Trains a kNN-based cell type classifier using a consensus cleaning approach. Core cells are iteratively validated across repeated cross-validation folds, and cells with low label agreement are reassigned as unknown before a clean reference set is returned for downstream prediction.
Usage
train_custom_knn(
spe,
label_col = "cutoff_label",
assay_name = "exprs",
unknown_label = "Unknown",
features = "all",
cv_folds = 5,
repeats = 10,
agreement_thresh = 0.8,
k = 5,
method = "pearson",
seed = NULL,
chunk_size = 250L,
BPPARAM = BiocParallel::SerialParam()
)Arguments
- spe
A
SpatialExperimentorSummarizedExperimentobject containing cell data.- label_col
Character string specifying the column in
colData(spe)containing the initial cell type labels. Default is"cutoff_label".- assay_name
Character string specifying the assay to use for marker expression. Default is
"exprs".- unknown_label
Character string specifying the label used to identify unknown or unclassified cells, which are excluded from training. Default is
"Unknown".- features
Either
"all"to use all features in the assay, or a character vector of feature names to subset. Default is"all".- cv_folds
Integer specifying the number of cross-validation folds used during consensus cleaning. Default is
5.- repeats
Integer specifying the number of cleaning repetitions. Higher values produce more stable agreement rates. Default is
10.- agreement_thresh
Numeric value between 0 and 1 specifying the minimum proportion of repeats a cell must be correctly predicted to be retained in the reference set. Default is
0.8.- k
Integer specifying the number of nearest neighbours used in the kNN classifier during consensus cleaning. Default is
5.- method
Character string specifying the similarity or distance metric used for kNN. Options include
"pearson","spearman","cosine", or"euclidean". Default is"pearson".- seed
Optional integer for random seed to ensure reproducibility. Default is
NULL.- chunk_size
Integer number of test cells processed per block inside weighted kNN calls. Smaller values reduce peak RAM with identical predictions at the cost of runtime. Default is
250L.- BPPARAM
A
BiocParallelParamobject specifying the parallel back-end to use for processing repeats. UseMulticoreParam(Linux/Mac) orSnowParam(Windows) for speed. Default isBiocParallel::SerialParam().
Value
A named list containing:
speThe input
SpatialExperimentobject with a newcleaned_core_labelcolumn added tocolData.reference_dataA data frame of marker expression for the high-confidence reference cells.
reference_labelsA factor of cell type labels corresponding to
reference_data.features_usedCharacter vector of feature names used in training.
agreement_ratesNamed numeric vector of per-cell agreement rates from consensus cleaning.
cleaned_core_namesCharacter vector of cell names retained in the reference set after cleaning.
Examples
# \donttest{
data("cytoGateR_example", package = "cytoGateR")
image_ids <- SummarizedExperiment::colData(cytoGateR_example)$image_name
spe <- cytoGateR_example[, image_ids == image_ids[1L]]
knn_ref <- train_custom_knn(
spe,
label_col = "core_group",
unknown_label = "Unassigned",
features = c("CD3e", "CD20", "CD4", "CD8a"),
cv_folds = 2,
repeats = 1,
agreement_thresh = 0.5,
k = 3,
seed = 1
)
#> Starting Parallel Weighted kNN (pearson) cleaning on 1378 cells: 1 repeats...
#> Aggregating results from workers...
knn_ref$model
#> $type
#> [1] "wknn"
#>
#> $reference_data
#> CD3e CD20 CD4 CD8a
#> 12_3 3.39524542 3.851551835 3.7690527 1.31929606
#> 12_5 3.63190149 2.208968932 4.0885094 3.34655186
#> 12_6 2.88635626 0.731263114 3.1678455 0.64633934
#> 12_7 3.29043193 0.514135659 3.5361918 3.04833577
#> 12_9 1.65156133 3.398517078 2.1278379 1.90416255
#> 12_11 3.30015985 2.477635317 3.5017847 0.67379731
#> 12_13 3.38077586 4.306358013 3.7829223 0.86453300
#> 12_15 2.54531930 0.385641125 3.1922603 2.31716134
#> 12_23 3.65804004 1.541835190 3.5091469 2.90039754
#> 12_24 1.60614095 3.847995900 2.3321351 1.15827669
#> 12_37 2.55274275 3.948812893 3.1361473 0.99348693
#> 12_47 2.84558778 2.505220414 3.0840434 2.13161177
#> 12_49 3.03144384 3.366224789 3.6915878 1.18287488
#> 12_58 1.06087532 2.844396712 2.3020521 0.18406926
#> 12_62 3.12832735 3.078581575 3.4391220 0.59235793
#> 12_63 2.57125727 3.581752891 3.2988136 1.52568553
#> 12_75 2.70266467 3.513692044 2.9887747 1.93200474
#> 12_79 2.95347237 0.393356033 2.9256643 0.80426471
#> 12_95 3.11381190 0.380383121 3.2596738 2.41544252
#> 12_96 2.42350934 0.243265940 1.8971045 3.34362015
#> 12_98 3.37136192 2.384952502 3.5045995 0.89990454
#> 12_102 1.35454157 2.572484608 2.1532115 1.51577010
#> 12_112 2.34152461 0.328133325 0.8071041 3.52664815
#> 12_116 2.48680709 2.535005809 1.5849888 4.00784719
#> 12_118 3.18729762 2.205462048 3.1327209 3.17687742
#> 12_124 0.67409585 2.077611625 2.2718086 0.31620918
