{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introgressions from differentiated material."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/vnd.plotly.v1+html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import scipy\n",
"import numpy as np\n",
"from sklearn.neighbors import KernelDensity\n",
"from sklearn.decomposition import PCA\n",
"from sklearn.model_selection import GridSearchCV\n",
"from sklearn.cluster import estimate_bandwidth\n",
"\n",
"import pandas as pd\n",
"\n",
"from scipy import stats\n",
"from scipy.stats import beta\n",
"\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import itertools as it\n",
"\n",
"import plotly\n",
"import plotly.plotly as py\n",
"import plotly.graph_objs as go\n",
"from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
"\n",
"init_notebook_mode(connected=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In a previous post, we went through the motions of classifying unlabelled haplotypes given representative samples of different populations.\n",
"\n",
"However, we were dealing with a fairly clean scenario: one where all of our unlabelled haplotypes fell neatly within our reference distributions.\n",
"\n",
"But, what if that was not the case? How do we identify novel genetic material that might be carried by our unlabelled accessions?\n",
"\n",
"Here we shall begin to explore the added uses of Kernel Density Estimation i had mention before.\n",
"\n",
"Our first step will be simulate our populations and then reduce the dimension of our data."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Variance explained:\n",
"PC1: 0.196; PC2: 0.104; PC3: 0.021\n"
]
}
],
"source": [
"## Let's go ahead and define the density function of our allele frequencies. \n",
"# :: Refer to previous posts if you wish to visualize this density under the beta distriution ::\n",
"a, b = 1.5, .2\n",
"\n",
"\n",
"# number of populations to generate\n",
"N_pops= 4\n",
"\n",
"# length of haplotypes\n",
"L= 200\n",
"\n",
"# Size of each population\n",
"Sizes= [250,100,300]\n",
"labels= [0,1,2]\n",
"\n",
"# number of unlabelled individuals to draw from each population:\n",
"n_unlab= {\n",
" 0: 5,\n",
" 1: 3,\n",
" 2: 7,\n",
" 3: 20\n",
"}\n",
"\n",
"# population labels\n",
"label_vector= np.repeat(np.array([x for x in labels]),Sizes)\n",
"\n",
"## save the probability vectors that will characterize each population:\n",
"prob_vectors= np.array([beta.rvs(a, b, size=L) for x in range(N_pops)])\n",
"\n",
"data= []\n",
"\n",
"for k in range(len(labels)):\n",
" \n",
" probs= prob_vectors[k,:]\n",
" probs[(probs > 1)]= 1 ## probabilities exceeding 1 are trimmed.\n",
" \n",
" m= Sizes[k]\n",
" \n",
" Haps= [[np.random.choice([1,0],p= [1-probs[x],probs[x]]) for x in range(L)] for acc in range(m)]\n",
" \n",
" data.extend(Haps)\n",
"\n",
"data= np.array(data)\n",
"\n",
"## create incognita haplotypes from both our known distributions as well as a fourth, uncharactrerized population.\n",
"admixed= {k:[[np.random.choice([1,0],p= [1-prob_vectors[k,:][x],prob_vectors[k,:][x]]) for x in range(L)] for acc in range(n_unlab[k])] for k in n_unlab.keys()}\n",
"\n",
"# Principal component analysis of the data generated.\n",
"## Number of components to retain:\n",
"n_comp = 3\n",
"\n",
"## Perform the PCA on the whole data set so as not to lose variation absent from our references populations.\n",
"pca = PCA(n_components=n_comp, whiten=False,svd_solver='randomized').fit(np.vstack((data,[y for y in it.chain(*admixed.values())])))\n",
"features = pca.transform(data)\n",
"\n",
"print(\"Variance explained:\")\n",
"print(\"; \".join(['PC{0}: {1}'.format(x+1,round(pca.explained_variance_ratio_[x],3)) for x in range(n_comp)]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at what we've got."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": true
},
"data": [
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "0",
"type": "scatter3d",
"uid": "66eeeb87-0cf2-4f61-9deb-6b409037adf2",
"x": [
2.163399113598996,
2.418888415742663,
2.41199439969349,
1.9708056147135604,
2.150362485807398,
2.238573977448451,
2.731858898396636,
2.320966118616161,
2.937476810093796,
2.37981045499455,
2.042398224782199,
2.2419321663815333,
2.0039146007247006,
3.009970559506833,
2.5427194198064886,
2.5205671977137167,
2.6400731300310576,
2.194684464013272,
2.186571439143738,
2.1829645371147093,
2.321664461240482,
2.1844330630711393,
1.9406951559372596,
1.9084437426285223,
2.290969311616759,
2.3460002623371055,
2.337051005222629,
2.283751213861328,
2.151914969974808,
2.261940461639127,
2.4601303690327647,
2.122498099875934,
2.60088193998212,
2.530227149091451,
2.0956249918934424,
2.181326808220659,
1.5018425827999273,
1.288835777729759,
1.7463537880761542,
1.9640433404045412,
2.626082885901581,
2.368649985440406,
2.194059017091971,
2.7645397030544636,
2.1515233339746804,
1.980441813565407,
1.4239721558933056,
2.3020434703126225,
2.4132819963905017,
2.1276078314987656,
2.2575401757690576,
1.873407547345207,
2.6029695369378656,
2.818886646738372,
2.179324444232249,
0.985018232083015,
1.97737296027474,
2.0292652046276056,
2.7357280899285468,
2.68921809167032,
2.6074596099671683,
1.3757088255684067,
2.1583578902074576,
2.1429633445462026,
1.9192511990806893,
2.2001252261994204,
1.874255574155896,
1.7742437624789713,
1.9472753538906575,
1.5605224425733604,
1.902737500294424,
1.4729563273006576,
1.6577210465255625,
2.2323425322759403,
1.9100043163057219,
2.2643992511546127,
2.4800646062792993,
2.4411654964310263,
2.552837707245762,
1.990250375239464,
2.24972496620781,
2.3276632990241564,
2.4523734444141563,
3.0199579661525395,
2.2560429115985667,
2.387809324016202,
2.029204189889609,
2.4266844834686854,
2.6386659641742725,
2.3516341509811762,
2.0677504328775007,
2.5610545609091764,
2.058472633315847,
2.171143397099592,
2.087332965323664,
2.1752005486355355,
1.925579362984474,
2.222131872349913,
2.1319613112464086,
2.7171565330346445,
2.187360112158833,
1.9748676269218124,
2.317738163355671,
2.650598453496329,
2.5164335263310202,
2.036901116621539,
2.4225296949482447,
1.1158041477323921,
2.535111260549482,
2.099340303497017,
2.099642614817344,
2.0737727933966363,
1.8303523491339804,
2.227899438753664,
2.6039012158891217,
2.198738717051572,
2.7765354766085877,
2.473167222268989,
2.118057844556766,
2.4784632010708223,
2.3889809129316903,
1.602474993917998,
2.2157073969011476,
2.3527735226486026,
2.3806859471692348,
1.7516059596340994,
2.627744706363905,
1.937076470534572,
2.59443410570491,
1.936548396276116,
2.5427008587437374,
2.548071353337183,
2.290978051845335,
2.7076689038154895,
2.207298760064523,
1.5888918336635849,
1.9642122129681057,
2.3520181544436833,
2.3692637177853375,
2.4182877747110907,
2.3453567507707636,
2.5417411111306847,
2.485618504771599,
1.8132618192111827,
2.0152841800975954,
1.9146518993732737,
2.080362197414351,
2.2017381191859218,
2.2103703597505464,
2.7677044745852646,
2.663098904136357,
2.2056933191299293,
2.690376517365396,
2.7484332783292134,
2.6224035799000034,
2.082134886171088,
2.3243812945716353,
3.075355756897689,
2.038923746968059,
2.207487766483544,
1.7927727281031538,
1.7078885627831766,
2.350590966112108,
2.4693467086868806,
1.9299434430812932,
2.4323924950076274,
2.6987603559777034,
1.7157698613012482,
2.2322286786498937,
2.2605588468694533,
2.3924601663761207,
2.3637221954016248,
2.0247425466311535,
1.399886287311707,
2.31565636804108,
2.4248699615680183,
3.203980534267806,
2.3580963090587015,
2.2748882770232237,
2.1177434590589055,
2.629133454004985,
2.2102166875290115,
2.2940900581528285,
2.692406726714216,
2.2682029502963723,
2.7952994650180574,
2.1567380437467585,
2.219779364516367,
2.1512963419846565,
1.6264737836711687,
2.2099383870139917,
2.7393470642826627,
1.7254510304389696,
2.527680635810616,
2.6672942332333673,
1.4851656451341047,
2.651554167399733,
2.0660337480165842,
2.2212400821731384,
2.2668009450398463,
2.1795565548085785,
2.5633896629450583,
2.39694533522289,
2.194928905861953,
1.8936784396073638,
2.150399924461532,
1.9847169710693349,
2.256497373489875,
2.2577039021641734,
1.8150976594318804,
2.3610438968754934,
2.1638743796737305,
2.2114627144806223,
2.4397970321467186,
2.6559269729505144,
2.1913634570888707,
2.3714683917876718,
2.217029280246081,
2.0219804187197674,
2.035183961867955,
1.9315270302641863,
2.259536253200219,
2.536634123624291,
2.646444806650005,
2.7641945384392157,
1.6667449120157443,
2.1040126329322857,
2.3372653273435477,
2.057623938382885,
2.3384401668924677,
2.50269167494872,
2.713710805352641,
1.7706181724516719,
2.447397636824283,
1.9022491836942383,
2.187860016845565,
2.461407674181639,
2.165321386351654,
2.2162058625806718,
2.1396734581432018,
1.554641858377673,
1.7870520119896112,
2.2508750081611093,
2.799526380076311,
1.8509820998710442,
2.4080154794047393,
2.197996084559753,
2.65448905881363,
2.173059363458763,
1.693545073205797
],
"y": [
-0.73970519325464,
-0.40902577678718016,
-0.9627392190029578,
-0.4386510727143428,
-0.355512408353207,
-1.1088818283190893,
0.07507579772464344,
-0.9583505925745656,
-0.38884000308144273,
-0.6834435848809494,
-1.064146365508784,
0.3075601459271404,
-1.1542928143472244,
-0.6777645568344557,
-0.42690075528243815,
-0.8823657965414771,
-0.6852883897167562,
-0.6440990428831758,
-0.8054596118923709,
-0.8150779701361334,
-0.9543601645148614,
-1.0112933288124857,
-0.6517248332958583,
-0.8080847913607907,
-0.2821036053066214,
-0.9719522950136258,
-0.765039286515339,
-1.0905105691080559,
-0.5748232201547323,
-0.9380401274905176,
-0.9458634970035902,
-0.7820753539843478,
-1.0109131605622492,
-0.7740374921639998,
-0.6502920632053704,
-0.8425054454193175,
-0.5823441798179466,
-0.5698213024691544,
-0.3191520775608273,
-0.22593335469129586,
-0.9493554512450497,
-0.6324104028883848,
-0.9939692541789327,
-0.2249419780838485,
-0.4549254701050904,
-0.7119105648525568,
-0.536411901611831,
-1.3864162368206583,
-0.6715727181724501,
-0.5936286406839388,
-0.6144895903555719,
-0.9101164078357377,
-1.1247713098289611,
-1.0469393674794873,
-0.039033045054023253,
-0.6890642083772215,
-1.0363765737863926,
-1.0132349499198532,
-0.9153525987549799,
-1.1815174578571472,
-0.4088647289499837,
-0.6895498821346543,
-0.5943515405188263,
-0.9642694191977232,
-0.6282397180491412,
-0.9540817946626873,
-0.40116061725956753,
-0.35836688293241975,
-0.9377506913454607,
-0.8217435633240603,
-0.5116834267854464,
-0.7424722948959862,
-0.6876780231986509,
-0.6918622423125924,
-0.2472385273806341,
-0.6992162482093066,
-0.8417908610980823,
-0.6225518550268795,
-0.9409765953975393,
-0.09138743293138188,
-1.095351603229725,
-0.16217879814144917,
-0.7380662250252743,
-0.8129650903956283,
-0.6046268786683735,
-0.7695053954762016,
-0.8115170002786873,
-0.982556473026089,
-0.5974996074038066,
-0.30626937871313686,
-0.36246468885262983,
-0.6327304789481084,
-1.0511267215428146,
-0.8001699385822963,
-0.5699661414977447,
-0.6058676015919362,
-1.1079706281204866,
-0.7756078467601571,
-1.2585804243566348,
-0.8373152793162569,
-1.0718110202350404,
-0.8502999031186315,
-0.4655632842536222,
-0.45761116877602837,
-0.9285793236934371,
-0.8756488482476711,
-0.8095158054021604,
-0.4313118567316982,
-0.6642091040592959,
-0.5409252091364601,
-0.485307123342785,
-0.10927000882380414,
-0.4768214554597401,
-0.49312583436034285,
-0.6230069761231486,
-0.6910460125631239,
-0.7351692722347832,
-0.4998509628677271,
-0.42216283639579055,
-0.9906500127463261,
-0.748017291638086,
-0.8715137107284691,
-1.0392750461504403,
-0.3018487358732116,
-0.5361099092581065,
-0.46789752813680957,
-0.44158613147091924,
-0.6780703289047441,
-0.9224524390412129,
-0.3051970872174456,
-0.7452154328218256,
-1.2854824023444693,
-0.8341663453702607,
-0.5661064285954772,
-0.7966368858623925,
-0.302245550651573,
-0.8216279665429201,
-0.4483847305077941,
-0.7442320883597638,
-0.2364324778955583,
-0.961378812783952,
-0.622879107578713,
-0.790445713226609,
-1.0387326347698786,
-0.7377408495354735,
-0.4988410905043782,
-0.8903848948153111,
-0.9351623214606398,
-0.4263746878195481,
-0.7573314256777409,
