e-06	8.39663971419213e-06	1.45216999953846e-05	0.726917028427124	-999.0	-999.0	-2.24283994612051e-05	1.38397999762674e-05	5.11721991642844e-05	0.768527984619141	-999.0	-999.0	16416	-0.0307941995561123	-0.871084988117218	27	7	6	6	3	3	3	6.37801986158593e-06	1.64607001806871e-06	1.14728999137878	21.8883991241455	0.280211001634598	2.26896991080139e-05	6.4675500652811e-06	3.29941010475159	20.5104999542236	0.309480994939804	3.04565000988077e-05	6.0811898947577e-06	7.58496999740601	20.1909008026123	0.216786995530128	1.15780994747183e-06	8.24512972030789e-06	2.54021997534437e-05	0.840721011161804	23.7409992218018	7.73188018798828	1.02932999652694e-05	1.29004001792055e-05	4.66603014501743e-05	0.854744017124176	21.3687000274658	1.36073005199432	1.30265998450341e-05	2.06509994313819e-05	0.000110943001345731	0.850831985473633	21.113000869751	1.72121000289917	16416	-0.855605006217957	1.44457995891571	12	1	1	1	0	0	0	5.2894902182743e-06	5.90881018069922e-06	-999.0	22.0914993286133	1.21285998821259	-0.000105844002973754	2.77685994660715e-05	-999.0	-999.0	-999.0	-1.27970997709781e-05	5.90881018069922e-06	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0	18	3	3	2	0	0	0	1.16121000246494e-05	2.02380997507134e-05	3.0813000202179	21.2378005981445	1.89226996898651	6.92038011038676e-05	7.9132296377793e-05	18.4437999725342	19.2996997833252	1.24150002002716	8.61053995322436e-05	3.43540996254887e-05	9.0955696105957	19.0625	0.433183997869492	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	16416	-999.0	-999.0
STAR	0.013104182	0.97511476	0.011781078	-999.0	-999.0	215972212048211215	3937891000001521	361666311107137	0.882625562029542	165	3937891	3	22	6	6	5	0	0	0	4.27990016760305e-05	1.21689004117798e-06	1.5507800579071	19.8215007781982	0.0308699999004602	3.89335000363644e-05	2.00596991817292e-06	2.73924994468689	19.9242992401123	0.0559399984776974	4.11736982641742e-05	1.92119000530511e-06	3.22670006752014	19.8635005950928	0.0506610013544559	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	-999.0	115000	-999.0	-999.0	35	10	10	8	3	3	3	7.49929968151264e-05	1.31679996684397e-06	1.48949003219604	19.2124996185303	0.01906399987638	6.75120027153753e-05	2.51506003223767e-06	2.61616992950439	19.3265991210938	0.0404479987919331	7.04733029124327e-05	3.04665991279762e-06	6.9282398223877	19.2800006866455	0.0469379983842373	4.32755005022045e-05	7.7781096479157e-06	3.03468004858587e-05	0.881246984004974	19.8094997406006	0.19514499604702	3.37523015332408e-05	1.19982996693579e-05	4.49955987278372e-05	0.882465004920959	20.0792999267578	0.385957986116409	2.64978007180616e-05	1.89988004422048e-05	8.04638984845951e-05	0.863170981407166	20.3419990539551	0.778469979763031	115000	-0.0277392007410526	-0.0658807009458542	51	17	17	16	8	8	8	9.40199970500544e-05	1.29788998037839e-06	1.17748999595642	18.9669990539551	0.01498799957335	8.72375967446715e-05	2.38357006310252e-06	2.80322003364563	19.0482997894287	0.0296650007367134	9.61062032729387e-05	1.99773990061658e-06	2.36469006538391	18.9431991577148	0.0225690007209778	8.44411988509819e-05	6.94766004016856e-06	5.12459992023651e-05	0.949955999851227	19.0837001800537	0.0893319994211197	8.89518996700644e-05	1.06593997770688e-05	5.2115399739705e-05	0.963319003582001	19.0272006988525	0.130107000470161	7.84239018685184e-05	1.67718008015072e-05	5.63971989322454e-05	0.949234008789063	19.1639003753662	0.232197001576424	115000	0.00799410045146942	-0.049440398812294	22	7	7	6	2	2	2	0.000113617003080435	9.48377021359192e-07	0.395862996578217	18.7614994049072	0.00906299985945225	0.000111988003482111	1.12514999273117e-06	0.167748004198074	18.777099609375	0.0109080001711845	0.000121343997307122	1.549949956825e-06	0.506164014339447	18.6900005340576	0.0138680003583431	7.03939003869891e-05	1.20422000691178e-05	1.76415996975265e-05	0.974824011325836	19.2812004089355	0.185736000537872	8.75601035659201e-05	1.88564008567482e-05	2.53696998697706e-05	1.00258994102478	19.0443000793457	0.233816996216774	0.000159995004651137	3.00933006656123e-05	2.54182996286545e-05	0.991778016090393	18.389799118042	0.204215005040169	115000	-0.0024937700945884	0.00997505988925695	35	14	14	12	2	2	2	0.000114841997856274	7.19052013664623e-06	2.5483500957489	18.7497997283936	0.0679799988865852	0.000105869999970309	1.03619995570625e-05	4.58826017379761	18.8381004333496	0.106265999376774	9.80037002591416e-05	1.50958003359847e-05	19.9044990539551	18.9220008850098	0.167238995432854	0.000273990008281544	1.91638991964282e-05	2.15367999771843e-05	0.974824011325836	17.805700302124	0.0759399980306625	0.000295481993816793	2.98454997391673e-05	5.02192015119363e-05	1.00258994102478	17.7236995697021	0.109665997326374	0.000279867992503569	4.77376997878309e-05	0.00015027800691314	1.00093996524811	17.7826995849609	0.185196995735168	115000	-0.201290994882584	0.239612996578217