#> 12_129 2.56551694 0.540046828 1.6359397 3.71561425
#> 12_130 0.79509920 2.077381516 2.5461322 1.26450708
#> 12_143 3.04854693 2.899180622 3.2162490 2.75893369
#> 12_147 1.77740750 0.344526269 2.7147578 0.62389545
#> 12_157 2.24704049 0.374963133 1.6075317 3.53415420
#> 12_164 0.84296519 1.427255636 2.0609265 0.74774986
#> 12_165 2.85599625 1.001197139 2.1711242 3.59564724
#> 12_170 3.00267000 2.706696955 3.3082859 0.81053761
#> 12_188 1.53433362 3.459703528 1.9483621 0.36021042
#> 12_194 2.72313696 3.360998953 2.9202694 1.45804978
#> 12_195 3.55419884 2.382665730 3.6684687 3.93098381
#> 12_205 2.88443128 0.258513588 3.3282617 1.26237383
#> 12_206 2.26256898 0.718893665 2.8857167 0.87581540
#> 12_224 2.20607753 0.029417743 0.9838715 3.41797946
#> 12_225 1.45451997 2.874572970 1.7982916 2.85186692
#> 12_230 2.75277323 0.410624754 1.0324720 4.17204171
#> 12_233 0.62760388 0.557151152 0.7020801 0.81473822
#> 12_235 1.00692130 2.517337999 1.1937401 2.52431383
#> 12_244 2.97819887 2.195791450 3.1581365 0.61739175
#> 12_252 1.98248941 0.427171080 1.4332777 3.35102049
#> 12_254 3.13394446 2.443098008 3.2470287 1.38589308
#> 12_256 3.40990168 3.217450622 3.5847728 2.63883246
#> 12_261 2.25996576 0.544256476 1.9977138 3.29169924
#> 12_263 3.02947974 0.400245861 2.4391191 4.03410294
#> 12_269 0.81678448 2.841318477 1.5380080 0.27282891
#> 12_290 1.69373783 0.466029870 1.9867571 2.84968981
#> 12_294 3.03079232 0.967136083 3.4537165 0.64626077
#> 12_297 3.00152244 0.715279503 1.6158174 4.25886788
#> 12_300 1.05938401 0.265648433 2.0709999 0.48012346
#> 12_313 2.98567391 3.883908259 2.8662500 1.86948522
#> 12_319 0.27283429 2.425274827 0.7364324 0.26925290
#> 12_331 1.12259406 2.901797619 2.3161604 1.03612824
#> 12_354 0.86760289 1.950535177 1.2110718 0.24543220
#> 12_359 3.08068630 1.881448431 3.1942084 3.43841494
#> 12_368 2.30684881 0.233800957 1.0777375 3.33002292
#> 12_371 2.57274905 0.232201554 1.9220153 4.11680310
#> 12_376 1.01366561 3.196756818 1.6534045 0.75186734
#> 12_378 2.95257296 0.286658459 3.1269515 1.37480885
#> 12_395 0.66652580 1.561294493 1.8126087 0.48654104
#> 12_397 2.48370310 0.273699329 2.9299173 1.99167866
#> 12_406 3.22512316 0.802719876 3.4088306 1.30613467
#> 12_415 1.01602745 2.731413863 1.2579362 2.74736338
#> 12_420 2.56589051 0.244015951 3.0598847 1.14844234
#> 12_433 2.61162248 0.209835374 3.0271530 0.86200237
#> 12_436 0.90793897 0.352673584 1.2657158 1.96055170
#> 12_440 3.12061091 0.746072836 3.0345781 4.01554282
#> 12_443 0.62692782 1.735211793 1.5211791 0.59080552
#> 12_451 2.20604174 0.421511122 1.7044813 3.68636366
#> 12_455 2.95887635 1.184451633 1.8468761 4.28476657
#> 12_458 0.69441150 2.458202927 0.8048531 1.90573834
#> 12_462 2.31904499 0.653233643 3.0833992 0.52487172
#> 12_472 0.65810412 2.257605097 0.7459851 0.56190398
#> 12_475 3.12138071 0.595199919 3.5308908 1.41403075
#> 12_480 1.08555206 3.529792461 1.5083299 0.56779038
#> 12_483 2.32737664 0.474308430 2.1262912 3.56047263
#> 12_489 1.01488035 2.547495133 1.7783361 0.99271071
#> 12_491 0.97141710 0.215524663 2.0478954 1.13116068
#> 12_497 2.06746796 0.321384822 2.6118024 0.30607473
#> 12_503 0.97220206 0.168126270 1.1101673 1.99745692
#> 12_513 2.50458204 0.334113607 3.0204749 1.12768614
#> 12_514 2.95697862 2.673150720 3.1644554 2.43281506
#> 12_520 1.08592671 2.566018131 2.6837906 0.43574644
#> 12_525 0.93495398 2.422409606 2.2794030 0.53674554
#> 12_537 0.23786273 0.479635862 0.9764825 0.26120810
#> 12_559 2.88899223 0.381467879 2.2074722 4.40401801
#> 12_566 0.57346978 2.619639521 1.8830152 0.43003528
#> 12_577 2.26173803 2.982957101 2.9163915 1.12796991
#> 12_587 3.01148836 2.341577775 2.7790890 0.47388167
#> 12_605 2.46836476 0.369679599 2.8108051 1.37675194
#> 12_610 0.70865806 0.164723459 1.9181387 0.06847232
#> 12_611 2.22257340 0.673213836 2.7349271 0.40954530
#> 12_626 2.52928820 1.087111571 2.9388479 0.22644278
#> 12_629 2.70179179 0.402024418 1.7420742 3.84305639
#> 12_630 2.98774988 0.234160756 1.6182101 3.94203985
#> 12_636 0.85440412 3.119992689 1.3658885 0.72604477
#> 12_637 1.02231367 2.980031497 1.6454626 0.67978699
#> 12_638 0.76163375 2.926043515 1.8966255 0.31084425
#> 12_639 2.79791720 0.805512939 2.8368845 0.58769610
#> 12_644 2.71652348 0.310621489 1.8930755 4.06396026
#> 12_662 3.02988114 2.149151283 3.1778298 3.18716561
#> 12_665 2.54276282 0.811307564 1.9070617 3.84099244
#> 12_666 1.43124672 0.237627809 1.3273654 2.73563142
#> 12_667 2.51237838 0.938771376 3.0823669 0.53760794
#> 12_671 3.07539741 0.413057304 2.4779868 4.08485739
#> 12_679 1.82568806 0.640987615 2.5276928 0.18787250
#> 12_688 2.94892771 0.451969279 3.3410098 1.83830395
#> 12_690 1.02427328 3.118635312 1.5522537 1.40412609
#> 12_700 2.34740287 0.549792522 2.0599634 2.94200192
#> 12_707 2.68380845 2.862278106 2.7762344 1.65475920
#> 12_717 2.35589355 0.384460569 2.1644255 3.87212986