-0.6795172898282674,
-1.1078441711786202,
-0.6611226975295618,
-0.9574685160742862,
-0.841900869593606,
-0.9686624025818943,
-0.6936920138718378,
-1.1276225402255993,
-0.5419895528946951,
-0.4265278863306154,
-0.32889600249315615,
-0.628398544375067,
-1.0387196986617186,
-1.1737929920010515,
-0.8371890217680403,
-1.1715334125048356,
-0.7628707244926406,
-0.6768280771608383,
-0.8926139289894449,
-0.4187818027361634,
-0.469088989523819,
-0.6900636108027892,
-0.9125726806852672,
0.09582689133986783,
-0.4236456834793947,
-0.4481934272143699,
-0.979549860429339,
-0.5501227963986882,
-0.7925645382954597,
-0.476788295389494,
-0.9724046443064566,
-1.0670571731915712,
-0.6220051048308801,
-0.8708122593990012,
-0.6588466089139736,
-0.948860078480018,
-0.8943856571645578,
-1.2192667281572476,
-0.48000380119254904,
-0.603021621322483,
-0.6845052499340756,
-1.3690015174967705,
-0.6674553259238172,
-0.70485830330367,
-1.2688244136860503,
-0.7432262862168969,
-0.923359297987529,
-0.26286699854079254,
0.07854725984816384,
-1.1175060058846833,
-0.7061410287225635,
-0.7270095935956756,
-0.5417205552757131,
-0.3732116109925633,
-0.415321473144536,
-0.8603962150968838,
-0.6215285642435379,
-1.0019718278038938,
-0.6995373551151984,
-0.3357061428230834,
-0.443624046527311,
-0.5397746992408037,
-0.9193436866577803,
-0.4577482464822564,
-0.6970517284471432,
-0.2923414972194926,
-0.8477213853338844,
-0.8657963357004034,
-0.21032533168049475,
-0.5745603338889388,
-0.19406163727292344,
-0.7669158194137955,
-0.39074785986461197,
-0.9316633667322947,
-0.28153196833001826,
-0.7433800084018878,
-0.7496902275507826,
-0.784646632839486,
-0.9893667825670641,
-1.0270043055799232,
-1.115805189502925,
-1.039938770953521,
-0.7833515480824181,
-0.6518293660217866,
-0.7511882808018538,
-0.6032513657518901,
-0.8784106555351358,
-0.7898658082058019,
-0.6532581337834383,
-0.5723108993832154,
-0.17177997397375813,
-0.9061287441572395,
-0.5272641981702428,
-1.115209371519661,
-0.8055890299877342,
-0.5708560844085845,
-0.9167552298490611,
-1.210063562889679,
-0.5151774147851261,
-1.0708039170202264
],
"z": [
-0.4446545249559114,
-0.19282537569494634,
-0.233228802862386,
-0.7251333919535009,
-0.5772259902619234,
-0.23821364175803691,
-0.4485644185930268,
-0.11178898297010025,
-0.3757870902759686,
0.11894892610415525,
-0.16238202146851394,
-0.31142088616817337,
0.011500240563979046,
-0.31873286618294544,
0.07810186718781416,
-0.027633766645748275,
0.2028042435744557,
-0.017915247453307703,
-0.10842039646243389,
0.09642061785922115,
-0.19114270979876274,
-0.04625266330006963,
-0.23491235766525087,
-0.7912973771727742,
-0.23250785606280258,
0.17839570345320854,
0.39981659940680975,
0.24017816237768733,
0.5017705946369354,
0.12077627662976811,
-0.5033077550080315,
0.3471087418507731,
-0.3203312960073215,
-0.26285399503071727,
0.04517469145271351,
0.09680070759805434,
0.48665011971578215,
0.44753938793922804,
0.019824088194308472,
0.07516074475520948,
-0.28739391458288915,
-0.49934983853233794,
-0.17439702622858003,
-0.49036627900481333,
0.4221810289923718,
0.2743075207573234,
-0.2436823894810728,
-0.12527151452062138,
-0.7560394423819775,
-0.3671379014802247,
0.06386556989509908,
-0.012860137881167029,
0.4757902558759155,
-0.15165707476160328,
-0.5711174253534798,
-0.07071355358758888,
0.16667131006897828,
-0.3890035811021058,
-0.3622663717587438,
-0.5635992799252768,
-0.3309764216920285,
-0.41660683686032024,
0.44382847936314473,
0.2421299865179283,
-0.20893608995995389,
-0.09064232947385069,
-0.0712308649827872,
-0.12214378351015297,
0.17794241616000372,
0.12112625995622098,
-0.38277716160112585,
0.022018803716223147,
-0.2552411197544269,
-0.5889371075061124,
-0.020770622725457318,
-0.1410543891029475,
0.1509418091257106,
-0.5610813725343607,
0.27164690894441157,
-0.13328066260250218,
0.030810823734787596,
0.08928198838482712,
-0.49905899898337025,
-0.019336512578148026,
-0.7508478423228283,
-0.45618552557078434,
0.12048597941475322,
0.2808499481070221,
-0.5391506396468043,
-0.21919106439986605,
0.6898556839511804,
-0.15251037728470185,
0.279595179770873,
0.03313372858709409,
0.36444904012470003,
-0.12198707635351062,
-0.03812251126142178,
-0.2047653409515252,
-0.015291626961508787,
0.20096442828160976,
-0.27920571398746835,
-0.07853314471747522,
-0.13118264401593083,
-0.48544513628140884,
0.019800624515581112,
-0.11104620659258306,
-0.7232116832187668,
0.398636815528728,
0.040078560412612325,
-0.10431793417019884,
0.012911983654072735,
-0.7090649401985819,
-0.0495095203688014,
-0.42242357619524684,
0.0813735961518603,
0.33620894576128074,
-0.580548387144126,
-0.30156134464270884,
-0.29385129290869005,
0.01640601462287593,
0.24577021232028134,
-0.09015109786196304,
0.07324726024133951,
-0.2950046598876836,
0.03902995824676916,
0.4490870557250579,
-0.3993095798031265,
-0.1889825520315161,
-0.2098989419059098,
0.556765425572384,
0.08889102852683649,
-0.24456723754972598,
0.359467138587662,
-0.5139442373070421,
-0.26384061321618507,
0.4506926542268842,
-0.09782244713425496,
0.21041295798552978,
-0.2965886816804331,
0.2510680046590336,
-0.05762170360064626,
-0.03053603240027999,
-0.2967721830783272,
0.42425869550118955,
0.0015899853145013745,
0.534459078024727,
0.11613898807323478,
-0.3239228200849414,
-0.13416311281879328,
-0.5094945157983626,
-0.2638999528634505,
-0.1179857255157825,
-0.793242288614371,
0.0037878893579397703,
-0.5654359579243478,
-0.18250893644149913,
-0.3512671800237597,
-0.7304018965565352,
0.20883598363006833,
0.024407490162122243,
-0.1946356372607519,
0.04071187932629559,
-0.0521815648900661,
0.1159240869046557,
0.40316648373432956,
0.6078478372642528,
-0.3696987836923401,
0.2515907931224442,
0.07960163539297502,
-0.04058789101390419,
-0.13144902897255095,
-0.030429103830199086,
0.2343697515596025,
-0.1889123993236756,
-0.4271704283345241,
-0.1804361233044735,
-0.3244961160938709,
0.0015947005275194557,
0.18436706358929295,
0.35378605457617324,
-0.2014309162696722,
-0.2314347369701159,
-0.45357066322129796,
-0.5146313067641941,
-0.39342097929673153,
-0.17179827710404844,
-0.01294411792556014,
0.1342549621794076,
0.2840746423922951,
0.17274990408283752,
-0.24996283471704925,
-0.01854598048821225,
0.16282752889440966,
0.15659573802371918,
-0.769363578120089,
0.23408781987257415,
-0.5644603291996159,
0.055341868340188276,
0.15956086390900942,
-0.1895391639116477,
-0.2612691199774319,
-0.2224362324001306,
-0.30082277022482656,
-0.2949408019425108,
-0.4051373651107412,
-0.08107587894408944,
0.36590998609611664,
0.33016400317497674,
-0.24501790892000846,
-0.0780839970210787,
-0.019229349916193402,
0.19051546152510573,
0.0005858187268839365,
-0.3802834480750688,
-0.4051865826540753,
0.10260345593490255,
0.16892752494109708,
-0.1397667118283608,
-0.3343988120509405,
-0.002719160631547459,
-0.08215871923788749,
0.11220795985104834,
-0.04438465526078152,
-0.24622341005494755,
-0.1734088553878311,
0.567075994856319,
0.15061374140859707,
0.1375413625107889,
-0.12222094701636398,
-0.12821074083132405,
-0.5933466664576826,
-0.6532259502195442,
0.13246411259553686,
-0.7986328968023805,
0.07455073516140723,
0.10513223443503039,
-0.007749315832917138,
-0.1958492045867281,
-0.13956890187503573,
-0.13303115629177586,
-0.28818285376246766,
0.33522592543827645,
0.018934449420697365,
-0.5502684915572986,
-0.02828276231049252,
-0.2562884748241902,
-0.07366032413895085,
-0.8605801271144194,
0.269687065351098,
0.5102921278629459
]
},
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "1",
"type": "scatter3d",
"uid": "f45bd552-fca1-408b-bb66-a057d994d3d9",
"x": [
0.6283225491609941,
0.016508963603080427,
0.6847749486749324,
0.531436630690354,
0.5030154616320242,
-0.4292647179109327,
0.6375878224998321,
0.041929989485824035,
-0.028854913665043787,
0.3878526132372429,
0.46877939070636493,
-0.11295286430896428,
0.3511434079643744,
-4.1424052521128046e-05,
0.2038593654113843,
0.18836021416972304,
0.26853863879846906,
0.6619998930576351,
0.42549602918846857,
0.18349220877090294,
0.4431943680466618,
0.5671753082861226,
0.3018353130441776,
0.40248599080308106,
0.35824291754316684,
0.5166292892919576,
0.044525428697058445,
0.7275200695733959,
-0.02734103008560079,
0.5173127910232518,
0.43912302094658745,
0.3698442292665822,
0.5444945632379303,
0.10507232654251378,
0.3538785353394005,
0.36621076676254977,
0.32389833089509057,
0.478165024586309,
0.09524960001078828,
-0.14498170798892368,
0.16674336600926007,
0.4779478548055982,
0.1589846164440178,
-0.16265180748935987,
0.319361824106097,
0.03986294998768962,
0.3320285342024497,
-0.17802110747921326,
0.7668734685995577,
0.22688598492676756,
-0.047204477953232016,
0.009330944142374595,
0.6731376041726861,
0.5060116405493732,
0.4268872411514652,
0.3237883433117498,
0.6924509926929561,
0.11152793734893424,
-0.002182911159800184,
0.09805361655670183,
-0.3471612210131001,
0.30781434725060564,
-0.27067766677775346,
0.4523734636543931,
0.48587100809983663,
0.44956365200999115,
0.25854151017882454,
0.12363447793296259,
0.6625874436980478,
-0.04491506752496784,
0.1962719585275748,
0.4264764128212213,
-0.0979618762193337,
-0.1918149607948368,
-0.08903937910499618,
0.013070919036722993,
0.15906047337400653,
0.44034975779682434,
0.41582203940997153,
-0.24081413793640974,
0.10658449372360992,
0.7546764286391711,
0.08525325878294301,
0.3502769420317392,
0.2177283221243278,
0.632259676766839,
0.3630259763146747,
0.2982007745749284,
0.24731650740960404,
0.22145346603941204,
0.2685035724118612,
0.38911965618898986,
0.5235923076786316,
0.3764176447705663,
-0.20521940645254824,
0.23116722612566856,
-0.14367158907194655,
0.30290764135022996,
-0.2360606894397154,
0.01980705835344864
],
"y": [
2.7172913017655635,
3.351285539050423,
3.5160597675070857,
3.071990704908696,
2.935600033434921,
2.999952365669498,
3.14744597483714,
2.6025092253406124,
3.2643800270389676,
3.6739160915094344,
3.419845702062968,
2.8805151655104284,
3.4763341392042055,
3.4997860222531854,
3.2077592551567067,
3.568545933881613,
3.2109394305525223,
2.915196561975085,
3.070132879348561,
2.947639104456681,
3.4300529602088363,
2.9784672575976496,
3.19468259049027,
4.076586004643985,
3.3701887263044363,
2.865399902169982,
2.9562132773769703,
3.4424594762817513,
3.7276040562242096,
3.1742228683469427,
2.741052639270511,
3.234577066216317,
2.85953661648099,
3.611326951593647,
3.648536204276967,
2.4951903721212885,
3.316383184358666,
2.7928584150197966,
3.475209835995468,
3.1944859036122897,
2.5976734924941454,
3.8146495400848965,
3.1527143030526723,
2.6679131142071153,
3.408533900197411,
2.674899856592259,
3.4809873523720567,
3.350160017806055,
3.3857915436475694,
3.0285463485913446,
3.148205959274292,
2.362765708358585,
3.669173795410503,
3.2792419942188333,
3.189394356020554,
3.069121318907187,
2.7452891571416123,
3.377135040046638,
3.349738686033515,
3.637662565864969,
3.5599431335982237,
3.204910344532639,
3.2234856206074047,
3.438679113716594,
2.757186468618297,
2.69159353298092,
3.2521345764246554,
3.7176968870071065,
3.3708595218976325,
3.547692529112246,
3.2515351135215327,
3.318854319768736,
3.0450770109804335,
3.410850292554316,
2.428565414283542,
2.719616078053418,
2.8785852856696543,
3.4910870555818434,
3.0412474632362203,
3.1395095195209706,
2.8566787906785276,
3.428760273222531,
3.0174840755781838,
3.664625205202584,
3.454700878364493,
3.2140905634601062,
3.053017555165027,
3.3049656842615147,
3.7305445436043825,
3.475795348404468,
3.6015458896125447,
3.130401878290953,
3.7899198180550577,
3.5434398872832404,
2.9814118664999167,
3.0677150155154003,
3.2760144977169765,
3.7505256682317736,
3.204326460111309,
3.0547704825223754
],
"z": [
0.12055465998642023,
-0.44957199454408087,
0.06079515551512806,
-0.020472871944736622,
0.06771493620938515,
-0.015271041647316986,
0.21271198526696586,
-0.31505027289487764,
-0.2961821218526685,
-0.4852183221110371,
-0.03177108148194154,
-0.17732952856301926,
0.009404930396707723,
0.09978291537655543,
-0.3836483124842474,
-0.11518129665596635,
-0.5850169421146237,
-0.16433897965638894,
-0.4118925331033499,