2. Clean the data

As our interest is to classify the sources, we first “encode” the PS1-STRM classifications from string values to integers:

label_encoder = LabelEncoder()
tab['class_encode'] = label_encoder.fit_transform(tab['class'])

Next, we will select a subset of the table, specifically the “FPSFMag” magnitude values for the five PS1 bands (g, r, i z, and y). Following the strategy of Beck et al. 2020, we will normalize these magnitudes by subtracting the median. Then, we will impute missing values by setting them equal to the median. NOTE this may be a risky move! An alternative strategy is to simply remove the missing values from the training set, or to impose an N-\(\sigma\) limit.

bands = ['g', 'r', 'i', 'z', 'y']
tt = 'FPSFMag'

tags_f = np.ravel([[b+tt] for b in bands])
fluxes = [tab[tag] for tag in tags_f]
for k in range(len(tags_f)):
    fluxes[k] = fluxes[k] - np.median(fluxes[k]) 
    
    fluxes[k] = np.where(fluxes[k] < -100, np.median(fluxes[k]), fluxes[k])
    fluxes[k] = np.where(fluxes[k] > 100, np.median(fluxes[k]), fluxes[k])

In addition to measured fluxes, we will add galaxy colors to the sample. For the unique combinations of filters we will compute colors. As for the fluxes, we normalize by subtracting the medians, and then all missing values are set to the medians as above (but see note!).

combos = list(combinations(bands, 2))
colors = []
tags_c = []
for c in list(combos): 
    color = np.array(tab[c[0]+tt]-tab[c[1]+tt])
    
    color = color - np.median(color)
    color[color < -100] = np.median(color)
    color[color > 100] = np.median(color)

    colors.append(color)
    tags_c.append(c[0]+','+c[1]+','+tt)

We then combine the flux sample with the color sample to produce a 100000 x 15 catalog

sample = np.array(np.vstack([fluxes, colors]))
sample = np.array(sample).T

np.shape(sample)