#> 12_720 2.38433401 0.457982128 1.0535448 3.50105145
#> 12_721 2.23218454 0.410270837 1.6397915 3.48706384
#> 12_723 2.73334748 2.653263898 3.1258481 1.33752368
#> 12_729 1.77241935 0.539130493 2.8284365 0.96315702
#> 12_734 2.00694779 0.759052097 2.9935084 0.52207347
#> 12_736 3.55200327 0.588025686 3.8364510 2.42917774
#> 12_739 3.27105305 2.671088539 3.4488400 2.63607883
#> 12_746 2.74701498 0.388006437 2.9649467 0.25849018
#> 12_756 0.58058042 2.849545982 1.8014442 0.38181363
#> 12_783 2.14331182 0.219182537 2.5633765 0.41036074
#> 12_786 2.24194541 0.700743433 2.8610553 0.56198274
#> 12_798 3.01151040 0.860885762 3.3613150 0.56594344
#> 12_807 2.50865990 0.819669899 3.4610070 0.66302717
#> 12_809 2.79949761 0.528287128 3.2467790 2.12521939
#> 12_810 1.22429637 0.320866085 1.7359803 1.87863398
#> 12_812 1.95861997 0.429350253 2.9928636 0.72586158
#> 12_831 1.14642032 2.531189811 1.8729307 2.86853270
#> 12_840 1.40055240 3.008698537 1.9512889 2.04772164
#> 12_849 2.99465595 2.215234464 3.0708947 2.81366490
#> 12_856 2.49298302 0.361719272 2.7162116 0.78965821
#> 12_880 1.88991533 0.009314741 2.0270304 3.64822478
#> 12_894 0.26587456 0.315053695 1.7496790 0.19569360
#> 12_903 3.17745513 2.154498416 3.4504269 1.10125174
#> 12_919 1.88774944 0.533770513 2.7040797 0.62456352
#> 12_936 0.75058047 2.871108102 1.9378548 0.49232021
#> 12_937 3.07405285 2.856270629 2.7594373 2.46274669
#> 12_951 2.66024571 0.649507583 3.2105770 1.05145809
#> 12_958 3.38188009 0.646726231 3.3434971 0.48620756
#> 12_963 0.90207217 3.303483392 1.4077599 0.67502364
#> 12_968 2.45355447 0.665596249 2.6445271 0.64783647
#> 12_969 1.56541734 3.423645394 1.4286164 2.96176774
#> 12_975 0.22768194 0.120659805 1.5232430 0.34226668
#> 12_979 0.51934551 2.761185396 1.4468044 1.61984913
#> 12_983 1.99076187 3.310521654 2.5816172 0.33469434
#> 12_984 0.69278840 1.600668368 2.1335361 0.98945084
#> 12_994 2.54579677 0.202798791 1.6308690 3.64370900
#> 12_1003 2.37532085 0.272624302 3.0060797 1.08801852
#> 12_1005 2.29327556 0.255547705 1.5368322 3.85868518
#> 12_1008 0.92657207 0.306446865 1.6690259 0.99142229
#> 12_1009 3.01385055 1.028367745 3.1412395 0.68289081
#> 12_1013 3.01433885 0.453646601 3.2674666 0.88250393
#> 12_1021 2.83220311 2.574073104 3.2022192 0.58765033
#> 12_1024 0.41322235 2.287536080 1.5163035 0.32099032
#> 12_1032 2.44412140 0.209186470 2.9852144 0.44746868
#> 12_1033 1.32254465 0.201251938 2.1663944 2.33570410
#> 12_1036 0.52993444 0.638769658 2.0059872 1.49789295
#> 12_1047 2.56893301 0.281643244 3.2167342 1.01830496
#> 12_1052 2.43558942 0.615804115 1.0739891 4.11448979
#> 12_1058 2.64524771 0.182716169 1.6021372 3.44139423
#> 12_1059 2.27048697 0.733861745 1.3538863 3.59969048
#> 12_1061 0.95118818 0.234485973 1.7404338 0.36068031
#> 12_1063 3.21763947 2.420428325 3.2973944 0.20497151
#> 12_1064 3.37988751 2.827797976 3.3472617 0.58361187
#> 12_1067 1.14753949 2.434896327 1.9815302 0.56534551
#> 12_1078 2.69542412 2.719916756 2.4128251 2.93604749
#> 12_1086 0.59762163 2.190631719 1.3052965 0.87482813
#> 12_1093 1.14290843 2.148409020 2.5595339 2.84227962
#> 12_1096 0.24864117 0.114259662 0.9553849 0.25809105
#> 12_1105 0.23238663 0.178521764 0.7013208 0.14961266
#> 12_1109 2.48556387 0.584272236 2.9053410 0.60011454
#> 12_1116 2.88296023 0.459420736 2.9188045 0.46823646
#> 12_1118 0.83191352 3.225617308 1.4289171 0.25735610
#> 12_1120 3.10302884 2.831194507 3.4571181 0.69317395
#> 12_1123 2.79004882 1.585630087 1.3727381 3.88212443
#> 12_1126 3.35733065 0.543896975 3.6450481 3.16303818
#> 12_1128 1.35680200 2.806124135 2.5334622 0.88145774
#> 12_1133 0.60012919 2.236061006 2.3199293 0.66712368
#> 12_1136 2.61760449 0.358424203 3.1229984 0.66173311
#> 12_1137 2.65164859 0.242009747 2.8370395 0.51156109
#> 12_1142 2.91297137 0.679717999 2.9307126 3.01756930
#> 12_1149 2.90171844 0.579847153 1.6696083 4.50086972
#> 12_1150 1.82045144 0.229572807 0.9269260 3.03078124
#> 12_1151 1.29367370 0.581582433 2.5208092 0.49820648
#> 12_1167 1.69425063 0.192683250 2.7235670 0.48105319
#> 12_1169 1.18794446 2.631586148 1.3198741 1.80927050
#> 12_1170 1.86873791 0.148511871 2.4297523 0.46353507
#> 12_1177 2.38899903 0.585730647 2.8651157 0.62864899
#> 12_1188 0.49770111 3.344334609 0.7614464 0.32000366
#> 12_1197 2.40406557 0.406340712 2.9327141 0.41427056
#> 12_1199 3.19899797 0.314267486 3.4190433 1.55475194
#> 12_1203 0.31491551 0.183231908 0.7468275 0.61753888
#> 12_1206 3.16691009 0.518139461 2.4554933 4.34775478
#> 12_1219 2.78221285 1.360569991 1.8737940 3.66114327
#> 12_1224 2.43227973 0.314897368 1.3035823 3.63472610
#> 12_1233 2.04415360 0.271692063 1.3061108 3.31448181
#> 12_1250 1.98583511 0.701832179 2.5528422 0.48026900
#> 12_1257 1.64552564 2.688125582 2.6730500 1.25037738
#> 12_1262 3.37702859 2.472364036 3.6314808 1.12276193
#> 12_1270 3.20637977 2.880099952 2.8861168 1.64908948