0.021114966874835932,
-0.06053460957348052,
-0.5907284059770078,
0.040351068206657355,
0.009618914504114045,
0.13031712180159427,
-0.24826171574806583,
-0.3373889276526838,
-0.13038856345842842,
0.06232174650891265,
-0.26652831741496114,
-0.19486052801515058,
-0.16860402531892632,
0.5476283233934784,
-0.45432207894013327,
-0.01599691288610799,
-0.26859195315536366,
-0.3794395455163097,
0.018572924634214,
-0.3826703251723394,
-0.41983751640113304,
-0.15918196799212692,
0.04761406715520867,
-0.4663692400784653,
0.79058548077908,
-0.660726069588328,
-0.05482390534041911,
-0.5855659365074094,
-0.5404590558218385,
-0.6552561918188183,
-0.2851250040392448,
-0.21274210015694134,
0.33527731163983726,
0.1449082547211097,
-0.18408212586245565,
0.4693027839104472,
-0.06771610758604728,
0.26882096032615593,
-0.3626206742903196,
-0.2571880149821491,
-0.16794143319982424,
-0.5983202391829906,
-0.6318898190504367,
0.35266367910434027,
-0.42233892676101287,
-0.4711293530177243,
0.11396134081841333,
-0.14358487340501164,
-0.23223726374643194,
-0.6437753082182627,
-0.42076325487347105,
-0.34818287425386785,
-0.3623045321147437,
0.12700348282801652,
-0.16352396931755142,
0.42289224680208237,
0.20015095346281664,
0.28846735244150207,
-0.2572791169901075,
0.1758910277455469,
-0.1817705501926919,
-0.1490703982813973,
-0.7253312875513642,
-0.6168330536054094,
-0.18778751681690475,
-0.42200066971379896,
-0.47703670475131726,
0.437806085530651,
-0.38505216187207897,
-0.42227915547739764,
0.06298888822076831,
-0.48963388679455155,
-0.4911902716930947,
-0.42524674993020023,
-0.20675139512436858,
-0.5103126988432716,
-0.3409064216321795,
-0.31805345311612115,
-0.29252002679075584,
0.3649830286807273,
0.04033911766029997
]
},
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "2",
"type": "scatter3d",
"uid": "2cc8d8a5-9339-4caa-823c-f204155d4224",
"x": [
-1.86593170524197,
-1.073108325321266,
-1.9385144836363697,
-2.452595873867519,
-2.2680010546570015,
-2.040917049859526,
-2.101609539890276,
-2.1249831472737273,
-1.730568057114529,
-2.1836382699035655,
-2.7447586010090843,
-1.9576105884507766,
-1.470304503417267,
-2.115962208670102,
-2.363839724392632,
-1.8809965847092585,
-2.015673064481509,
-2.2699018698638476,
-1.868556723367704,
-1.9343808349146396,
-1.9767330082168095,
-2.4834403263927287,
-2.074910160312289,
-1.866299710291053,
-1.484630870418841,
-2.0358051240258646,
-1.7450677422137366,
-2.717292226238242,
-1.991685758280978,
-1.3252198328198554,
-1.3961948670201398,
-1.9269802399791938,
-1.8920692942125195,
-1.2897177550582137,
-1.1580396162124829,
-2.5091126735913876,
-1.4711028869849812,
-1.8260442388447897,
-2.251863156323041,
-2.376439526778569,
-1.475957675826318,
-1.913785487211108,
-2.1628614654389864,
-2.1979238364164506,
-1.7367571324558477,
-2.158616870615533,
-2.3454779974223796,
-1.5881197119178831,
-1.7997015983533855,
-1.778548224627166,
-1.2660058005518273,
-2.4880113859697413,
-1.9016650077165764,
-1.6156918572002987,
-1.7723606168094197,
-2.1676721884160464,
-1.9496758810303116,
-1.5845128263897446,
-2.1865787460816697,
-2.054493184302069,
-1.9790961226649,
-2.034329122989533,
-1.7080620050508537,
-2.2767285818493734,
-2.1857348470561924,
-1.9176560369306181,
-1.9873724149432235,
-2.1176801638310963,
-1.9901737207271553,
-1.8465226628084772,
-1.8248650556646526,
-1.6385472222231927,
-1.548536360814577,
-2.379013730234932,
-1.4174664004015298,
-1.476156988620389,
-1.863585298997643,
-1.6775013117997577,
-1.4232730139794783,
-2.545626559227679,
-1.7199445997935618,
-1.6353578585581543,
-1.5532127791880632,
-1.8832677314337145,
-1.6279795699597313,
-1.9051338932782342,
-2.3135798069156013,
-1.6749865678663076,
-1.2080593342051764,
-2.355395433176288,
-1.6378436638430436,
-1.794268178893384,
-2.151152064974654,
-2.0021416582518077,
-1.52917720281952,
-1.7693395745021427,
-1.3450123232558147,
-2.129013346570139,
-1.6906729247647287,
-2.096270120258071,
-1.792528748333481,
-2.0182876818259885,
-2.337212914324572,
-1.7181974117969288,
-1.8418107310318372,
-2.138406663626885,
-1.554442647492551,
-1.973345507971675,
-2.4168815375731967,
-1.9460582216852047,
-1.8199469706018898,
-1.9633133988590699,
-1.7620876196130608,
-2.3636140661081133,
-1.8701765397781875,
-2.3317313884723347,
-1.7607374132980507,
-2.2681469542493535,
-1.6153172837509475,
-1.6855756694954902,
-1.9345346633149192,
-1.7226470862311305,
-2.2749068231369356,
-2.36777352929242,
-1.3370408037293047,
-2.294071904485629,
-1.5476885111167804,
-1.799139915386814,
-1.7767786573782283,
-2.5632899858112093,
-2.288621485048434,
-1.64858922692212,
-2.4180301408190266,
-2.410837365792887,
-1.8875525310188406,
-2.3791789690469924,
-2.565655024674165,
-1.6613413290263392,
-1.9489603184406536,
-2.546185978168669,
-2.370668682247205,
-1.817924665714697,
-2.3349423230394843,
-1.504031292969217,
-2.144589827804328,
-1.6312377989351559,
-2.179017716161712,
-2.1900647791293832,
-1.9589001329122468,
-2.1354278856079363,
-2.349602148546346,
-1.7561746497392732,
-2.1786027621799406,
-2.346437637965046,
-1.776660643957327,
-2.1748823397445203,
-1.8029795536394317,
-2.0555514277502875,
-1.7988908124121687,
-2.0338359495437652,
-2.2073084892300017,
-1.7649011294932742,
-2.0548420338067537,
-1.588521001242745,
-1.923088081725516,
-1.9575459950680971,
-2.1823526587941258,
-2.4145755022492263,
-2.150043720567658,
-1.9618075215001267,
-1.8757494513599136,
-1.610020441255829,
-1.9655477982794687,
-1.1899521341201165,
-2.292790206697526,
-2.210038801819379,
-2.2964852592777385,
-1.293786715383783,
-2.112719333544625,
-2.12601987827899,
-2.1558002523036603,
-2.25600290111905,
-2.2064304281853317,
-2.178823173926046,
-2.519160776340195,
-2.2883877822525767,
-1.7589953545593344,
-2.523147638550488,
-2.648559128341313,
-1.7584754703761358,
-2.4388030407229695,
-2.016127814681175,
-2.163408859375407,
-1.760565370445938,
-2.1694048092025873,
-1.8374853003320706,
-1.8618138552088308,
-2.4057885435230575,
-2.1172377546293633,
-2.088034348827958,
-2.4622280029917287,
-2.3477304233646077,
-2.007806881798538,
-0.9714624202472839,
-2.198295578017188,
-2.1754314193598616,
-2.199942774974283,
-1.735693100542808,
-1.7188943975421553,
-2.0647719576437025,
-1.7314860324403842,
-1.5938377289043333,
-1.8105195724265268,
-2.420144533808108,
-2.6726435593149502,
-2.4058121453890333,
-2.0004636712897486,
-1.5103351932148672,
-2.0843809212760074,
-1.9042805807782672,
-1.9215380071684391,
-2.2106549907856254,
-2.2849095810727413,
-1.5970178378063828,
-1.9149741430901694,
-2.221188373832396,
-1.7509445837992492,
-2.1628102955653206,
-2.229356812597061,
-1.877636921213696,
-2.054558880158514,
-1.9715969510660747,
-1.915108522680079,
-2.377185844816834,
-2.0400729395742836,
-1.600565076691486,
-1.4277881585528178,
-2.1805213808589095,
-2.2256900950948104,
-1.6843973572719761,
-1.8598835342441782,
-1.9125209558915286,
-1.7118237629463513,
-2.0104305060984102,
-1.9422237721864262,
-1.9928295507303506,
-1.7167347636673527,
-2.1760581500296885,
-1.9643518557177013,
-2.2723846515144923,
-2.4113481789687228,
-1.7810198941372726,
-2.3932319927090924,
-1.821679598395292,
-1.8720631958417853,
-2.0333885663783184,
-1.3515907030105667,
-1.860774115597194,
-1.9769723800533776,
-2.214122540521947,
-2.2168155521635216,
-2.5321722308079893,
-1.6499930181058406,
-1.776729438921847,
-2.2105719520949934,
-1.6455044816723985,
-1.8542633673144193,
-1.959224533059593,
-1.9233736021301249,
-1.832096797621125,
-1.9552976944542109,
-2.00546841890309,
-2.0776791895695115,
-1.6089371051634442,
-1.654457553644183,
-1.8268832055511501,
-2.0122924654326604,
-1.6460737481194243,
-1.4005105025478541,
-1.5734193329988702,
-1.903380526613211,
-1.4185201879530704,
-1.674843347687447,
-1.797079429721397,
-1.7520722368192863,
-1.0320135527587786,
-1.667969969760403,
-2.2166244607983776,
-2.02906202048813,
-1.9556148229330232,
-2.0389796600184145,
-1.9229807786328126,
-2.268779809378239,
-2.0898789885711047,
-2.3408158863750965,
-2.0082274535655853,
-1.7144024577219301,
-1.5242146814616884,
-2.671955221275385,
-1.9766810524142362
],
"y": [
-0.7480476731703602,
-0.4798010188170707,
-0.7910779416401352,
-0.5066698163563332,
-0.42924610185858963,
-0.8124056072524081,
-0.6972391965089733,
-0.47387400040025407,
-0.9521296847676707,
-0.3046834466574721,
-0.47264727086288394,
-0.8214752964993041,
-0.6760595639404182,
-1.0584103280486772,
-0.1293253415296898,
0.03566196635185578,
-0.7774924441717918,
-0.4096205100271988,
-0.7815955267435581,
-0.48556225351270443,
-0.7697031426330616,
-0.3854088679536805,
-0.2821373169425384,
0.03865117476576667,
-0.5766042187646644,
-0.3409774936162615,
-0.5351984646188815,
-0.48437357123791025,
-0.6287631229446455,
-0.2061434079851491,
-0.4589219389300029,
-0.28365694665775765,
-0.2334417856757199,
-0.20951587987955375,
-0.47916689114082767,
-0.6065899180407229,
-0.8446827682700618,
-0.3219647235585702,
-0.5454304282948373,
-0.7871329170656273,
-0.2273097739137607,
-0.6205847780223334,
-0.40645947506148833,
-0.5246714589532354,
-0.2907098500928251,
-0.416432461226166,
-0.8336522042442934,
-0.617970489361941,
-1.1449196027341981,
0.09394432134394473,
-0.5794520840722354,
-0.6229776981301431,
-0.6929932514254704,
-0.4470133579141082,
-0.5978667548080436,
-0.5816326767487352,
-0.7944057138266065,
-0.8174485364577326,
-0.8513541206434562,
-0.4656889256561145,
-0.36000025501331745,
-0.6617928979860839,
-0.5033707368976718,
-0.6627420657020042,
-0.47739491448686416,
-1.0193270571956337,
-0.415715771382933,
-0.7326533202402502,
-0.44734907183782735,
-0.04420383230787451,
-0.6895203495333562,
-0.3916309791739144,
-0.479056094020914,
-1.0842126554139013,
-0.23364948548091644,
-0.0674500123731329,
-0.7403105374173674,
-0.6543268793845224,
-0.763944035532087,
-0.5387013500613385,
-0.47065227118842207,
-0.1680869288471768,
-0.5944765614480729,
-0.7332170942928706,
-0.1977846062802541,
-0.5607510795664178,
-1.313784049295395,
-0.09979119944419626,
-0.3732641208710766,
-0.7966448440172457,
-0.3771810342725384,
-0.740718886694054,
-0.8537890987110318,
-0.6810391691752506,
-0.5308330872923402,
0.07455660029655349,
-0.600669847677781,
-0.5274138262539289,
-0.925891766039609,
-0.08683774923441291,
-0.36972912615146886,
-0.5080187839402855,
-0.5932232770019329,
-0.12835677112100644,
-0.36440769885772056,
-0.14411693775391848,
-0.44236729589084983,
-0.5498813189558697,
-0.8920174117035365,
-0.17241170281682605,
-0.5729337742009446,
-0.9181993860170594,
-0.4722374658090766,
-0.38328291829096744,
-0.7988996019858731,
-0.5836891995621077,
-0.34570575412584786,
-0.5452173468755104,
-0.4148774899730568,
-0.08669293669733207,
-0.05689259403848893,
-0.7640738196551022,
-0.09976593459368657,
-0.9951065001176418,
-0.5178661259756451,
-0.5894192522091698,
-0.5565387880934023,
-0.25159732745467867,
-0.4321185667114061,
-0.9104651655044136,
-0.44557972066048307,
-0.048627858273932324,
-0.2885882927504109,
-0.7756795404373434,
-0.5897918801166879,
-0.5152211785161916,
-0.4386668804840281,
-0.45511193051859,
-0.619569048497606,
-0.5367505545051754,
-1.0170363159888502,
-0.49759829954837603,
-0.39908987500473575,
-0.2410653608986206,
-0.9771017432592443,
-0.36802682025342603,
-0.598452796530036,
-0.6303373338174235,
-1.0396661547189856,
-0.691619908073387,
-0.5253785667375135,
-0.20924982994118688,
-0.48629557708631743,
-0.7473170688768335,
-0.7536546741529773,
-0.24434306758054622,
-0.333067889758947,
-0.5344327402527612,
-0.4291110625888237,
-0.689879761223155,
-0.6704164653625472,
-0.8334166858740527,
-0.3803748061934928,
-0.31393043022399103,
-0.5270275571090697,
-0.10388625574870718,
-0.3160224668189895,
-0.5222532455122572,
-0.6746573701880494,
-0.32635690545053353,
-0.23742516772745045,
-0.23511158641109195,
-0.600869456941046,
-0.08914030925102316,
-0.8903460713222058,
-0.5893595097745178,
-0.5832357033405561,
-0.3875377182705656,
-0.6140995256413345,
-0.943693470557182,
-0.7661326540458792,
-0.9668859061059406,
-0.6629048988388994,
-0.6648063246332483,
-0.7220283558965778,
-0.5581096761273286,
-0.19423395901780618,
-0.8316106747784028,