(100000, 15)

3. Reduce dimensionality with PCA and tSNE

To explore how our selected features recover the classifications from PS1-STRM, we will apply PCA to the full sample.

pca_sample = PCA(n_components=2).fit_transform(sample)
print(pca_sample.shape)

(100000, 2)

The shape of the reduced PCA sample is now 100000 x 2. To visualize the results, we plot the reduced sample and over-plot the populations for each of the four PS1 classes:

classes = ['GALAXY', 'QSO', 'STAR', 'UNSURE']

xmin, xmax = -6, 16
ymin, ymax = -6, 4

# Peform the kernel density estimate
xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([xx.ravel(), yy.ravel()])

fig = plt.figure(figsize=(10, 10))
colors = ['dodgerblue', 'orange', 'limegreen', 'magenta']
for k, c in enumerate(classes):
    spots = tab['class'] == c
    
    plt.subplot(2, 2, k+1)
    plt.scatter(pca_sample[:, 0], pca_sample[:, 1], s=2, marker='.', color='grey', alpha=0.01)# bins='log', cmap='Greys', alpha=0.5) 
    
    values = np.vstack([pca_sample[:, 0][spots], pca_sample[:, 1][spots]])
    kernel = st.gaussian_kde(values)
    f = np.reshape(kernel(positions).T, xx.shape)
    cntr = plt.contour(xx, yy, f, colors=colors[k])
    h1, _ = cntr.legend_elements()
    
    plt.legend([h1[0]], [c])
    plt.xlim(-7, 16)
    plt.ylim(-6, 6)
    plt.xlabel('PCA 1')
    plt.ylabel('PCA 2')
    
plt.show()

By inspection of the above panels, it looks like the different classes occupy unique regions of the simple PCA parameter space, with considerable overlap. As a next test, we will use tSNE to reduce dimensionality of the original dataset. In this example we will randomly subset the sample by 10% so that the tSNE algorithm runs quickly:

%%time
idx = np.random.choice(sample.shape[0], 10000)
tsne_sample = TSNE(n_components=2, init='pca', perplexity=10, learning_rate = 10).fit_transform(sample[idx])

CPU times: user 1min 6s, sys: 263 ms, total: 1min 6s
Wall time: 1min 6s

And similar to the PCA analysis, we will visualize the results:

xmin, xmax = -45, 45
ymin, ymax = -45, 45

# Peform the kernel density estimate
xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([xx.ravel(), yy.ravel()])

fig = plt.figure(figsize=(10, 10))

for k, c in enumerate(classes):
    spots = tab['class'][idx] == c
    plt.subplot(2, 2, k+1)
    plt.scatter(tsne_sample[:, 0], tsne_sample[:, 1], c='black', s=2, alpha=0.01)
    
    values = np.vstack([tsne_sample[:, 0][spots], tsne_sample[:, 1][spots]])
    kernel = st.gaussian_kde(values)
    f = np.reshape(kernel(positions).T, xx.shape)
    cntr = plt.contour(xx, yy, f, colors=colors[k]) 
    h1, _ = cntr.legend_elements()
    
    plt.legend([h1[0]], [c])
    plt.title(c)
    plt.xlabel('tSNE Dimension 1')
    plt.ylabel('tSNE Dimension 2')
plt.show()

Again, it looks like each class occupies a distinct region of tSNE parameter space, although it is a bit noisy with lots of overlap, especially between the “galaxy” and “unsure” classes.