#> 12_1274 2.36142443 0.556618420 2.8025634 0.81545814
#> 12_1276 3.32106803 0.527580434 3.5633804 2.82016389
#> 12_1277 2.42178232 3.299746578 2.6289638 0.50930530
#> 12_1283 2.59141233 0.340099793 2.2527085 3.59177744
#> 12_1285 2.11957054 0.269281430 2.6220805 0.68237496
#> 12_1286 0.55442853 2.369009696 0.9064342 0.72526313
#> 12_1289 2.93634903 2.171374455 3.1787144 0.74205123
#> 12_1290 2.25433777 0.587110171 3.1980228 1.27804446
#> 12_1292 2.92082416 0.563527988 2.3478854 3.93037854
#> 12_1302 0.67605034 0.171425864 1.6103090 1.73878284
#> 12_1303 2.69848984 0.449952974 2.9011522 0.63824173
#> 12_1308 1.21129756 2.857958263 1.7239155 1.96520949
#> 12_1318 3.34107810 0.690879043 3.8006611 1.47577540
#> 12_1320 3.01979073 0.664450004 3.4169041 1.28408589
#> 12_1326 2.55740811 0.268029426 2.8514265 0.39066270
#> 12_1336 2.82186822 0.628417023 3.1423001 0.50035412
#> 12_1345 3.16650992 0.357614603 3.1244354 1.67346377
#> 12_1346 0.50233913 0.255376877 1.3312143 0.53099077
#> 12_1354 2.02829494 0.424596795 1.8108539 3.37011329
#> 12_1355 1.96946902 0.341921048 2.6948101 0.32489117
#> 12_1358 2.40874418 0.308224591 2.8116472 0.87230922
#> 12_1367 3.00614016 0.541418055 2.8725389 0.26622135
#> 12_1369 2.88421028 0.626049511 3.2713067 1.03193762
#> 12_1372 2.35605823 0.317064684 1.7516640 4.06532554
#> 12_1379 2.77231519 0.725127195 2.9512846 0.22114390
#> 12_1382 2.67155053 0.603838976 2.8653484 0.28170743
#> 12_1398 1.16436351 2.463194586 1.7405506 0.60728332
#> 12_1402 2.77158724 0.448581899 2.9399337 1.53178846
#> 12_1403 3.48504269 2.135634106 3.6437644 3.14964489
#> 12_1408 2.04016970 0.331589537 2.8964571 1.03800373
#> 12_1421 2.36908362 0.562665242 1.7445407 3.83810111
#> 12_1434 2.42139334 0.729871181 2.4133465 0.41279906
#> 12_1449 3.15962361 0.538282135 3.3875785 1.53163715
#> 12_1453 0.72118940 3.380341497 1.2669193 1.15658582
#> 12_1456 3.01123097 0.459322048 2.2012724 4.02799014
#> 12_1465 3.07382490 3.247991573 2.9229130 3.43314558
#> 12_1472 2.56633542 0.426811416 1.8541720 3.82702010
#> 12_1482 2.65481867 2.871610106 2.8370386 0.59981381
#> 12_1484 1.34835897 2.341830596 2.1953649 1.70236951
#> 12_1487 2.80083577 0.723321881 3.0411153 0.71417385
#> 12_1493 3.46627437 0.371305476 3.4541247 3.45600077
#> 12_1495 1.84709668 0.339248910 1.2578111 3.23057186
#> 12_1496 3.11039185 3.028823712 3.1517158 1.60382802
#> 12_1502 3.21659411 0.592080859 3.3345883 3.56349226
#> 12_1510 3.43744901 1.194711158 3.0895501 3.83722902
#> 12_1512 2.99074982 0.639216692 2.9536173 3.94205576
#> 12_1516 3.03340009 0.519969073 1.8572698 4.43742161
#> 12_1518 2.79743985 3.128941947 2.1236814 3.79177959
#> 12_1527 2.85126817 0.666857258 1.7333313 4.40437090
#> 12_1540 0.55536265 2.968574694 0.9304286 0.34715891
#> 12_1545 2.89985091 3.524984258 3.1921065 1.09945466
#> 12_1555 3.02743637 1.952727080 3.3576982 0.83228031
#> 12_1562 2.94357584 0.390981720 2.9911151 1.74883341
#> 12_1567 0.59231713 3.353509406 1.1038209 0.83832845
#> 12_1577 0.41012619 0.240624806 1.3582224 0.41773811
#> 12_1578 2.60988586 0.182521611 2.8063897 0.26995590
#> 12_1579 2.39505765 0.226062115 1.9643744 3.69384939
#> 12_1581 2.95999317 2.400793939 3.1413919 1.68012711
#> 12_1594 0.84964705 2.897803874 1.7104783 0.90152590
#> 12_1596 2.90659257 3.199422468 2.7240263 2.97030569
#> 12_1597 3.50986487 0.584245838 3.5785410 3.43721157
#> 12_1598 2.77338917 0.488161898 3.2433190 1.43427085
#> 12_1601 2.94146819 0.275416723 3.1208330 1.01954043
#> 12_1608 3.46089492 2.989944603 3.4296987 3.66437974
#> 12_1614 2.69446960 0.452825276 2.0116009 3.98881896
#> 12_1621 2.72158641 3.330613235 3.0566712 1.16428983
#> 12_1623 3.01450414 2.762331454 3.2643229 1.30892976
#> 12_1636 2.51944785 0.517756988 0.8727619 3.45230978
#> 12_1641 0.30373828 0.064424046 1.5270879 0.16702489
#> 12_1651 2.73340236 3.022179204 2.6864417 3.53457400
#> 12_1653 3.10082565 0.691251022 2.9173555 3.41815990
#> 12_1658 3.47280457 1.727116902 3.3261044 3.38507705
#> 12_1677 3.26819351 3.509238562 3.3997120 2.55779293
#> 12_1680 3.27017558 3.020859855 3.4215887 1.92793310
#> 12_1682 1.44736420 2.759003166 2.3093494 2.63554443
#> 12_1685 2.68464344 0.819022646 1.8092255 3.93397839
#> 12_1687 2.41791667 0.690819663 2.1159942 3.80009239
#> 12_1693 2.19086928 0.376199632 2.8088296 0.67722079
#> 12_1700 2.76291381 3.161803544 2.9524211 2.17890633
#> 12_1701 2.99668643 2.280356004 2.8681149 1.14373732
#> 12_1702 3.06099784 0.789111131 3.0173360 1.02579134
#> 12_1703 1.90326481 0.531221560 2.1535528 3.16278651
#> 12_1707 2.35124890 0.497918122 0.9371583 3.73359984
#> 12_1714 1.01400047 0.197667423 1.8220938 0.48946020
#> 12_1717 2.80549754 0.437818867 3.0518510 1.40622383
#> 12_1733 2.87691943 3.166315016 2.8156163 3.79675224
#> 12_1735 3.04506803 0.287670175 3.1624984 0.82392576
#> 12_1736 2.55806158 0.392618159 2.4096316 0.68772920