-0.18215376549362103,
-0.720370402641743,
-0.934055529064026,
-0.5687481304985992,
-0.42910417167127307,
-0.32559334688582414,
-0.8472301930803469,
-0.9955694762851091,
-0.4549576279712369,
-0.5084595619277573,
-0.257976881449834,
-0.7217081509498344,
-0.32598607095069676,
-0.6629283396631969,
-0.6709462850947799,
-0.22800528625077462,
-0.45958717513058284,
-0.28873167858236554,
-0.7249842502545151,
-0.49950157864716976,
-0.3970515198881514,
-0.7841481768228481,
-0.5158422067381019,
-0.4401162381722685,
-0.3297055639259461,
-0.4157562183991906,
-0.6285856333946566,
-0.8414931895368314,
-1.3764051629048513,
-0.5874557139198154,
-0.7058847547509043,
-0.41462264910223434,
-0.4246262477019801,
-0.4344894727520066,
-0.13488673726624528,
-0.1777813555583739,
0.15796030713395445,
-0.6000357345458095,
-0.8239544426720611,
-0.4169133959477868,
-0.22822135990753054,
-0.79520637832586,
-0.35817853200115574,
-0.12111675824787184,
-0.5678935068697744,
-0.2327921360594247,
-0.5356971614775387,
-0.47928430935840405,
-0.798767749507784,
-0.6396245488647935,
-0.3086129350788875,
-0.3677246932354574,
-0.7456954835551979,
-0.22384853085248987,
-0.48324441254608563,
-0.13589887748643367,
-0.8146562215548272,
-0.3619542648226693,
-0.5446483650757448,
-0.4887515583054699,
-0.5950380507954404,
-0.32379416155147234,
-0.4523735518951523,
-0.6235861610020692,
-0.8524078126999518,
-0.624992695451351,
-0.2687580135967621,
-0.9142029143532834,
-0.6659105307473407,
-0.5107419286693737,
-0.1977513307563077,
-0.9428853906456206,
-0.3253209568307786,
-0.22727349963052632,
-0.5793151779856947,
-0.23718711893540165,
-0.5271495158439357,
-0.6343520795149911,
-0.238815912969396,
-0.6990789188926911,
-0.24633171628795617,
-0.4062347602342654,
-0.13615609372168275,
-0.5216821949290152,
-0.4942204270716243,
-0.2220401390451773,
-0.020747595192913953,
-0.8214853052136477,
-0.6875869322752399,
-0.22152857450956379,
-0.29745642236257747,
-0.35784823104789754,
-0.5523106218284762,
-0.45943183381522734,
-0.468981548871973,
-0.7153616997835629,
-0.772736368649511,
-0.8434804313925567,
-0.5007809738640613,
-0.4066847172852109,
-0.684276716683085,
-0.9002068907942674,
-0.667093776343055,
-0.6130982621503599,
-0.7474263618159979,
-0.430559922478364,
-1.0427198734072751,
-0.483205252606335,
-0.744982998763404,
-0.015679896270428966,
-0.6994937694356036,
-0.45558564877217206
],
"z": [
-0.4157805329604104,
-0.017887586934806115,
0.8097303759161899,
-0.4320626189945605,
-0.08183797663196185,
-0.4722083805579565,
0.0062022309301678,
0.06790189611503132,
-0.15748984049905101,
-0.46789431163602063,
-0.38791808819307744,
-0.2275539825046795,
-0.052083608565449975,
0.07367079776003062,
-0.3901745789411522,
0.3268143517350413,
-0.2471782706345768,
-0.06053400767369111,
-0.26227182389688397,
-0.02117837642250375,
-0.21872512357277224,
-0.34200787972101354,
-0.22195248476442403,
0.0976665851578857,
0.2805073353192304,
0.01608808049475981,
-0.07741379829393705,
-0.4567618702638782,
-0.38382819842847093,
0.20460563535082982,
-0.11142748474737951,
-0.023012282481962906,
0.05656703042647703,
0.09072849162713938,
-0.408094798012628,
-0.2451805136088429,
0.31033239613279756,
-0.014443297202818596,
-0.3122644717846063,
0.0202061104406828,
-0.07104427525510186,
-0.34716608451653636,
-0.08838997796250964,
0.2599242548097161,
-0.6332312874885185,
-0.11994446932489598,
-0.31195250176623135,
0.38056271171491807,
-0.17107970612546938,
0.06504909573959074,
0.1837067002124125,
-0.31677437349110205,
0.4237928408286671,
0.3999442168114798,
-0.08277990721577871,
0.4130425328759305,
0.07761362684441199,
0.15476354159091274,
0.5301282624025921,
-0.04966518449337113,
-0.4472746641628041,
0.21943385306413754,
0.4585748536589704,
0.1844117131083236,
-0.4226826961449522,
-0.23607920098243718,
0.4266846619549208,
0.011887234031796028,
-0.22776883006989856,
0.2174174814884322,
-0.006512742370307224,
-0.12448491698919271,
0.3830195679989099,
-0.3938720974355373,
0.11126484569150269,
-0.14169394796059326,
-0.19807021553283854,
0.5665112051645512,
-0.08123366688839473,
-0.4964947958796984,
0.48012222680738503,
0.4390869615504073,
0.34192982211262174,
-0.5049303658681064,
0.011436050078022338,
-0.05592715097255995,
-0.5062403052038711,
0.5178021556047561,
0.38607304657816205,
-0.9839316193387816,
0.4460748082910173,
-0.1450393361733375,
-0.24671340624518207,
0.1551829197623859,
0.4165896653131426,
-0.3935170175969771,
0.2885709430847422,
-0.14958128438113144,
-0.43108199244953976,
-0.2606337398222067,
-0.24693646877020964,
0.10813915765383264,
0.13518059647637737,
0.19651078299353547,
0.3346796911053841,
-0.060596181559737526,
-0.5256967442468717,
-1.1861792293382316,
0.022210446281885947,
-0.2741377166130673,
-0.4329607367035386,
0.4640030953791651,
0.13026326435644048,
-0.06645446085975179,
-0.3996482491090819,
-0.2053049217090835,
-0.3459463620881171,
-0.3707133428718404,
0.421254230541472,
-0.25377508809291205,
0.04145555538328596,
0.008442803037008444,
-0.07954886513277742,
-0.6060228231921211,
0.40297190598893246,
-0.3345500153664418,
0.009314508920045116,
0.6762539966936302,
-0.5704179050362163,
-0.1263521998237061,
-0.5992108742481282,
-0.03055922421027146,
-0.006894548897019799,
0.028698166423031364,
-0.5868778162568317,
-0.3428405219264621,
-0.31804897105959457,
0.14047576518556426,
0.1621870659747589,
0.2666764979205449,
-0.2587345788840568,
-0.2996780212679969,
-0.057924612760875606,
0.29767223202878396,
-0.17534340712373664,
0.07070794042618732,
-0.44500398841395494,
-0.267968862636731,
-0.05255758081942998,
0.0565583671316676,
0.24126183681891547,
-0.0020810359384243267,
0.19623209142123266,
-0.8406633146074663,
-0.048996975156284116,
-0.07026224467836181,
0.1729559726741388,
-0.03472083447830932,
-0.07183391629938951,
0.030907159241310593,
-0.5146639782542198,
-0.2681773875251901,
-0.06651238269619006,
-0.1250370337516696,
-0.3361773924210964,
-0.025953243315192578,
-0.4296194382232437,
-0.5320245382085108,
-0.17041333533849645,
0.16091963598480377,
0.26581668122441876,
0.6243291094792643,
-0.039852850454125975,
0.1233749962893025,
-0.03720514296383549,
0.5129439437964421,
0.41688827522755195,
0.5987348634041113,
-0.2331818212548434,
-0.41906273638857544,
-0.3120140747503437,
-0.6152668968077735,
-0.16544483703260057,
-0.45977804613364187,
-0.10865200752603187,
0.29723065313205854,
-0.04422266407056089,
0.33761831070587955,
-0.09293972238725229,
0.34597696371912035,
-0.2794549704364716,
-0.11008558583045318,
0.3213873446582724,
0.6092451732713532,
-0.6816520613741289,
-0.4248047736780112,
-0.15061582346117763,
-0.0752043258239884,
-0.1882342000340685,
-0.5141744955788906,
-0.024630704470984584,
-0.2399428604451668,
0.12139437614213062,
0.3157993823910308,
-0.40021931119626775,
0.2505445672507751,
-0.4693214719766291,
-0.22383924741474912,
-0.22575315152544911,
-0.04861466429845294,
-0.2212081383829006,
-0.06861285189068105,
0.23569479312378133,
0.16811565221558888,
0.11401615820590842,
-0.7194575221612561,
0.36974896039673455,
-0.16868436560397904,
-0.15857431565435615,
-0.02628338462134717,
0.35126965063130694,
-0.17201050003768503,
-0.4118212302435588,
0.27982780230009946,
-0.04504790929274315,
-0.4074354340052161,
-0.12401995525303965,
0.6054957158891072,
0.0257881966172531,
-0.2199015049662167,
0.03787623151920525,
0.15535521303755573,
0.0628370328994742,
0.2509817419666257,
-0.2614458433245504,
0.19377589786497978,
0.44204477431855044,
0.22914314436270805,
-0.04173402297969279,
0.19554587396813483,
-0.0384808267975992,
-0.07005406333732585,
-0.5590390972855782,
0.03536153402827057,
-0.6691461270773521,
-0.09268908039319129,
-0.2442005558738212,
0.10898091290419629,
-0.00949291465747363,
-0.0657066354293465,
-0.21149239650364277,
-0.02318676218973342,
-0.2697122993347724,
0.2511952643304413,
-0.6856215247207155,
-0.006228224925896524,
-0.01254320889811459,
-0.18276657890939024,
-0.017519073285072472,
-0.35431721526433163,
-0.3001557409846582,
0.02927997602508509,
-0.42869605292695834,
-0.36688663103946617,
-0.04646354780349623,
0.35684284727564747,
-0.07549642843534005,
-0.07823661688303908,
-0.07819569657891356,
-0.35072978109652614,
-0.475954307213145,
-0.08352876261925338,
-0.13856299730485433,
-0.2227263213998339,
0.2849630839294529,
-0.22221095014307884,
-0.2669199298588034,
0.0024577648955696435,
0.12253874694708264,
0.3238425701922114,
0.007724159393919176,
0.38565434567494733,
0.2664415637982581,
0.10043080880014683,
0.18703257114041527,
0.26336187155565294,
0.09099831725989505,
0.087858625277845,
-0.26002760016044274,
-0.22239759297372758,
-0.3198790713896881,
-0.2964188689644238,
-0.5856969992262336,
-0.3360548679089505,
-0.31005555028898957,
-0.5034316231912971,
-0.17252409715170802,
-0.1457743794133612,
-0.2606478327205058,
-0.1464006814319549
]
},
{
"marker": {
"color": "rgb(0,0,0)",
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "unlabelled",
"type": "scatter3d",
"uid": "9d2085dd-1f50-4785-9511-394abda143ca",
"x": [
2.2064242836412786,
2.113816341910332,
2.6220230023716335,
1.7352908996213308,
2.3525615357611303,
0.4462448384251028,
0.3607140312008184,
0.3027383037000555,
-1.9620480812726646,
-1.4434020643433463,
-2.1464248695817867,
-1.7245644181082425,
-2.0399214759117763,
-1.6708035771480572,
-2.0508608425166037,
0.3945269850866559,
0.3899816386849093,
0.5376430237789295,
0.3126053481835842,
0.6394085286953741,
0.3412604131901168,
0.224916487052315,
-0.31249569857206866,
0.07587755713390476,
-0.14839436819970808,
0.45055255429414875,
0.18621875216202735,
0.2358570976653463,
0.5184614446882938,
0.6138472775558009,
0.07386990439951267,
0.05317624716668619,
0.08700299505842657,
0.16209580758599393,
0.21438619717846197
],
"y": [
-0.8198905009204427,
-0.8193871257558728,
-0.403269599598251,
-0.603455800741723,
-1.0016226683210763,
4.006223240857248,
3.018156939087044,
3.3441954742381026,
-0.8758759025297919,
-0.4858568015338327,
-0.5032178449626296,
-0.486445691276817,
-0.6044253152586662,
-0.026723185049607617,
-0.7384214307963308,
0.7650186372486267,
0.6825151590573117,
0.31451662807112185,
0.8300589335926524,
0.09610129282432836,
0.40055700433681757,
0.4570827758631466,
0.357803878072331,
0.2480038093644584,
0.914758577119137,
0.8666810346463998,
0.1300087543578536,
0.448299275221888,
0.09551735475562226,
0.2568793173482379,
0.43113887975635473,
0.10869751734142356,
0.3019601281792028,
0.8185073629393802,
0.42082947469885423
],
"z": [
-0.2266024374285758,
-0.0339723625285479,
-0.5722808655989252,
0.079029891371847,
0.39302891287498865,
-0.051366412772509897,
0.20773989605730026,
-0.4480681841297374,
-0.4545954885041011,
-0.5899574477424782,
-0.375197865153605,
0.1682924884456958,
-0.08817125765377914,
-0.08047498842614154,
0.22980061318870149,
3.485128410105509,
3.5703529027184797,
3.1381198608076377,
3.004078936814322,
3.1204921684307547,
3.151542431290013,
3.0082995060713014,
2.214309179793431,
2.97718513500447,
3.3624712682072184,
3.18276524089809,
2.6941237421617785,
3.17966511577167,
3.331803971780043,
3.193420078368326,
3.706015092793436,
3.1648719350008077,
3.315208068295153,
3.024594124166767,
2.7725981179425587
]
}
],
"layout": {
"margin": {
"b": 0,
"l": 0,
"r": 0,
"t": 0
}
}
},
"text/html": [
""
],
"text/vnd.plotly.v1+html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Our reference populations\n",
"fig_data= [go.Scatter3d(\n",
" x = features[[x for x in range(sum(Sizes)) if label_vector[x] == i],0],\n",
" y = features[[x for x in range(sum(Sizes)) if label_vector[x] == i],1],\n",
" z = features[[x for x in range(sum(Sizes)) if label_vector[x] == i],2],\n",
" mode= \"markers\",\n",
" marker= {\n",
" 'line': {'width': 1},\n",
" 'size': 4,\n",
" 'symbol': 'circle',\n",
" \"opacity\": 1\n",
" },\n",
" name= str(i)\n",
" ) for i in labels]\n",
"\n",
"\n",
"## The incognita:\n",
"admx_t= [y for y in it.chain(*admixed.values())] \n",
"admx_t= np.array(admx_t)\n",
"admx_t= pca.transform(admx_t)\n",
"\n",
"fig_data.append(\n",
" go.Scatter3d(\n",
" x = admx_t[:,0],\n",
" y = admx_t[:,1],\n",
" z = admx_t[:,2],\n",
" mode= \"markers\",\n",