4. Perform unsupervised classification

Next we will perform unsupervised classification with clustering. There are many choices of algorithms (see the sklearn clustering documentation), and here we will apply the k-means algorithm, which requires that we specify the number of clusters a priori (4 in this case):

First, we will split the sample into training and test sets:

labels = tab['class_encode']

# Split off 30% of the data for testing
X_train, X_test, y_train, y_test, idx_train, idx_test = train_test_split(sample, labels, np.arange(len(labels)), test_size=0.3, random_state=42, shuffle=True)

kmeans = KMeans(init="k-means++", n_clusters=4)
kmeans.fit(X_train)

KMeans(n_clusters=4)

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To visualize the results of the unsupervised clustering model, we will use the PCA representation of the test dataset and color the points by their labels assigned by k-means:

fig = plt.figure(figsize=(5, 5))

xmin, xmax = -10, 20
ymin, ymax = -10, 20

# Set up a grid for the kernel density estimate
xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([xx.ravel(), yy.ravel()])

pca_sample_test = pca_sample[idx_test]
kmeans_labels = kmeans.predict(X_test)

for k in range(4):
    pca_cluster = pca_sample_test[kmeans_labels == k]
    
    values = np.vstack([pca_cluster[:, 0], pca_cluster[:, 1]])
    kernel = st.gaussian_kde(values)
    f = np.reshape(kernel(positions).T, xx.shape)
    cntr = plt.contour(xx, yy, f, colors=colors[k], levels = np.linspace(0.01,0.12,6))

plt.title("Unsupervised Clustering\nk-means")
plt.xlabel("PCA 1")
plt.ylabel("PCA 2")
plt.xlim(-7, 16)
plt.ylim(-6, 6)
plt.show()

When given the number of clusters, the k-means algorithm does a reasonable job of identifying distinct clusters. However, comparing these results with the true locations of the “galaxy”, “qso”, “star” and “unsure” classes in the PCA figure in Section 3, we can see that there is not a perfect correspondence between them.

5. Perform supervised clustering

Given the class labels from the CNN analysis by Beck et al. 2020, we will also apply supervised classification (i.e., training the algorithm using a sample of known answers). Here we’ll use stochastic gradient descent (SGD).

Initialize the SGD classifier via sklearn. Here we will use the default parameters, but please see the SGDClassifier() documentation for more information on the available options.

%%time
sgd = SGDClassifier()

sgd.fit(X_train, y_train)

CPU times: user 566 ms, sys: 12 ms, total: 578 ms
Wall time: 561 ms

SGDClassifier()

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To visualize the results of the supervised classification model, we will use the PCA representation of the test dataset and color the points by their labels assigned by SGD:

fig = plt.figure(figsize=(5, 5))

xmin, xmax = -10, 20
ymin, ymax = -10, 20

# Peform the kernel density estimate
xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([xx.ravel(), yy.ravel()])

pca_sample_test = pca_sample[idx_test]
sgd_labels = sgd.predict(X_test)

for k in range(4):
    pca_cluster = pca_sample_test[sgd_labels == k]
    
    values = np.vstack([pca_cluster[:, 0], pca_cluster[:, 1]])
    kernel = st.gaussian_kde(values) 
    f = np.reshape(kernel(positions).T, xx.shape)
    cntr = plt.contour(xx, yy, f, colors=colors[k], levels = np.linspace(0.01,0.12,6))


plt.title("Supervised Classification\nSGD")
plt.xlabel("PCA 1")
plt.ylabel("PCA 2")
plt.xlim(-7, 16)
plt.ylim(-6, 6)
plt.show() 

Unlike the unsupervised k-means classifier, the supervised SGD classifier appears to do a better job of identifying the true classifications (see Section 3), especially in the case of overlapping clusters in the PCA representation.

6. Assess the model performance

To visulize the performance of the supervised and unsupervised model results, we will use a confusion matrix.

def plot_confusion_matrix(predictions, input_data, input_labels):
    
    # Compute the confusion matrix by comparing the test labels (ds.test_labels) with the test predictions
    cm = metrics.confusion_matrix(input_labels, predictions, labels=[0, 1, 2, 3])
    cm = cm.astype('float')