#> 12_1740 2.70033214 1.160237820 2.0202111 3.70620020
#> 12_1743 3.19676745 0.466784324 3.3925131 1.61196166
#> 12_1744 2.69122959 0.286586225 2.9056695 0.53295449
#> 12_1746 3.11096396 1.519936907 3.2444676 2.54515817
#> 12_1754 3.36441808 0.814106648 3.5463532 3.74583727
#> 12_1789 3.40603200 2.433909699 3.3914999 3.78019299
#> 12_1799 2.73673826 0.665638535 3.5039125 2.85321337
#> 12_1807 2.73569264 0.748791725 3.0892326 2.22113521
#> 12_1809 2.57818594 0.410808466 2.2360785 3.54572311
#> 12_1813 2.95842056 2.430882150 1.5898977 4.53580082
#> 12_1818 2.85656291 0.488621982 3.2261841 1.69989220
#> 12_1826 2.10273156 0.247690407 2.5157229 0.37611471
#> 12_1830 1.40951619 2.787829933 2.0768195 0.35109082
#> 12_1832 2.63511375 0.205229625 2.5293096 0.89912358
#> 12_1837 2.93355122 0.482356826 2.9860523 0.48179042
#> 12_1846 2.29211263 0.176301295 2.5728135 0.50142034
#> 12_1856 0.83130886 2.777186367 1.5062662 1.77880509
#> 12_1857 3.03039990 2.981268078 3.4224977 2.16982410
#> 12_1866 0.31696059 0.106105487 1.7071593 0.10220367
#> 12_1868 3.06727735 0.278785839 3.1714357 2.73844307
#> 12_1875 0.39093551 0.302831797 1.8904613 0.38118718
#> 12_1885 3.40237742 1.273376462 3.5120717 4.25904059
#> 12_1891 0.98281753 2.979814793 1.8630180 0.23623625
#> 12_1903 3.57780864 1.096269680 3.4286150 4.37350038
#> 12_1925 3.14471399 2.744631836 3.5919826 1.99270383
#> 12_1928 2.62852744 1.018228278 1.5867797 4.19503961
#> 12_1932 2.19045251 0.502231136 2.5161989 0.67210353
#> 12_1935 3.26106742 0.647783496 3.5649141 2.62989308
#> 12_1938 2.93477531 3.545575252 3.1773698 2.30562577
#> 12_1947 3.55914473 1.971511375 3.5501724 3.93566023
#> 12_1950 2.89623019 1.872749207 3.2252001 0.92308337
#> 12_1958 2.84358798 3.149938306 3.1496388 0.99882495
#> 12_1960 2.32238998 1.108239841 1.4822064 3.69155375
#> 12_1964 3.32222472 0.616358749 3.4294545 3.05350724
#> 12_1971 2.31012408 0.465031830 2.3131746 3.43350895
#> 12_1977 3.20851934 0.668298237 3.4120592 2.51501856
#> 12_1980 3.79449358 3.023841975 4.0120552 1.81031266
#> 12_1981 3.26394232 2.372425011 3.3923060 2.00946669
#> 12_1989 0.18060618 0.303144790 0.6710799 0.24576549
#> 12_1991 3.19530510 0.610342582 3.4129560 3.20468409
#> 12_1994 3.61941665 1.668937085 3.7679248 3.34931607
#> 12_1995 3.23536528 0.728943147 2.7001571 3.50823794
#> 12_1996 2.68192188 0.057505217 2.7706275 0.42517849
#> 12_2006 2.06729049 0.111999867 2.4715992 0.32188652
#> 12_2007 2.94355771 1.996100986 3.4288446 0.88655427
#> 12_2013 3.06917474 2.713600473 3.3871891 2.44496216
#> 12_2027 3.41305673 2.728761931 3.8541215 2.36441385
#> 12_2028 3.17963111 0.625936454 3.2850774 3.21804117
#> 12_2032 3.02737704 2.746025199 3.3373040 2.44665277
#> 12_2036 2.64745325 0.321153514 2.1401435 3.70895771
#> 12_2041 3.41830661 2.906272839 3.3800588 2.27894796
#> 12_2042 3.35856526 0.705183070 3.4451053 2.81554772
#> 12_2047 2.40525476 0.660569140 2.8618780 0.64904753
#> 12_2050 3.26490736 3.228323115 3.0790474 4.11797508
#> 12_2060 2.89545311 3.349493205 3.1017657 2.14200983
#> 12_2076 3.01114242 3.180686049 3.3343371 2.42755368
#> 12_2081 2.22327500 0.679631127 2.8828881 0.61212022
#> 12_2084 3.43607258 2.542890263 3.5482396 3.21459473
#> 12_2088 2.54353827 0.311773166 2.9514590 0.39002680
#> 12_2090 2.84638181 0.458259098 2.9677401 2.29743263
#> 12_2091 3.16137041 2.688144135 3.2891923 1.29044683
#> 12_2096 1.85588441 0.727387585 2.7003147 0.47457553
#> 12_2097 2.30844831 0.199734365 0.6795948 3.78984407
#> 12_2100 3.14257685 0.736373516 3.2300961 2.70255459
#> 12_2104 2.02526837 2.644947346 2.4311127 2.25295288
#> 12_2105 0.31070302 0.569989780 1.1239968 0.23548910
#> 12_2109 2.78716924 2.411766658 3.2225142 2.14986860
#> 12_2111 2.54139778 2.916201180 3.0958511 1.93953052
#> 12_2112 3.62195992 1.604258479 3.5375501 3.92998523
#> 12_2114 3.26629440 3.671505438 3.5217432 2.62051417
#> 12_2119 1.13760442 3.843386553 1.0867399 2.03103420
#> 12_2131 1.10714594 0.090677106 2.2710928 0.28851689
#> 12_2132 1.78921527 3.065708411 2.3475475 1.19181214
#> 12_2134 2.69206599 0.223741886 2.1555743 3.40334335
#> 12_2137 2.21353164 3.797751608 2.5197766 0.79797786
#> 12_2139 1.38023837 1.938198846 2.3451588 1.00956246
#> 12_2140 2.60516012 0.386516312 2.8858738 0.27337021
#> 12_2142 3.29772400 1.603356901 3.4716638 2.88981190
#> 12_2144 3.12317213 3.137436158 2.6676763 4.10459765
#> 12_2145 1.70184423 4.065865719 2.2084007 1.09541788
#> 12_2147 1.18499429 0.068619855 1.2511740 2.60415139
#> 12_2148 3.73900160 1.136627166 3.5240781 4.30074765
#> 12_2157 3.16198606 1.814229085 3.1147714 3.38962565
#> 12_2161 2.58423199 0.907402928 3.1601840 0.53462807
#> 12_2163 1.75265578 0.847214934 1.2762002 3.13126679
#> 12_2164 2.70408485 3.383167646 3.1686160 0.82774468
#> 12_2170 2.93926920 2.428028437 3.1134370 0.97044046
#> 12_2178 2.56484064 0.203886456 2.5144763 0.78056413