" marker= {\n",
" 'color':'rgb(0,0,0)',\n",
" 'line': {'width': 1},\n",
" 'size': 4,\n",
" 'symbol': 'circle',\n",
" \"opacity\": 1\n",
" },\n",
" name= 'unlabelled'\n",
" ))\n",
"\n",
"\n",
"layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" )\n",
")\n",
"\n",
"fig = go.Figure(data=fig_data, layout=layout)\n",
"iplot(fig)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In feature space, accessions drawn from our 'ghost' population stand out. How do we avoid classing them into our known populations? \n",
"\n",
"We had previously used maximum normalized log-likelihoods to assign our haplotypes. KDE extracted log-likelihoods represent the density, in feature space, of a reference distribution at the selected coordinates.\n",
"\n",
"By normalizing log-likelihoods across the dataset by those of the references only, we obtain an estimate of how different the density at a given coordinate is from the mean density across haplotypes pertaining to that reference population.\n",
"\n",
"This normalization is possible in part because the kernels used to construct our KDEs are Gaussian themselves. It also works as a way of circumventing the sample size denpendency of KDE-derived likelihoods. \n",
"\n",
"All of this considered, the method is quite straightforward: A lower threshold is set below which haplotypes are flagged as outliers."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First twenty assignments:\n",
"[ 0 0 0 0 0 1 1 1 2 2 2 2 2 2 2 -1 -1 -1 -1 -1]\n",
"label 0: 255, label 1: 103, label 2: 307, label -1: 20\n"
]
}
],
"source": [
"## setting our lower limit.\n",
"Outlier_threshold= 1e-4\n",
"\n",
"## stacking our data.\n",
"global_data= np.vstack((admx_t,features))\n",
"\n",
"## calculating kernel bandwidth. A proxy of local differentiation allowed.\n",
"params = {'bandwidth': np.linspace(np.min(features), np.max(features),20)}\n",
"grid = GridSearchCV(KernelDensity(algorithm = \"ball_tree\",breadth_first = False), params,verbose=0)\n",
"\n",
"Scores= []\n",
"\n",
"for lab in labels:\n",
" Quanted_set= features[[x for x in range(len(label_vector)) if label_vector[x] == lab],:]\n",
" \n",
" grid.fit(Quanted_set)\n",
" \n",
" kde = grid.best_estimator_\n",
" \n",
" P_dist = kde.score_samples(Quanted_set)\n",
" Fist = kde.score_samples(global_data)\n",
" \n",
" ## Normalizing log-likelihood estimates by those of the reference set.\n",
" Fist = scipy.stats.norm(np.mean(P_dist),np.std(P_dist)).cdf(Fist)\n",
" Scores.append(Fist)\n",
"\n",
"\n",
"Scores= np.array(Scores).T\n",
"\n",
"new_labels= np.argmax(Scores,axis= 1)\n",
"\n",
"below_threshold= [n for n in range(len(new_labels)) if np.amax(Scores,axis= 1)[n] < Outlier_threshold]\n",
"\n",
"new_labels[below_threshold]= -1\n",
"\n",
"print('First twenty assignments:')\n",
"print(new_labels[:20])\n",
"print(', '.join(['label {0}: {1}'.format(x,new_labels.tolist().count(x)) for x in list(set(new_labels))]))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": true
},
"data": [
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "0",
"type": "scatter3d",
"uid": "df8b2910-f4ea-4ea0-907f-09188dad37ea",
"x": [
2.2064242836412786,
2.113816341910332,
2.6220230023716335,
1.7352908996213308,
2.3525615357611303,
2.163399113598996,
2.418888415742663,
2.41199439969349,
1.9708056147135604,
2.150362485807398,
2.238573977448451,
2.731858898396636,
2.320966118616161,
2.937476810093796,
2.37981045499455,
2.042398224782199,
2.2419321663815333,
2.0039146007247006,
3.009970559506833,
2.5427194198064886,
2.5205671977137167,
2.6400731300310576,
2.194684464013272,
2.186571439143738,
2.1829645371147093,
2.321664461240482,
2.1844330630711393,
1.9406951559372596,
1.9084437426285223,
2.290969311616759,
2.3460002623371055,
2.337051005222629,
2.283751213861328,
2.151914969974808,
2.261940461639127,
2.4601303690327647,
2.122498099875934,
2.60088193998212,
2.530227149091451,
2.0956249918934424,
2.181326808220659,
1.5018425827999273,
1.288835777729759,
1.7463537880761542,
1.9640433404045412,
2.626082885901581,
2.368649985440406,
2.194059017091971,
2.7645397030544636,
2.1515233339746804,
1.980441813565407,
1.4239721558933056,
2.3020434703126225,
2.4132819963905017,
2.1276078314987656,
2.2575401757690576,
1.873407547345207,
2.6029695369378656,
2.818886646738372,
2.179324444232249,
0.985018232083015,
1.97737296027474,
2.0292652046276056,
2.7357280899285468,
2.68921809167032,
2.6074596099671683,
1.3757088255684067,
2.1583578902074576,
2.1429633445462026,
1.9192511990806893,
2.2001252261994204,
1.874255574155896,
1.7742437624789713,
1.9472753538906575,
1.5605224425733604,
1.902737500294424,
1.4729563273006576,
1.6577210465255625,
2.2323425322759403,
1.9100043163057219,
2.2643992511546127,
2.4800646062792993,
2.4411654964310263,
2.552837707245762,
1.990250375239464,
2.24972496620781,
2.3276632990241564,
2.4523734444141563,
3.0199579661525395,
2.2560429115985667,
2.387809324016202,
2.029204189889609,
2.4266844834686854,
2.6386659641742725,
2.3516341509811762,
2.0677504328775007,
2.5610545609091764,
2.058472633315847,
2.171143397099592,
2.087332965323664,
2.1752005486355355,
1.925579362984474,
2.222131872349913,
2.1319613112464086,
2.7171565330346445,
2.187360112158833,
1.9748676269218124,
2.317738163355671,
2.650598453496329,
2.5164335263310202,
2.036901116621539,
2.4225296949482447,
1.1158041477323921,
2.535111260549482,
2.099340303497017,
2.099642614817344,
2.0737727933966363,
1.8303523491339804,
2.227899438753664,
2.6039012158891217,
2.198738717051572,
2.7765354766085877,
2.473167222268989,
2.118057844556766,
2.4784632010708223,
2.3889809129316903,
1.602474993917998,
2.2157073969011476,
2.3527735226486026,
2.3806859471692348,
1.7516059596340994,
2.627744706363905,
1.937076470534572,
2.59443410570491,
1.936548396276116,
2.5427008587437374,
2.548071353337183,
2.290978051845335,
2.7076689038154895,
2.207298760064523,
1.5888918336635849,
1.9642122129681057,
2.3520181544436833,
2.3692637177853375,
2.4182877747110907,
2.3453567507707636,
2.5417411111306847,
2.485618504771599,
1.8132618192111827,
2.0152841800975954,
1.9146518993732737,
2.080362197414351,
2.2017381191859218,
2.2103703597505464,
2.7677044745852646,
2.663098904136357,
2.2056933191299293,
2.690376517365396,
2.7484332783292134,
2.6224035799000034,
2.082134886171088,
2.3243812945716353,
3.075355756897689,
2.038923746968059,
2.207487766483544,
1.7927727281031538,
1.7078885627831766,
2.350590966112108,
2.4693467086868806,
1.9299434430812932,
2.4323924950076274,
2.6987603559777034,
1.7157698613012482,
2.2322286786498937,
2.2605588468694533,
2.3924601663761207,
2.3637221954016248,
2.0247425466311535,
1.399886287311707,
2.31565636804108,
2.4248699615680183,
3.203980534267806,
2.3580963090587015,
2.2748882770232237,
2.1177434590589055,
2.629133454004985,
2.2102166875290115,
2.2940900581528285,
2.692406726714216,
2.2682029502963723,
2.7952994650180574,
2.1567380437467585,
2.219779364516367,
2.1512963419846565,
1.6264737836711687,
2.2099383870139917,
2.7393470642826627,
1.7254510304389696,
2.527680635810616,
2.6672942332333673,
1.4851656451341047,
2.651554167399733,
2.0660337480165842,
2.2212400821731384,
2.2668009450398463,
2.1795565548085785,
2.5633896629450583,
2.39694533522289,
2.194928905861953,
1.8936784396073638,
2.150399924461532,
1.9847169710693349,
2.256497373489875,
2.2577039021641734,
1.8150976594318804,
2.3610438968754934,
2.1638743796737305,
2.2114627144806223,
2.4397970321467186,
2.6559269729505144,
2.1913634570888707,
2.3714683917876718,
2.217029280246081,
2.0219804187197674,
2.035183961867955,
1.9315270302641863,
2.259536253200219,
2.536634123624291,
2.646444806650005,
2.7641945384392157,
1.6667449120157443,
2.1040126329322857,
2.3372653273435477,
2.057623938382885,
2.3384401668924677,
2.50269167494872,
2.713710805352641,
1.7706181724516719,
2.447397636824283,
1.9022491836942383,
2.187860016845565,
2.461407674181639,
2.165321386351654,
2.2162058625806718,
2.1396734581432018,
1.554641858377673,
1.7870520119896112,
2.2508750081611093,
2.799526380076311,
1.8509820998710442,
2.4080154794047393,
2.197996084559753,
2.65448905881363,
2.173059363458763,
1.693545073205797
],
"y": [
-0.8198905009204427,
-0.8193871257558728,
-0.403269599598251,
-0.603455800741723,
-1.0016226683210763,
-0.73970519325464,
-0.40902577678718016,
-0.9627392190029578,
-0.4386510727143428,
-0.355512408353207,
-1.1088818283190893,
0.07507579772464344,
-0.9583505925745656,
-0.38884000308144273,
-0.6834435848809494,
-1.064146365508784,
0.3075601459271404,
-1.1542928143472244,
-0.6777645568344557,
-0.42690075528243815,
-0.8823657965414771,
-0.6852883897167562,
-0.6440990428831758,
-0.8054596118923709,
-0.8150779701361334,
-0.9543601645148614,
-1.0112933288124857,
-0.6517248332958583,
-0.8080847913607907,
-0.2821036053066214,
-0.9719522950136258,
-0.765039286515339,
-1.0905105691080559,
-0.5748232201547323,
-0.9380401274905176,
-0.9458634970035902,
-0.7820753539843478,
-1.0109131605622492,
-0.7740374921639998,
-0.6502920632053704,
-0.8425054454193175,
-0.5823441798179466,
-0.5698213024691544,
-0.3191520775608273,
-0.22593335469129586,
-0.9493554512450497,
-0.6324104028883848,
-0.9939692541789327,
-0.2249419780838485,
-0.4549254701050904,
-0.7119105648525568,
-0.536411901611831,
-1.3864162368206583,
-0.6715727181724501,
-0.5936286406839388,
-0.6144895903555719,
-0.9101164078357377,
-1.1247713098289611,
-1.0469393674794873,
-0.039033045054023253,
-0.6890642083772215,
-1.0363765737863926,
-1.0132349499198532,
-0.9153525987549799,
-1.1815174578571472,
-0.4088647289499837,
-0.6895498821346543,
-0.5943515405188263,
-0.9642694191977232,
-0.6282397180491412,
-0.9540817946626873,
-0.40116061725956753,
-0.35836688293241975,
-0.9377506913454607,
-0.8217435633240603,
-0.5116834267854464,
-0.7424722948959862,
-0.6876780231986509,
-0.6918622423125924,
-0.2472385273806341,
-0.6992162482093066,
-0.8417908610980823,
-0.6225518550268795,
-0.9409765953975393,
-0.09138743293138188,
-1.095351603229725,
-0.16217879814144917,
-0.7380662250252743,
-0.8129650903956283,
-0.6046268786683735,
-0.7695053954762016,
-0.8115170002786873,
-0.982556473026089,
-0.5974996074038066,
-0.30626937871313686,
-0.36246468885262983,
-0.6327304789481084,
-1.0511267215428146,
-0.8001699385822963,
-0.5699661414977447,
-0.6058676015919362,
-1.1079706281204866,
-0.7756078467601571,
-1.2585804243566348,
-0.8373152793162569,
-1.0718110202350404,
-0.8502999031186315,
-0.4655632842536222,
-0.45761116877602837,
-0.9285793236934371,
-0.8756488482476711,
-0.8095158054021604,
-0.4313118567316982,
-0.6642091040592959,
-0.5409252091364601,
-0.485307123342785,
-0.10927000882380414,
-0.4768214554597401,
-0.49312583436034285,
-0.6230069761231486,
-0.6910460125631239,
-0.7351692722347832,
-0.4998509628677271,
-0.42216283639579055,
-0.9906500127463261,
-0.748017291638086,
-0.8715137107284691,
-1.0392750461504403,
-0.3018487358732116,
-0.5361099092581065,
-0.46789752813680957,
-0.44158613147091924,
-0.6780703289047441,
-0.9224524390412129,
-0.3051970872174456,
-0.7452154328218256,
-1.2854824023444693,
-0.8341663453702607,
-0.5661064285954772,
-0.7966368858623925,
-0.302245550651573,
-0.8216279665429201,
-0.4483847305077941,
-0.7442320883597638,
-0.2364324778955583,
-0.961378812783952,
-0.622879107578713,
-0.790445713226609,
-1.0387326347698786,
-0.7377408495354735,
-0.4988410905043782,
-0.8903848948153111,
-0.9351623214606398,
-0.4263746878195481,
-0.7573314256777409,
-0.6795172898282674,
-1.1078441711786202,
-0.6611226975295618,
-0.9574685160742862,
-0.841900869593606,
-0.9686624025818943,
-0.6936920138718378,
-1.1276225402255993,
-0.5419895528946951,
-0.4265278863306154,
-0.32889600249315615,
-0.628398544375067,
-1.0387196986617186,
-1.1737929920010515,
-0.8371890217680403,
-1.1715334125048356,
-0.7628707244926406,
-0.6768280771608383,
-0.8926139289894449,
-0.4187818027361634,
-0.469088989523819,
-0.6900636108027892,
-0.9125726806852672,
0.09582689133986783,
-0.4236456834793947,
-0.4481934272143699,
-0.979549860429339,
-0.5501227963986882,
-0.7925645382954597,
-0.476788295389494,
-0.9724046443064566,