    # Normalize the confusion matrix results. 
    cm_norm = cm / cm.sum(axis=1)[:, np.newaxis]
    
    # Plotting
    fig = plt.figure()
    ax = fig.add_subplot(111)

    ax.matshow(cm_norm)

    plt.title('Confusion matrix', y=1.08)
    
    ax.set_xticks([0, 1, 2, 3])
    ax.set_xticklabels(['Galaxy', 'QSO', 'Star', 'Unsure'])
    
    ax.set_yticks([0, 1, 2, 3])
    ax.set_yticklabels(['Galaxy', 'QSO', 'Star', 'Unsure'])

    plt.xlabel('Predicted')
    plt.ylabel('True')

    fmt = '.2f'
    thresh = cm_norm.max() / 2.
    for i in range(cm_norm.shape[0]):
        for j in range(cm_norm.shape[1]):
            ax.text(j, i, format(cm_norm[i, j], fmt), 
                    ha="center", va="center", 
                    color="white" if cm_norm[i, j] < thresh else "black")
    plt.show()

plot_confusion_matrix(kmeans_labels, X_test, y_test)

From the above plot, it is clear that the unsupervised clustering algorithm does an extremely poor job of identifying the correct classes!

plot_confusion_matrix(sgd_labels, X_test, y_test)

Based on the above confusion matrix, the SGD classifier performs very well at identifying stars (~94% true positive) whereas it does not perform as well at distinguishing between the galaxy, QSO and unsure classes.

FAQs

• How do I interpret these results? The analysis above indicates that meaningful information about unresolved astronomical sources can be extracted from their simple measured fluxes and colors. In particular, the SGD classifier is able to identify stars well, even with the out-of-the-box parameters from sklearn. However, unsupervised k-means clustering is not able to successfully classify sources.

• Can I improve the model by changing it? Yes! In the k-means clustering and SGD classifier cases, there are many model parameters which can be tuned to improve the performance of the model. For example, in SGD, you can select the loss function (here we use the default, “hinge” which gives a linear support vector machine.

• Can I try a different model? I think the results could be improved. Yes! Check out the documentation at sklearn about classification. In particular, the sklearn flowchart is a useful tool for figuring out which (of the many!) options might be useful.

• I want to test my model on my training data! No. You will convince yourself that your results are much better than they actually are. Always keep your training, validation, and testing sets completely separate!

Appendix

How to extract the subset of data analyzed here from the PS1 and PS1-STRM catalogs

Instead of working with the full PS1-STRM catalog, we extracted a subset of 100,000 sources.

First, we downloaded a single PS1-STRM file (all sources with Declinations between 77 and 90) from MAST. We then randomly selected objects so that each of the four classes (“galaxy”, “qso”, “star”, “unsure”) had equal representation in a sample of 100,000 objects. We then saved the object IDs and unique internal object identifiers to a csv catalog file.

Then, we uploaded this file to MAST CasJobs as “MyTable”. We first cross-matched the object IDs we selected with the PS1-STRM catalog via the following query:

select t.objid, s.class, s.prob_Galaxy, s.prob_Star, s.prob_QSO, s.z_phot, s.z_photErr
into MyDB.ps1strm_fmo1
from MyDB.MyTable t
join catalogRecordRowStore s on s.objid=t.objid and s.uniquePspsOBid=t.uniquePspsOBid

We then cross-matched this catalog with the full PS1 ForcedMeanObject table with the following query:

select s.class, s.prob_Galaxy, s.prob_Star, s.prob_QSO, s.z_phot, s.z_photErr, fmo.
into MyDB.ps1strm_fmo
from MyDB.ps1strm_fmo1 s
join ForcedMeanObject fmo on fmo.objid=s.objid

About this Notebook

Author:
Claire Murray, Assistant Astronomer, cmurray1@stsci.edu

Info:
This notebook is based on the PS1-STRM catalog (Beck et al. 2020).

Updated On: 2022-5-25

Citations

If you use this data set, astropy, or sklearn for published research, please cite the authors. Follow these links for more information:

• Citing the data set

• Citing astropy

• Citing sklearn

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