#> 12_2180 2.42037205 0.172138262 2.9078507 0.18652699
#> 12_2185 2.84116153 3.115556314 3.2388913 0.82101001
#> 12_2190 2.76998829 2.831029159 3.1307669 1.08385097
#> 12_2191 0.84243836 4.350382074 1.5726664 1.04545997
#> 12_2192 2.45633096 0.217457800 1.9154928 3.70775718
#> 12_2193 0.84938339 1.475757935 2.0054233 0.49663180
#> 12_2196 2.63804907 3.253752460 2.8399629 0.84776542
#> 12_2198 2.06944210 0.354548526 2.6245630 0.36082546
#> 12_2199 3.01382263 0.705625198 1.5597059 3.74803203
#> 12_2207 1.35322128 3.551984527 1.7305628 0.78729861
#> 12_2212 0.93070348 0.302347456 1.8374294 0.44757178
#> 12_2213 0.91143110 3.508288993 1.3639916 0.71894298
#> 12_2217 1.65909872 3.738520504 2.1290463 0.54537268
#> 12_2221 2.25027194 0.457371229 2.3783464 0.36318985
#> 12_2228 2.58989770 2.986354702 2.8773663 1.69765416
#> 12_2229 0.38278203 2.913412724 1.0342424 0.36134062
#> 12_2234 0.72243967 3.904546230 1.0540997 0.49218098
#> 12_2244 3.24954733 3.573491456 2.9687092 4.12189179
#> 12_2252 0.80612528 2.329974056 1.4901638 0.50558717
#> 12_2260 2.35460030 0.363706338 1.9692638 3.54555323
#> 12_2262 3.00016824 3.573834294 3.3456910 2.40217367
#> 12_2266 1.83213619 3.885771232 2.3563239 0.58502037
#> 12_2267 0.53419152 3.482753437 0.8662347 1.00677737
#> 12_2271 1.92883251 0.244494698 2.6525502 0.27784035
#> 12_2272 1.26984715 4.351647499 1.9825527 1.55276041
#> 12_2273 2.08770015 0.148904495 1.5337095 3.77235211
#> 12_2274 3.13574376 0.422262958 3.0593653 2.36810222
#> 12_2283 2.89436526 0.307394964 3.1719608 2.07618228
#> 12_2285 2.69731614 3.493863219 2.9532428 0.67322585
#> 12_2289 0.82675040 0.545605314 1.3247411 0.61180251
#> 12_2290 1.04508457 3.756046133 2.2350006 0.52712782
#> 12_2295 0.30836848 0.250312676 0.9490682 0.34912438
#> 12_2300 3.44533534 1.986281028 2.8333130 3.25140322
#> 12_2301 3.06021809 2.144270564 3.3831614 1.18243432
#> 12_2312 0.22213671 0.258028546 1.5598215 0.22056841
#> 12_2315 2.71748504 3.673837020 2.1489797 3.89019383
#> 12_2318 1.78194526 3.933339901 2.9344311 0.64899544
#> 12_2319 1.84867692 4.113025663 2.4639007 0.66754116
#> 12_2323 0.66671308 4.309381741 1.3722521 0.71318489
#> 12_2324 2.55826639 0.159049789 1.6661923 3.66648754
#> 12_2330 2.44407452 0.395326725 1.7853183 3.48295343
#> 12_2334 0.96609843 3.019120332 2.1854688 0.44014724
#> 12_2339 2.61124292 0.202964721 1.5132223 3.79742813
#> 12_2353 3.11465560 3.457650661 3.0282502 1.49025829
#> 12_2354 3.19834180 3.547737562 2.2066568 4.19875029
#> 12_2356 3.42940944 2.880185632 3.4116768 2.17251690
#> 12_2357 2.64626531 2.433904883 2.9394817 0.51350460
#> 12_2358 2.99698645 2.872190643 3.1365456 0.18771892
#> 12_2360 0.31145782 0.104300640 0.9672498 0.12045340
#> 12_2365 0.76045737 1.450107788 1.7208177 0.20561964
#> 12_2366 0.26360643 0.663372229 0.8612754 0.35458814
#> 12_2367 1.08722162 3.877162125 1.3593075 0.86325868
#> 12_2373 3.33654016 2.536435474 3.4581468 3.50856677
#> 12_2377 2.58293653 0.248061065 2.8771090 0.32003885
#> 12_2382 1.88894869 4.141780373 2.0253656 3.27334246
#> 12_2389 1.73019360 3.630497317 1.9820342 2.70876580
#> 12_2393 0.39414690 0.401782406 2.2165117 0.47129215
#> 12_2404 2.97189028 0.445167086 2.6855574 2.85996953
#> 12_2407 0.15627324 0.058886580 1.1576816 0.12787803
#> 12_2409 2.63407691 3.229432251 2.4146926 3.68737050
#> 12_2410 3.28058336 3.916203736 3.3729665 1.26148186
#> 12_2414 1.10253684 4.446614198 1.6217466 1.95115560
#> 12_2417 2.89745151 2.648022021 2.5260832 4.03012693
#> 12_2423 2.76421310 0.731322871 2.9366853 0.40216121
#> 12_2429 1.44495328 4.191523929 1.0930678 2.72181334
#> 12_2431 2.89210543 0.435981512 3.2876481 1.41011922
#> 12_2432 2.63195816 4.262410376 1.1622880 3.27302550
#> 12_2433 2.73491827 3.263190900 2.0358882 3.91200887
#> 12_2438 2.72883016 0.760251386 2.7295460 0.26807318
#> 12_2449 2.27890855 0.465132726 2.4328999 0.30234535
#> 12_2453 3.08182924 2.749264813 2.9835604 3.07298366
#> 12_2456 2.47711009 3.666259538 1.9022601 3.77520236
#> 12_2458 1.63254769 4.394253477 2.0182236 2.29508340
#> 12_2459 3.34074432 0.503956523 3.4529678 2.92820318
#> 12_2462 0.03141788 3.044224813 0.9328931 0.49388975
#> 12_2463 1.33811884 4.103561948 1.3331080 1.34166803
#> 12_2469 1.66798932 0.374013253 2.4175727 0.18340734
#> 12_2473 2.55310131 0.187718444 2.7148328 0.62509591
#> 12_2480 2.71636887 3.640968021 2.7019043 1.09783277
#> 12_2484 2.99677884 3.431817344 2.3020787 3.48240494
#> 12_2486 3.09198737 2.025165957 3.0226711 3.48822397
#> 12_2503 2.18238944 2.634731304 1.2545556 3.73594582
#> 12_2504 1.43739267 4.125638579 1.8871398 0.46312497
#> 12_2507 2.69376074 4.220205012 3.0852017 0.82856379
#> 12_2517 2.16786671 0.364654999 2.6001416 0.85942812
#> 12_2518 2.45088789 0.720567914 3.0321027 0.99631733
#> 12_2524 3.28215673 4.215989279 3.0727603 0.64609261
#> 12_2526 2.72556873 0.370847793 2.8949294 0.33489036