-1.0670571731915712,
-0.6220051048308801,
-0.8708122593990012,
-0.6588466089139736,
-0.948860078480018,
-0.8943856571645578,
-1.2192667281572476,
-0.48000380119254904,
-0.603021621322483,
-0.6845052499340756,
-1.3690015174967705,
-0.6674553259238172,
-0.70485830330367,
-1.2688244136860503,
-0.7432262862168969,
-0.923359297987529,
-0.26286699854079254,
0.07854725984816384,
-1.1175060058846833,
-0.7061410287225635,
-0.7270095935956756,
-0.5417205552757131,
-0.3732116109925633,
-0.415321473144536,
-0.8603962150968838,
-0.6215285642435379,
-1.0019718278038938,
-0.6995373551151984,
-0.3357061428230834,
-0.443624046527311,
-0.5397746992408037,
-0.9193436866577803,
-0.4577482464822564,
-0.6970517284471432,
-0.2923414972194926,
-0.8477213853338844,
-0.8657963357004034,
-0.21032533168049475,
-0.5745603338889388,
-0.19406163727292344,
-0.7669158194137955,
-0.39074785986461197,
-0.9316633667322947,
-0.28153196833001826,
-0.7433800084018878,
-0.7496902275507826,
-0.784646632839486,
-0.9893667825670641,
-1.0270043055799232,
-1.115805189502925,
-1.039938770953521,
-0.7833515480824181,
-0.6518293660217866,
-0.7511882808018538,
-0.6032513657518901,
-0.8784106555351358,
-0.7898658082058019,
-0.6532581337834383,
-0.5723108993832154,
-0.17177997397375813,
-0.9061287441572395,
-0.5272641981702428,
-1.115209371519661,
-0.8055890299877342,
-0.5708560844085845,
-0.9167552298490611,
-1.210063562889679,
-0.5151774147851261,
-1.0708039170202264
],
"z": [
-0.2266024374285758,
-0.0339723625285479,
-0.5722808655989252,
0.079029891371847,
0.39302891287498865,
-0.4446545249559114,
-0.19282537569494634,
-0.233228802862386,
-0.7251333919535009,
-0.5772259902619234,
-0.23821364175803691,
-0.4485644185930268,
-0.11178898297010025,
-0.3757870902759686,
0.11894892610415525,
-0.16238202146851394,
-0.31142088616817337,
0.011500240563979046,
-0.31873286618294544,
0.07810186718781416,
-0.027633766645748275,
0.2028042435744557,
-0.017915247453307703,
-0.10842039646243389,
0.09642061785922115,
-0.19114270979876274,
-0.04625266330006963,
-0.23491235766525087,
-0.7912973771727742,
-0.23250785606280258,
0.17839570345320854,
0.39981659940680975,
0.24017816237768733,
0.5017705946369354,
0.12077627662976811,
-0.5033077550080315,
0.3471087418507731,
-0.3203312960073215,
-0.26285399503071727,
0.04517469145271351,
0.09680070759805434,
0.48665011971578215,
0.44753938793922804,
0.019824088194308472,
0.07516074475520948,
-0.28739391458288915,
-0.49934983853233794,
-0.17439702622858003,
-0.49036627900481333,
0.4221810289923718,
0.2743075207573234,
-0.2436823894810728,
-0.12527151452062138,
-0.7560394423819775,
-0.3671379014802247,
0.06386556989509908,
-0.012860137881167029,
0.4757902558759155,
-0.15165707476160328,
-0.5711174253534798,
-0.07071355358758888,
0.16667131006897828,
-0.3890035811021058,
-0.3622663717587438,
-0.5635992799252768,
-0.3309764216920285,
-0.41660683686032024,
0.44382847936314473,
0.2421299865179283,
-0.20893608995995389,
-0.09064232947385069,
-0.0712308649827872,
-0.12214378351015297,
0.17794241616000372,
0.12112625995622098,
-0.38277716160112585,
0.022018803716223147,
-0.2552411197544269,
-0.5889371075061124,
-0.020770622725457318,
-0.1410543891029475,
0.1509418091257106,
-0.5610813725343607,
0.27164690894441157,
-0.13328066260250218,
0.030810823734787596,
0.08928198838482712,
-0.49905899898337025,
-0.019336512578148026,
-0.7508478423228283,
-0.45618552557078434,
0.12048597941475322,
0.2808499481070221,
-0.5391506396468043,
-0.21919106439986605,
0.6898556839511804,
-0.15251037728470185,
0.279595179770873,
0.03313372858709409,
0.36444904012470003,
-0.12198707635351062,
-0.03812251126142178,
-0.2047653409515252,
-0.015291626961508787,
0.20096442828160976,
-0.27920571398746835,
-0.07853314471747522,
-0.13118264401593083,
-0.48544513628140884,
0.019800624515581112,
-0.11104620659258306,
-0.7232116832187668,
0.398636815528728,
0.040078560412612325,
-0.10431793417019884,
0.012911983654072735,
-0.7090649401985819,
-0.0495095203688014,
-0.42242357619524684,
0.0813735961518603,
0.33620894576128074,
-0.580548387144126,
-0.30156134464270884,
-0.29385129290869005,
0.01640601462287593,
0.24577021232028134,
-0.09015109786196304,
0.07324726024133951,
-0.2950046598876836,
0.03902995824676916,
0.4490870557250579,
-0.3993095798031265,
-0.1889825520315161,
-0.2098989419059098,
0.556765425572384,
0.08889102852683649,
-0.24456723754972598,
0.359467138587662,
-0.5139442373070421,
-0.26384061321618507,
0.4506926542268842,
-0.09782244713425496,
0.21041295798552978,
-0.2965886816804331,
0.2510680046590336,
-0.05762170360064626,
-0.03053603240027999,
-0.2967721830783272,
0.42425869550118955,
0.0015899853145013745,
0.534459078024727,
0.11613898807323478,
-0.3239228200849414,
-0.13416311281879328,
-0.5094945157983626,
-0.2638999528634505,
-0.1179857255157825,
-0.793242288614371,
0.0037878893579397703,
-0.5654359579243478,
-0.18250893644149913,
-0.3512671800237597,
-0.7304018965565352,
0.20883598363006833,
0.024407490162122243,
-0.1946356372607519,
0.04071187932629559,
-0.0521815648900661,
0.1159240869046557,
0.40316648373432956,
0.6078478372642528,
-0.3696987836923401,
0.2515907931224442,
0.07960163539297502,
-0.04058789101390419,
-0.13144902897255095,
-0.030429103830199086,
0.2343697515596025,
-0.1889123993236756,
-0.4271704283345241,
-0.1804361233044735,
-0.3244961160938709,
0.0015947005275194557,
0.18436706358929295,
0.35378605457617324,
-0.2014309162696722,
-0.2314347369701159,
-0.45357066322129796,
-0.5146313067641941,
-0.39342097929673153,
-0.17179827710404844,
-0.01294411792556014,
0.1342549621794076,
0.2840746423922951,
0.17274990408283752,
-0.24996283471704925,
-0.01854598048821225,
0.16282752889440966,
0.15659573802371918,
-0.769363578120089,
0.23408781987257415,
-0.5644603291996159,
0.055341868340188276,
0.15956086390900942,
-0.1895391639116477,
-0.2612691199774319,
-0.2224362324001306,
-0.30082277022482656,
-0.2949408019425108,
-0.4051373651107412,
-0.08107587894408944,
0.36590998609611664,
0.33016400317497674,
-0.24501790892000846,
-0.0780839970210787,
-0.019229349916193402,
0.19051546152510573,
0.0005858187268839365,
-0.3802834480750688,
-0.4051865826540753,
0.10260345593490255,
0.16892752494109708,
-0.1397667118283608,
-0.3343988120509405,
-0.002719160631547459,
-0.08215871923788749,
0.11220795985104834,
-0.04438465526078152,
-0.24622341005494755,
-0.1734088553878311,
0.567075994856319,
0.15061374140859707,
0.1375413625107889,
-0.12222094701636398,
-0.12821074083132405,
-0.5933466664576826,
-0.6532259502195442,
0.13246411259553686,
-0.7986328968023805,
0.07455073516140723,
0.10513223443503039,
-0.007749315832917138,
-0.1958492045867281,
-0.13956890187503573,
-0.13303115629177586,
-0.28818285376246766,
0.33522592543827645,
0.018934449420697365,
-0.5502684915572986,
-0.02828276231049252,
-0.2562884748241902,
-0.07366032413895085,
-0.8605801271144194,
0.269687065351098,
0.5102921278629459
]
},
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "1",
"type": "scatter3d",
"uid": "606da09f-8d14-48b1-9a42-3e0d23cae7a6",
"x": [
0.4462448384251028,
0.3607140312008184,
0.3027383037000555,
0.6283225491609941,
0.016508963603080427,
0.6847749486749324,
0.531436630690354,
0.5030154616320242,
-0.4292647179109327,
0.6375878224998321,
0.041929989485824035,
-0.028854913665043787,
0.3878526132372429,
0.46877939070636493,
-0.11295286430896428,
0.3511434079643744,
-4.1424052521128046e-05,
0.2038593654113843,
0.18836021416972304,
0.26853863879846906,
0.6619998930576351,
0.42549602918846857,
0.18349220877090294,
0.4431943680466618,
0.5671753082861226,
0.3018353130441776,
0.40248599080308106,
0.35824291754316684,
0.5166292892919576,
0.044525428697058445,
0.7275200695733959,
-0.02734103008560079,
0.5173127910232518,
0.43912302094658745,
0.3698442292665822,
0.5444945632379303,
0.10507232654251378,
0.3538785353394005,
0.36621076676254977,
0.32389833089509057,
0.478165024586309,
0.09524960001078828,
-0.14498170798892368,
0.16674336600926007,
0.4779478548055982,
0.1589846164440178,
-0.16265180748935987,
0.319361824106097,
0.03986294998768962,
0.3320285342024497,
-0.17802110747921326,
0.7668734685995577,
0.22688598492676756,
-0.047204477953232016,
0.009330944142374595,
0.6731376041726861,
0.5060116405493732,
0.4268872411514652,
0.3237883433117498,
0.6924509926929561,
0.11152793734893424,
-0.002182911159800184,
0.09805361655670183,
-0.3471612210131001,
0.30781434725060564,
-0.27067766677775346,
0.4523734636543931,
0.48587100809983663,
0.44956365200999115,
0.25854151017882454,
0.12363447793296259,
0.6625874436980478,
-0.04491506752496784,
0.1962719585275748,
0.4264764128212213,
-0.0979618762193337,
-0.1918149607948368,
-0.08903937910499618,
0.013070919036722993,
0.15906047337400653,
0.44034975779682434,
0.41582203940997153,
-0.24081413793640974,
0.10658449372360992,
0.7546764286391711,
0.08525325878294301,
0.3502769420317392,
0.2177283221243278,
0.632259676766839,
0.3630259763146747,
0.2982007745749284,
0.24731650740960404,
0.22145346603941204,
0.2685035724118612,
0.38911965618898986,
0.5235923076786316,
0.3764176447705663,
-0.20521940645254824,
0.23116722612566856,
-0.14367158907194655,
0.30290764135022996,
-0.2360606894397154,
0.01980705835344864
],
"y": [
4.006223240857248,
3.018156939087044,
3.3441954742381026,
2.7172913017655635,
3.351285539050423,
3.5160597675070857,
3.071990704908696,
2.935600033434921,
2.999952365669498,
3.14744597483714,
2.6025092253406124,
3.2643800270389676,
3.6739160915094344,
3.419845702062968,
2.8805151655104284,
3.4763341392042055,
3.4997860222531854,
3.2077592551567067,
3.568545933881613,
3.2109394305525223,
2.915196561975085,
3.070132879348561,
2.947639104456681,
3.4300529602088363,
2.9784672575976496,
3.19468259049027,
4.076586004643985,
3.3701887263044363,
2.865399902169982,
2.9562132773769703,
3.4424594762817513,
3.7276040562242096,
3.1742228683469427,
2.741052639270511,
3.234577066216317,
2.85953661648099,
3.611326951593647,
3.648536204276967,
2.4951903721212885,
3.316383184358666,
2.7928584150197966,
3.475209835995468,
3.1944859036122897,
2.5976734924941454,
3.8146495400848965,
3.1527143030526723,
2.6679131142071153,
3.408533900197411,
2.674899856592259,
3.4809873523720567,
3.350160017806055,
3.3857915436475694,
3.0285463485913446,
3.148205959274292,
2.362765708358585,
3.669173795410503,
3.2792419942188333,
3.189394356020554,
3.069121318907187,
2.7452891571416123,
3.377135040046638,
3.349738686033515,
3.637662565864969,
3.5599431335982237,
3.204910344532639,
3.2234856206074047,
3.438679113716594,
2.757186468618297,
2.69159353298092,
3.2521345764246554,
3.7176968870071065,
3.3708595218976325,
3.547692529112246,
3.2515351135215327,
3.318854319768736,
3.0450770109804335,
3.410850292554316,
2.428565414283542,
2.719616078053418,
2.8785852856696543,
3.4910870555818434,
3.0412474632362203,
3.1395095195209706,
2.8566787906785276,
3.428760273222531,
3.0174840755781838,
3.664625205202584,
3.454700878364493,
3.2140905634601062,
3.053017555165027,
3.3049656842615147,
3.7305445436043825,
3.475795348404468,
3.6015458896125447,
3.130401878290953,
3.7899198180550577,
3.5434398872832404,
2.9814118664999167,
3.0677150155154003,
3.2760144977169765,
3.7505256682317736,
3.204326460111309,
3.0547704825223754
],
"z": [
-0.051366412772509897,
0.20773989605730026,
-0.4480681841297374,
0.12055465998642023,
-0.44957199454408087,
0.06079515551512806,
-0.020472871944736622,
0.06771493620938515,
-0.015271041647316986,
0.21271198526696586,
-0.31505027289487764,
-0.2961821218526685,
-0.4852183221110371,
-0.03177108148194154,
-0.17732952856301926,
0.009404930396707723,
0.09978291537655543,
-0.3836483124842474,
-0.11518129665596635,
-0.5850169421146237,
-0.16433897965638894,
-0.4118925331033499,
0.021114966874835932,
-0.06053460957348052,
-0.5907284059770078,
0.040351068206657355,
0.009618914504114045,
0.13031712180159427,
-0.24826171574806583,
-0.3373889276526838,
-0.13038856345842842,
0.06232174650891265,
-0.26652831741496114,
-0.19486052801515058,
-0.16860402531892632,
0.5476283233934784,
-0.45432207894013327,
-0.01599691288610799,
-0.26859195315536366,