#> 12_2530 2.47842761 0.578915679 1.9964108 3.36174690
#> 12_2537 2.74042772 2.990998381 2.5575767 3.67432795
#> 12_2544 1.73539896 4.148494187 1.8542854 2.35173575
#> 12_2547 2.95971006 0.306457551 2.2084784 3.65168219
#> 12_2562 1.77656847 4.090978359 2.1689254 1.27220173
#> 12_2573 2.60428246 3.062096640 2.6160108 2.75228468
#> 12_2575 1.66120862 0.510321167 0.6937867 2.88751551
#> 12_2578 3.56527751 4.040019274 3.5934708 0.98723092
#> 12_2587 1.36074262 4.026459240 1.6868410 0.84559826
#> 12_2598 1.99927536 0.745186839 2.8448023 0.30228879
#> 12_2600 3.13831531 2.681641464 3.2046640 0.68386483
#> 12_2601 2.91357861 2.268734128 3.1398003 1.41677045
#> 12_2605 2.37963403 0.579379732 2.6319479 0.33850402
#> 12_2608 3.35767231 3.416289581 3.0027058 3.87400664
#> 12_2616 2.05836425 0.112781020 1.9517975 0.71164789
#> 12_2624 0.74186028 2.975377894 2.1895144 1.31349196
#> 12_2631 2.91351967 3.841860165 2.6786774 1.00862004
#> 12_2632 3.27494484 2.549175172 3.5134451 0.48118379
#> 12_2637 2.57247906 3.572367929 3.1980670 0.44189921
#> 12_2645 2.22886855 0.142654805 1.5213523 0.33768322
#> 12_2649 2.99333475 4.004678824 2.4518395 4.08464894
#> 12_2654 2.90304452 2.761185502 3.0633417 2.35546777
#> 12_2658 2.77242653 0.504991674 3.4310501 1.28338559
#> 12_2663 2.72823231 2.342356338 3.2607897 0.43903895
#> 12_2664 3.07919031 2.632088602 3.4792250 2.05920764
#> 12_2667 1.33459507 4.147721238 2.0062557 0.98928223
#> 12_2670 2.93824451 0.470544975 3.1573760 0.24423689
#> 12_2671 1.49061084 3.579997820 1.9365102 1.75561297
#> 12_2676 2.22584537 0.243684554 2.6295312 0.41824074
#> 12_2680 1.56927884 3.907433365 2.5144818 0.73009212
#> 12_2683 0.17201244 0.254889050 0.8516917 0.16190025
#> 12_2695 3.10541597 0.218128884 3.3987254 1.54086418
#> 12_2699 2.99250538 1.870448127 3.0048293 3.32908091
#> 12_2701 2.96240510 0.400100625 3.3178165 1.53295188
#> 12_2703 0.11981311 2.941136019 1.3271992 0.21451901
#> 12_2707 3.01333764 0.496210335 3.3409491 1.39453407
#> 12_2711 0.53327510 0.267078212 1.1514394 0.93548072
#> 12_2712 0.17827368 2.244806006 0.7373989 0.08182279
#> 12_2714 3.00431006 3.226360470 2.7052014 3.47680514
#> 12_2716 0.58230367 3.059704868 1.4706095 0.41709474
#> 12_2718 2.40885663 0.192743354 1.6416917 3.83977168
#> 12_2726 2.59894462 3.284871146 1.5298767 3.79809060
#> 12_2733 2.36315886 0.321609083 3.0492029 1.06619622
#> 12_2739 1.74419548 3.860421573 2.2971042 0.80938121
#> 12_2742 0.52856338 2.118848741 1.3411576 0.44435311
#> 12_2750 1.33710242 3.081778226 2.0976837 0.17434370
#> 12_2756 0.33585398 0.198305397 1.8454510 0.21621018
#> 12_2764 1.69776244 3.851177686 1.2665124 3.29669177
#> 12_2773 2.11222960 0.241102061 1.4031221 3.55780233
#> 12_2774 1.31675663 2.953163473 3.1700683 0.58296992
#> 12_2778 0.47280749 0.522997314 2.4428611 0.41912830
#> 12_2782 3.03347131 3.326341238 3.2239772 0.94681181
#> 12_2785 3.24957059 1.969170973 3.5043990 0.66191956
#> 12_2788 3.03069249 0.701556228 3.2114721 0.38001406
#> 12_2793 1.18949090 0.263064524 1.0484491 1.84567595
#> 12_2797 2.75035601 0.887593080 2.9489299 1.00401850
#> 12_2799 2.56946940 0.337044711 1.7414234 3.98797919
#> 12_2811 1.13042608 2.744196180 1.4419714 2.53042814
#> 12_2812 3.06954956 2.648284440 3.1261368 0.54379718
#> 12_2815 1.42159826 3.277948069 1.5323240 0.87077973
#> 12_2816 2.54858662 0.186873609 1.5798201 3.61133139
#> 12_2821 2.57435245 0.379932422 1.9279577 3.74748907
#> 12_2824 0.85921217 1.962980593 1.5530560 1.11257191
#> 12_2827 2.72769927 3.608403279 2.9000200 1.08511673
#> 12_2831 0.32769965 0.339196826 1.4312344 0.33357280
#> 12_2833 3.44507773 2.928293687 3.5026933 1.34122714
#> 12_2855 1.48402734 0.303722693 2.7051406 0.18127152
#> 12_2872 2.23747351 1.030968896 1.6029905 2.68140773
#> 12_2874 2.30718927 0.509762187 1.6676281 3.60909084
#> 12_2882 1.99343598 0.282945483 2.2443458 0.26516303
#> 12_2895 2.56148811 0.253970893 2.9704304 0.26822483
#> 12_2896 1.44911269 3.492664513 1.6243221 1.14399511
#> 12_2899 2.49115662 2.893912820 3.0645388 0.54527625
#> 12_2903 3.18198380 2.432634348 3.1079195 3.12483111
#> 12_2904 3.12024598 2.334180634 3.3391364 0.69046994
#> 12_2908 2.96754532 0.764408723 3.1807901 0.58740172
#> 12_2910 0.74816549 0.381117201 1.0426865 1.42203865
#> 12_2912 3.33596009 3.220763840 3.2658329 3.90613507
#> 12_2913 2.89087882 0.754579304 2.7256599 4.06915798
#> 12_2916 2.03324593 0.065836473 1.8419311 3.74628946
#> 12_2920 2.86997602 0.401000265 2.9811656 1.49306369
#> 12_2923 2.47281449 0.306892403 2.9815831 0.82250644
#> 12_2932 1.99429198 0.327471966 2.4486894 0.40928267
#> 12_2938 0.91082218 0.345549187 2.0110715 2.30743107
#> 12_2943 0.82918478 0.278393326 2.3332916 0.57417370
#> 12_2953 2.74642887 0.552330493 1.8183624 3.90933545
#> 12_2958 1.09483916 2.317744089 2.1423296 1.08496001
#> 12_2959 2.22598276 0.236396065 2.5902075 0.28434653