-0.3794395455163097,
0.018572924634214,
-0.3826703251723394,
-0.41983751640113304,
-0.15918196799212692,
0.04761406715520867,
-0.4663692400784653,
0.79058548077908,
-0.660726069588328,
-0.05482390534041911,
-0.5855659365074094,
-0.5404590558218385,
-0.6552561918188183,
-0.2851250040392448,
-0.21274210015694134,
0.33527731163983726,
0.1449082547211097,
-0.18408212586245565,
0.4693027839104472,
-0.06771610758604728,
0.26882096032615593,
-0.3626206742903196,
-0.2571880149821491,
-0.16794143319982424,
-0.5983202391829906,
-0.6318898190504367,
0.35266367910434027,
-0.42233892676101287,
-0.4711293530177243,
0.11396134081841333,
-0.14358487340501164,
-0.23223726374643194,
-0.6437753082182627,
-0.42076325487347105,
-0.34818287425386785,
-0.3623045321147437,
0.12700348282801652,
-0.16352396931755142,
0.42289224680208237,
0.20015095346281664,
0.28846735244150207,
-0.2572791169901075,
0.1758910277455469,
-0.1817705501926919,
-0.1490703982813973,
-0.7253312875513642,
-0.6168330536054094,
-0.18778751681690475,
-0.42200066971379896,
-0.47703670475131726,
0.437806085530651,
-0.38505216187207897,
-0.42227915547739764,
0.06298888822076831,
-0.48963388679455155,
-0.4911902716930947,
-0.42524674993020023,
-0.20675139512436858,
-0.5103126988432716,
-0.3409064216321795,
-0.31805345311612115,
-0.29252002679075584,
0.3649830286807273,
0.04033911766029997
]
},
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "2",
"type": "scatter3d",
"uid": "fd9e8dd2-d409-43c3-ba0c-c65683c00c67",
"x": [
-1.9620480812726646,
-1.4434020643433463,
-2.1464248695817867,
-1.7245644181082425,
-2.0399214759117763,
-1.6708035771480572,
-2.0508608425166037,
-1.86593170524197,
-1.073108325321266,
-1.9385144836363697,
-2.452595873867519,
-2.2680010546570015,
-2.040917049859526,
-2.101609539890276,
-2.1249831472737273,
-1.730568057114529,
-2.1836382699035655,
-2.7447586010090843,
-1.9576105884507766,
-1.470304503417267,
-2.115962208670102,
-2.363839724392632,
-1.8809965847092585,
-2.015673064481509,
-2.2699018698638476,
-1.868556723367704,
-1.9343808349146396,
-1.9767330082168095,
-2.4834403263927287,
-2.074910160312289,
-1.866299710291053,
-1.484630870418841,
-2.0358051240258646,
-1.7450677422137366,
-2.717292226238242,
-1.991685758280978,
-1.3252198328198554,
-1.3961948670201398,
-1.9269802399791938,
-1.8920692942125195,
-1.2897177550582137,
-1.1580396162124829,
-2.5091126735913876,
-1.4711028869849812,
-1.8260442388447897,
-2.251863156323041,
-2.376439526778569,
-1.475957675826318,
-1.913785487211108,
-2.1628614654389864,
-2.1979238364164506,
-1.7367571324558477,
-2.158616870615533,
-2.3454779974223796,
-1.5881197119178831,
-1.7997015983533855,
-1.778548224627166,
-1.2660058005518273,
-2.4880113859697413,
-1.9016650077165764,
-1.6156918572002987,
-1.7723606168094197,
-2.1676721884160464,
-1.9496758810303116,
-1.5845128263897446,
-2.1865787460816697,
-2.054493184302069,
-1.9790961226649,
-2.034329122989533,
-1.7080620050508537,
-2.2767285818493734,
-2.1857348470561924,
-1.9176560369306181,
-1.9873724149432235,
-2.1176801638310963,
-1.9901737207271553,
-1.8465226628084772,
-1.8248650556646526,
-1.6385472222231927,
-1.548536360814577,
-2.379013730234932,
-1.4174664004015298,
-1.476156988620389,
-1.863585298997643,
-1.6775013117997577,
-1.4232730139794783,
-2.545626559227679,
-1.7199445997935618,
-1.6353578585581543,
-1.5532127791880632,
-1.8832677314337145,
-1.6279795699597313,
-1.9051338932782342,
-2.3135798069156013,
-1.6749865678663076,
-1.2080593342051764,
-2.355395433176288,
-1.6378436638430436,
-1.794268178893384,
-2.151152064974654,
-2.0021416582518077,
-1.52917720281952,
-1.7693395745021427,
-1.3450123232558147,
-2.129013346570139,
-1.6906729247647287,
-2.096270120258071,
-1.792528748333481,
-2.0182876818259885,
-2.337212914324572,
-1.7181974117969288,
-1.8418107310318372,
-2.138406663626885,
-1.554442647492551,
-1.973345507971675,
-2.4168815375731967,
-1.9460582216852047,
-1.8199469706018898,
-1.9633133988590699,
-1.7620876196130608,
-2.3636140661081133,
-1.8701765397781875,
-2.3317313884723347,
-1.7607374132980507,
-2.2681469542493535,
-1.6153172837509475,
-1.6855756694954902,
-1.9345346633149192,
-1.7226470862311305,
-2.2749068231369356,
-2.36777352929242,
-1.3370408037293047,
-2.294071904485629,
-1.5476885111167804,
-1.799139915386814,
-1.7767786573782283,
-2.5632899858112093,
-2.288621485048434,
-1.64858922692212,
-2.4180301408190266,
-2.410837365792887,
-1.8875525310188406,
-2.3791789690469924,
-2.565655024674165,
-1.6613413290263392,
-1.9489603184406536,
-2.546185978168669,
-2.370668682247205,
-1.817924665714697,
-2.3349423230394843,
-1.504031292969217,
-2.144589827804328,
-1.6312377989351559,
-2.179017716161712,
-2.1900647791293832,
-1.9589001329122468,
-2.1354278856079363,
-2.349602148546346,
-1.7561746497392732,
-2.1786027621799406,
-2.346437637965046,
-1.776660643957327,
-2.1748823397445203,
-1.8029795536394317,
-2.0555514277502875,
-1.7988908124121687,
-2.0338359495437652,
-2.2073084892300017,
-1.7649011294932742,
-2.0548420338067537,
-1.588521001242745,
-1.923088081725516,
-1.9575459950680971,
-2.1823526587941258,
-2.4145755022492263,
-2.150043720567658,
-1.9618075215001267,
-1.8757494513599136,
-1.610020441255829,
-1.9655477982794687,
-1.1899521341201165,
-2.292790206697526,
-2.210038801819379,
-2.2964852592777385,
-1.293786715383783,
-2.112719333544625,
-2.12601987827899,
-2.1558002523036603,
-2.25600290111905,
-2.2064304281853317,
-2.178823173926046,
-2.519160776340195,
-2.2883877822525767,
-1.7589953545593344,
-2.523147638550488,
-2.648559128341313,
-1.7584754703761358,
-2.4388030407229695,
-2.016127814681175,
-2.163408859375407,
-1.760565370445938,
-2.1694048092025873,
-1.8374853003320706,
-1.8618138552088308,
-2.4057885435230575,
-2.1172377546293633,
-2.088034348827958,
-2.4622280029917287,
-2.3477304233646077,
-2.007806881798538,
-0.9714624202472839,
-2.198295578017188,
-2.1754314193598616,
-2.199942774974283,
-1.735693100542808,
-1.7188943975421553,
-2.0647719576437025,
-1.7314860324403842,
-1.5938377289043333,
-1.8105195724265268,
-2.420144533808108,
-2.6726435593149502,
-2.4058121453890333,
-2.0004636712897486,
-1.5103351932148672,
-2.0843809212760074,
-1.9042805807782672,
-1.9215380071684391,
-2.2106549907856254,
-2.2849095810727413,
-1.5970178378063828,
-1.9149741430901694,
-2.221188373832396,
-1.7509445837992492,
-2.1628102955653206,
-2.229356812597061,
-1.877636921213696,
-2.054558880158514,
-1.9715969510660747,
-1.915108522680079,
-2.377185844816834,
-2.0400729395742836,
-1.600565076691486,
-1.4277881585528178,
-2.1805213808589095,
-2.2256900950948104,
-1.6843973572719761,
-1.8598835342441782,
-1.9125209558915286,
-1.7118237629463513,
-2.0104305060984102,
-1.9422237721864262,
-1.9928295507303506,
-1.7167347636673527,
-2.1760581500296885,
-1.9643518557177013,
-2.2723846515144923,
-2.4113481789687228,
-1.7810198941372726,
-2.3932319927090924,
-1.821679598395292,
-1.8720631958417853,
-2.0333885663783184,
-1.3515907030105667,
-1.860774115597194,
-1.9769723800533776,
-2.214122540521947,
-2.2168155521635216,
-2.5321722308079893,
-1.6499930181058406,
-1.776729438921847,
-2.2105719520949934,
-1.6455044816723985,
-1.8542633673144193,
-1.959224533059593,
-1.9233736021301249,
-1.832096797621125,
-1.9552976944542109,
-2.00546841890309,
-2.0776791895695115,
-1.6089371051634442,
-1.654457553644183,
-1.8268832055511501,
-2.0122924654326604,
-1.6460737481194243,
-1.4005105025478541,
-1.5734193329988702,
-1.903380526613211,
-1.4185201879530704,
-1.674843347687447,
-1.797079429721397,
-1.7520722368192863,
-1.0320135527587786,
-1.667969969760403,
-2.2166244607983776,
-2.02906202048813,
-1.9556148229330232,
-2.0389796600184145,
-1.9229807786328126,
-2.268779809378239,
-2.0898789885711047,
-2.3408158863750965,
-2.0082274535655853,
-1.7144024577219301,
-1.5242146814616884,
-2.671955221275385,
-1.9766810524142362
],
"y": [
-0.8758759025297919,
-0.4858568015338327,
-0.5032178449626296,
-0.486445691276817,
-0.6044253152586662,
-0.026723185049607617,
-0.7384214307963308,
-0.7480476731703602,
-0.4798010188170707,
-0.7910779416401352,
-0.5066698163563332,
-0.42924610185858963,
-0.8124056072524081,
-0.6972391965089733,
-0.47387400040025407,
-0.9521296847676707,
-0.3046834466574721,
-0.47264727086288394,
-0.8214752964993041,
-0.6760595639404182,
-1.0584103280486772,
-0.1293253415296898,
0.03566196635185578,
-0.7774924441717918,
-0.4096205100271988,
-0.7815955267435581,
-0.48556225351270443,
-0.7697031426330616,
-0.3854088679536805,
-0.2821373169425384,
0.03865117476576667,
-0.5766042187646644,
-0.3409774936162615,
-0.5351984646188815,
-0.48437357123791025,
-0.6287631229446455,
-0.2061434079851491,
-0.4589219389300029,
-0.28365694665775765,
-0.2334417856757199,
-0.20951587987955375,
-0.47916689114082767,
-0.6065899180407229,
-0.8446827682700618,
-0.3219647235585702,
-0.5454304282948373,
-0.7871329170656273,
-0.2273097739137607,
-0.6205847780223334,
-0.40645947506148833,
-0.5246714589532354,
-0.2907098500928251,
-0.416432461226166,
-0.8336522042442934,
-0.617970489361941,
-1.1449196027341981,
0.09394432134394473,
-0.5794520840722354,
-0.6229776981301431,
-0.6929932514254704,
-0.4470133579141082,
-0.5978667548080436,
-0.5816326767487352,
-0.7944057138266065,
-0.8174485364577326,
-0.8513541206434562,
-0.4656889256561145,
-0.36000025501331745,
-0.6617928979860839,
-0.5033707368976718,
-0.6627420657020042,
-0.47739491448686416,
-1.0193270571956337,
-0.415715771382933,
-0.7326533202402502,
-0.44734907183782735,
-0.04420383230787451,
-0.6895203495333562,
-0.3916309791739144,
-0.479056094020914,
-1.0842126554139013,
-0.23364948548091644,
-0.0674500123731329,
-0.7403105374173674,
-0.6543268793845224,
-0.763944035532087,
-0.5387013500613385,
-0.47065227118842207,
-0.1680869288471768,
-0.5944765614480729,
-0.7332170942928706,
-0.1977846062802541,
-0.5607510795664178,
-1.313784049295395,
-0.09979119944419626,
-0.3732641208710766,
-0.7966448440172457,
-0.3771810342725384,
-0.740718886694054,
-0.8537890987110318,
-0.6810391691752506,
-0.5308330872923402,
0.07455660029655349,
-0.600669847677781,
-0.5274138262539289,
-0.925891766039609,
-0.08683774923441291,
-0.36972912615146886,
-0.5080187839402855,
-0.5932232770019329,
-0.12835677112100644,
-0.36440769885772056,
-0.14411693775391848,
-0.44236729589084983,
-0.5498813189558697,
-0.8920174117035365,
-0.17241170281682605,
-0.5729337742009446,
-0.9181993860170594,
-0.4722374658090766,
-0.38328291829096744,
-0.7988996019858731,
-0.5836891995621077,
-0.34570575412584786,
-0.5452173468755104,
-0.4148774899730568,
-0.08669293669733207,
-0.05689259403848893,
-0.7640738196551022,
-0.09976593459368657,
-0.9951065001176418,
-0.5178661259756451,
-0.5894192522091698,
-0.5565387880934023,
-0.25159732745467867,
-0.4321185667114061,
-0.9104651655044136,
-0.44557972066048307,
-0.048627858273932324,
-0.2885882927504109,
-0.7756795404373434,
-0.5897918801166879,
-0.5152211785161916,
-0.4386668804840281,
-0.45511193051859,
-0.619569048497606,
-0.5367505545051754,
-1.0170363159888502,
-0.49759829954837603,
-0.39908987500473575,
-0.2410653608986206,
-0.9771017432592443,
-0.36802682025342603,
-0.598452796530036,
-0.6303373338174235,
-1.0396661547189856,
-0.691619908073387,
-0.5253785667375135,
-0.20924982994118688,
-0.48629557708631743,
-0.7473170688768335,
-0.7536546741529773,
-0.24434306758054622,
-0.333067889758947,
-0.5344327402527612,
-0.4291110625888237,
-0.689879761223155,
-0.6704164653625472,
-0.8334166858740527,
-0.3803748061934928,
-0.31393043022399103,
-0.5270275571090697,
-0.10388625574870718,
-0.3160224668189895,
-0.5222532455122572,
-0.6746573701880494,
-0.32635690545053353,
-0.23742516772745045,
-0.23511158641109195,
-0.600869456941046,
-0.08914030925102316,
-0.8903460713222058,
-0.5893595097745178,
-0.5832357033405561,
-0.3875377182705656,
-0.6140995256413345,
-0.943693470557182,
-0.7661326540458792,
-0.9668859061059406,
-0.6629048988388994,
-0.6648063246332483,
-0.7220283558965778,
-0.5581096761273286,
-0.19423395901780618,
-0.8316106747784028,
-0.18215376549362103,
-0.720370402641743,
-0.934055529064026,
-0.5687481304985992,
-0.42910417167127307,
-0.32559334688582414,
-0.8472301930803469,
-0.9955694762851091,
-0.4549576279712369,
-0.5084595619277573,
-0.257976881449834,
-0.7217081509498344,
-0.32598607095069676,
-0.6629283396631969,
-0.6709462850947799,
-0.22800528625077462,
-0.45958717513058284,
-0.28873167858236554,
-0.7249842502545151,
-0.49950157864716976,
-0.3970515198881514,
-0.7841481768228481,
-0.5158422067381019,
-0.4401162381722685,
-0.3297055639259461,
-0.4157562183991906,
-0.6285856333946566,
-0.8414931895368314,
-1.3764051629048513,
-0.5874557139198154,
-0.7058847547509043,
-0.41462264910223434,
-0.4246262477019801,
-0.4344894727520066,
-0.13488673726624528,
-0.1777813555583739,
0.15796030713395445,
-0.6000357345458095,
-0.8239544426720611,
-0.4169133959477868,
-0.22822135990753054,
-0.79520637832586,
-0.35817853200115574,
-0.12111675824787184,
-0.5678935068697744,
-0.2327921360594247,
-0.5356971614775387,
-0.47928430935840405,
-0.798767749507784,
-0.6396245488647935,
-0.3086129350788875,
-0.3677246932354574,
-0.7456954835551979,
-0.22384853085248987,
-0.48324441254608563,
-0.13589887748643367,
-0.8146562215548272,
-0.3619542648226693,
-0.5446483650757448,
-0.4887515583054699,
-0.5950380507954404,
-0.32379416155147234,
-0.4523735518951523,
-0.6235861610020692,
-0.8524078126999518,
-0.624992695451351,
-0.2687580135967621,
-0.9142029143532834,
-0.6659105307473407,
-0.5107419286693737,
-0.1977513307563077,
-0.9428853906456206,
-0.3253209568307786,
-0.22727349963052632,
-0.5793151779856947,
-0.23718711893540165,
-0.5271495158439357,
-0.6343520795149911,
-0.238815912969396,
-0.6990789188926911,
-0.24633171628795617,
-0.4062347602342654,
-0.13615609372168275,
-0.5216821949290152,
-0.4942204270716243,
-0.2220401390451773,
-0.020747595192913953,
-0.8214853052136477,
-0.6875869322752399,
-0.22152857450956379,
-0.29745642236257747,
-0.35784823104789754,
-0.5523106218284762,
-0.45943183381522734,
-0.468981548871973,
-0.7153616997835629,
-0.772736368649511,
-0.8434804313925567,
-0.5007809738640613,
-0.4066847172852109,
-0.684276716683085,
-0.9002068907942674,
-0.667093776343055,
-0.6130982621503599,
-0.7474263618159979,
-0.430559922478364,
-1.0427198734072751,
-0.483205252606335,
-0.744982998763404,
-0.015679896270428966,
-0.6994937694356036,
-0.45558564877217206
],
"z": [
-0.4545954885041011,
-0.5899574477424782,
-0.375197865153605,
0.1682924884456958,
-0.08817125765377914,
-0.08047498842614154,
0.22980061318870149,
-0.4157805329604104,
-0.017887586934806115,
0.8097303759161899,
-0.4320626189945605,
-0.08183797663196185,
-0.4722083805579565,
0.0062022309301678,
0.06790189611503132,
-0.15748984049905101,
-0.46789431163602063,
-0.38791808819307744,
-0.2275539825046795,
-0.052083608565449975,
0.07367079776003062,
-0.3901745789411522,
0.3268143517350413,
-0.2471782706345768,
-0.06053400767369111,
-0.26227182389688397,
-0.02117837642250375,
-0.21872512357277224,
-0.34200787972101354,
-0.22195248476442403,
0.0976665851578857,
0.2805073353192304,
0.01608808049475981,
-0.07741379829393705,
-0.4567618702638782,
-0.38382819842847093,
0.20460563535082982,
-0.11142748474737951,
-0.023012282481962906,
0.05656703042647703,
0.09072849162713938,
-0.408094798012628,
-0.2451805136088429,
0.31033239613279756,
-0.014443297202818596,
-0.3122644717846063,
0.0202061104406828,
-0.07104427525510186,
-0.34716608451653636,
-0.08838997796250964,
0.2599242548097161,
-0.6332312874885185,
-0.11994446932489598,
-0.31195250176623135,
0.38056271171491807,
-0.17107970612546938,
0.06504909573959074,
0.1837067002124125,
-0.31677437349110205,
0.4237928408286671,
0.3999442168114798,
-0.08277990721577871,
0.4130425328759305,
0.07761362684441199,
0.15476354159091274,
0.5301282624025921,
-0.04966518449337113,
-0.4472746641628041,
0.21943385306413754,
0.4585748536589704,
0.1844117131083236,
-0.4226826961449522,
-0.23607920098243718,
0.4266846619549208,
0.011887234031796028,
-0.22776883006989856,
0.2174174814884322,
-0.006512742370307224,
-0.12448491698919271,
0.3830195679989099,
-0.3938720974355373,
0.11126484569150269,
-0.14169394796059326,
-0.19807021553283854,
0.5665112051645512,
-0.08123366688839473,
-0.4964947958796984,
0.48012222680738503,
0.4390869615504073,
0.34192982211262174,
-0.5049303658681064,
0.011436050078022338,
-0.05592715097255995,
-0.5062403052038711,
0.5178021556047561,
0.38607304657816205,
-0.9839316193387816,
0.4460748082910173,
-0.1450393361733375,
-0.24671340624518207,
0.1551829197623859,
0.4165896653131426,
-0.3935170175969771,
0.2885709430847422,
-0.14958128438113144,
-0.43108199244953976,
-0.2606337398222067,
-0.24693646877020964,
0.10813915765383264,
0.13518059647637737,
0.19651078299353547,
0.3346796911053841,
-0.060596181559737526,
-0.5256967442468717,
-1.1861792293382316,
0.022210446281885947,
-0.2741377166130673,
-0.4329607367035386,
0.4640030953791651,
0.13026326435644048,
-0.06645446085975179,
-0.3996482491090819,
-0.2053049217090835,
-0.3459463620881171,
-0.3707133428718404,
0.421254230541472,
-0.25377508809291205,
0.04145555538328596,
0.008442803037008444,
-0.07954886513277742,
-0.6060228231921211,
0.40297190598893246,
-0.3345500153664418,
0.009314508920045116,
0.6762539966936302,
-0.5704179050362163,
-0.1263521998237061,
-0.5992108742481282,
-0.03055922421027146,
-0.006894548897019799,
0.028698166423031364,
-0.5868778162568317,
-0.3428405219264621,
-0.31804897105959457,
0.14047576518556426,
0.1621870659747589,
0.2666764979205449,
-0.2587345788840568,
-0.2996780212679969,
-0.057924612760875606,
0.29767223202878396,
-0.17534340712373664,
0.07070794042618732,
-0.44500398841395494,
-0.267968862636731,
-0.05255758081942998,
0.0565583671316676,
0.24126183681891547,
-0.0020810359384243267,
0.19623209142123266,
-0.8406633146074663,
-0.048996975156284116,
-0.07026224467836181,
0.1729559726741388,
-0.03472083447830932,
-0.07183391629938951,
0.030907159241310593,
-0.5146639782542198,
-0.2681773875251901,
-0.06651238269619006,
-0.1250370337516696,
-0.3361773924210964,
-0.025953243315192578,
-0.4296194382232437,
-0.5320245382085108,
-0.17041333533849645,
0.16091963598480377,
0.26581668122441876,
0.6243291094792643,
-0.039852850454125975,
0.1233749962893025,
-0.03720514296383549,
0.5129439437964421,
0.41688827522755195,
0.5987348634041113,
-0.2331818212548434,
-0.41906273638857544,
-0.3120140747503437,
-0.6152668968077735,
-0.16544483703260057,
-0.45977804613364187,
-0.10865200752603187,
0.29723065313205854,
-0.04422266407056089,
0.33761831070587955,
-0.09293972238725229,
0.34597696371912035,
-0.2794549704364716,
-0.11008558583045318,
0.3213873446582724,
0.6092451732713532,
-0.6816520613741289,
-0.4248047736780112,
-0.15061582346117763,
-0.0752043258239884,
-0.1882342000340685,
-0.5141744955788906,
-0.024630704470984584,
-0.2399428604451668,
0.12139437614213062,
0.3157993823910308,
-0.40021931119626775,
0.2505445672507751,
-0.4693214719766291,
-0.22383924741474912,
-0.22575315152544911,
-0.04861466429845294,
-0.2212081383829006,
-0.06861285189068105,
0.23569479312378133,
0.16811565221558888,
0.11401615820590842,
-0.7194575221612561,
0.36974896039673455,
-0.16868436560397904,
-0.15857431565435615,
-0.02628338462134717,
0.35126965063130694,
-0.17201050003768503,
-0.4118212302435588,
0.27982780230009946,
-0.04504790929274315,
-0.4074354340052161,
-0.12401995525303965,
0.6054957158891072,
0.0257881966172531,
-0.2199015049662167,
0.03787623151920525,
0.15535521303755573,
0.0628370328994742,
0.2509817419666257,
-0.2614458433245504,
0.19377589786497978,
0.44204477431855044,
0.22914314436270805,
-0.04173402297969279,
0.19554587396813483,
-0.0384808267975992,
-0.07005406333732585,
-0.5590390972855782,
0.03536153402827057,
-0.6691461270773521,
-0.09268908039319129,
-0.2442005558738212,
0.10898091290419629,
-0.00949291465747363,
-0.0657066354293465,
-0.21149239650364277,
-0.02318676218973342,
-0.2697122993347724,
0.2511952643304413,
-0.6856215247207155,
-0.006228224925896524,
-0.01254320889811459,
-0.18276657890939024,
-0.017519073285072472,
-0.35431721526433163,
-0.3001557409846582,
0.02927997602508509,
-0.42869605292695834,
-0.36688663103946617,
-0.04646354780349623,
0.35684284727564747,
-0.07549642843534005,
-0.07823661688303908,
-0.07819569657891356,
-0.35072978109652614,
-0.475954307213145,
-0.08352876261925338,
-0.13856299730485433,
-0.2227263213998339,
0.2849630839294529,
-0.22221095014307884,
-0.2669199298588034,
0.0024577648955696435,
0.12253874694708264,
0.3238425701922114,
0.007724159393919176,
0.38565434567494733,
0.2664415637982581,
0.10043080880014683,
0.18703257114041527,
0.26336187155565294,
0.09099831725989505,
0.087858625277845,
-0.26002760016044274,
-0.22239759297372758,
-0.3198790713896881,
-0.2964188689644238,
-0.5856969992262336,
-0.3360548679089505,
-0.31005555028898957,
-0.5034316231912971,
-0.17252409715170802,
-0.1457743794133612,
-0.2606478327205058,
-0.1464006814319549
]
},
{
"marker": {
"line": {
"width": 1
},
"opacity": 1,
"size": 4,
"symbol": "circle"
},
"mode": "markers",
"name": "outlier",
"type": "scatter3d",
"uid": "a56e0035-1ca8-4537-9017-2de37c50f9e0",
"x": [
0.3945269850866559,
0.3899816386849093,
0.5376430237789295,
0.3126053481835842,
0.6394085286953741,
0.3412604131901168,
0.224916487052315,
-0.31249569857206866,
0.07587755713390476,
-0.14839436819970808,
0.45055255429414875,
0.18621875216202735,
0.2358570976653463,
0.5184614446882938,
0.6138472775558009,
0.07386990439951267,
0.05317624716668619,
0.08700299505842657,
0.16209580758599393,
0.21438619717846197
],
"y": [
0.7650186372486267,
0.6825151590573117,
0.31451662807112185,
0.8300589335926524,
0.09610129282432836,
0.40055700433681757,
0.4570827758631466,
0.357803878072331,
0.2480038093644584,
0.914758577119137,
0.8666810346463998,
0.1300087543578536,
0.448299275221888,
0.09551735475562226,
0.2568793173482379,
0.43113887975635473,
0.10869751734142356,
0.3019601281792028,
0.8185073629393802,
0.42082947469885423
],
"z": [
3.485128410105509,
3.5703529027184797,
3.1381198608076377,
3.004078936814322,
3.1204921684307547,
3.151542431290013,
3.0082995060713014,
2.214309179793431,
2.97718513500447,
3.3624712682072184,
3.18276524089809,
2.6941237421617785,
3.17966511577167,
3.331803971780043,
3.193420078368326,
3.706015092793436,
3.1648719350008077,
3.315208068295153,
3.024594124166767,
2.7725981179425587
]
}
],
"layout": {
"margin": {
"b": 0,
"l": 0,
"r": 0,
"t": 0
}
}
},
"text/html": [
""
],
"text/vnd.plotly.v1+html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"names= [\"0\",\"1\",\"2\",\"outlier\"]\n",
"\n",
"fig_features= [go.Scatter3d(\n",
" x = global_data[[x for x in range(len(new_labels)) if new_labels[x] == i],0],\n",
" y = global_data[[x for x in range(len(new_labels)) if new_labels[x] == i],1],\n",
" z = global_data[[x for x in range(len(new_labels)) if new_labels[x] == i],2],\n",
" mode= \"markers\",\n",
" marker= {\n",
" 'line': {'width': 1},\n",
" 'size': 4,\n",
" 'symbol': 'circle',\n",
" \"opacity\": 1\n",
" },\n",
" name= names[i]\n",
" ) for i in list(set(new_labels))]\n",
"\n",
"\n",
"layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" )\n",
")\n",
"\n",
"fig = go.Figure(data=fig_features, layout=layout)\n",
"iplot(fig)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our final classification. We have successfully identified material from a foreign population, while at the same time correctly assigning other haplotypes to populations known to us (the bearers of labels).\n",
"\n",
"However, we can also observe that some haplotypes were wrongly labelled as outliers. This could be solved by lowering the outlier threshold, but that entails its own risks. Namely in regions where the outlier population is not as differentiated. In my opinion some degree of error will always exist. Classification should be treated an exploratory analysis, its errors to be identified and treated downstream - see post on **cluster profiles**.\n",
"\n",
"\n",
"Next up, Mis-labelling! Introgressions and what to do when the foreign material has seeped into our reference sets."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}