#> 12_2963 2.76961445 2.598293409 2.9191370 0.81829469
#> 12_2966 3.02993783 0.602912678 3.0646194 0.27680370
#> 12_2967 0.68511693 0.380751098 1.8232082 1.48343886
#> 12_2977 0.28541555 0.392060218 0.6139215 0.30963192
#> 12_3013 0.48382167 2.826921625 1.3750229 1.09200292
#> 12_3014 2.77486662 0.333803962 2.9229813 0.73288678
#> 12_3015 0.42156269 2.511163436 1.6679524 0.41432189
#> 12_3019 2.51097410 0.313080481 2.7959072 0.95038300
#> 12_3022 3.11983940 0.936210733 3.2282850 0.48228913
#> 12_3023 2.86309455 2.512223738 3.2560665 0.55005946
#> 12_3027 3.42805509 1.634996209 3.5270306 3.23764500
#> 12_3033 2.45752955 0.427316724 2.8649125 0.67018757
#> 12_3037 1.10288266 3.509108543 1.1835836 3.23402005
#> 12_3045 2.63845497 0.352358296 1.6179340 3.55210229
#> 12_3049 2.47449291 0.330469487 2.1698765 3.90755711
#> 12_3051 2.11417411 0.174127515 2.6987719 0.37351328
#> 12_3052 1.99128996 0.497088451 1.8831620 3.48823394
#> 12_3054 0.83857831 2.906829087 1.5268717 1.19957922
#> 12_3062 0.83412158 0.323418116 1.0457000 1.48068839
#> 12_3065 2.83638756 0.419216672 3.1478965 0.73774542
#> 12_3069 2.42075656 0.504869059 1.6978280 3.80629684
#> 12_3074 0.82624426 3.120662932 1.4941345 0.31444711
#> 12_3094 2.99287291 0.879066700 3.3380445 0.88243938
#> 12_3095 1.69273640 0.391442522 0.9771849 3.12401303
#> 12_3102 2.36834565 0.166609826 2.8835735 1.81041593
#> 12_3104 2.42355693 0.261519592 2.7434515 0.37702517
#> 12_3107 2.06989596 0.413996607 1.5592928 3.45938113
#> 12_3110 0.84488260 2.919829420 2.1874238 0.70389647
#> 12_3122 0.62292053 1.671370007 1.0507916 0.41895792
#> 12_3128 1.89746640 0.201759989 2.3726975 0.19486654
#> 12_3135 2.12004545 0.578021353 1.1030343 3.89229397
#> 12_3137 1.96997742 0.141905798 2.3590699 0.31072141
#> 12_3145 0.74612590 0.294584555 1.5478363 0.28218977
#> 12_3150 2.61964520 0.542423844 2.4586585 0.11607295
#> 12_3155 1.86222929 0.374833422 2.7017299 0.50177200
#> 12_3161 2.01102402 0.284883476 2.5655345 0.38026828
#> 12_3187 2.40396383 0.156086511 2.8979272 0.84808116
#> 12_3188 2.19675381 0.200276995 2.1622178 0.14335924
#> 12_3191 0.56151547 0.625401357 1.8395897 0.30461055
#> 12_3194 2.53660252 0.786867008 3.0471928 0.30903414
#> 12_3213 2.68429209 0.225390882 2.7353432 0.23779561
#> 12_3215 0.91173091 0.378540796 1.6333562 2.02643571
#> 12_3226 0.88305347 1.772379353 1.8991783 0.54392956
#> 12_3243 2.43820804 0.210661451 1.4960824 4.01140538
#> 12_3246 0.54196971 2.921152585 1.2300077 0.44558885
#> 12_3257 1.37576740 0.356395920 2.7864090 0.63528011
#> 12_3260 2.23537856 0.397855898 1.0631358 3.76723896
#> 12_3264 2.19135584 0.434256728 1.6253161 3.43398194
#> 12_3268 2.23766869 0.156171604 2.7473314 1.71405253
#> 12_3271 2.44519424 0.660581538 2.8678870 0.63197238
#> 12_3274 2.48888965 0.108742250 1.2565880 4.01045763
#> 12_3279 2.57897685 0.560274483 3.3964909 0.99251269
#> 12_3293 0.83431379 2.723809792 1.8795375 0.62855153
#> 12_3298 2.51580161 0.182582100 1.7324963 3.94525197
#> 12_3302 2.77316592 0.396080636 2.4981087 0.68207254
#> 12_3310 2.32486840 0.528447774 1.9166828 3.57860506
#> 12_3311 1.04818141 0.344919134 1.0311005 2.21396879
#> 12_3318 2.08923998 0.283127472 2.7231776 0.88941427
#> 12_3341 0.77243231 2.466547501 1.9124704 0.35837943
#> 12_3349 1.03226114 2.655489085 1.8279551 0.38786248
#> 12_3363 0.26899832 2.595944738 1.4109224 0.23197696
#> 12_3373 2.09135577 0.135717284 2.3692319 0.57539507
#> 12_3378 1.16967306 0.343809881 1.3579955 1.83618767
#> 12_3381 2.48414352 0.771980580 1.0451444 3.66575766
#> 12_3404 2.03333606 0.191726671 2.2837582 0.39956813
#> 12_3411 2.64248709 0.568207103 1.4564857 3.61056543
#> 12_3416 1.47180765 0.687555052 0.8078917 3.21074823
#> 12_3417 2.43675575 0.303623817 1.9091291 3.86075635
#> 12_3444 1.33876178 0.180732194 0.5840136 3.21407294
#> 12_3446 1.76853747 0.167572521 2.3386644 0.29039605
#> 12_3448 0.70265531 0.433105185 1.8005932 0.33214056
#> 12_3454 1.22481780 3.395419575 1.4831202 2.16432724
#> 12_3460 2.06221205 0.336021955 1.5590308 3.39906155
#> 12_3462 2.87218577 0.336816506 2.3446501 3.70722233
#> 12_3486 0.40441205 0.268490849 1.1096351 0.40478918
#> 12_3496 0.70324530 2.797397627 1.7526187 1.35192810
#> 12_3499 2.56439501 0.251880318 2.9373913 1.97234170
#> 12_3501 0.58851706 2.503065019 1.0143348 0.15354971
#> 12_3504 2.80618993 0.183885530 0.6881539 4.14378580
#> 12_3518 0.59532994 0.264879018 1.8507417 0.15437847
#> 12_3520 1.11370988 2.255206356 1.9272847 0.98951981
#> 12_3532 2.36565780 0.291075931 1.4099555 3.21836519
#> 12_3554 2.40953942 0.489665844 2.6120769 0.33102501
#> 12_3555 2.57039867 0.233184034 2.5145956 1.08829920
#> 12_3557 0.30852343 0.187582813 1.3454729 0.22482383
#> 12_3564 0.13287617 0.235073390 0.4851177 0.10929892
#> 12_3576 1.86734107 0.417755696 2.3094136 0.24913208
#> 12_3593 0.24612512 2.668473097 0.7718899 0.36118748
#> 12_3602 2.15375763 0.439909967 1.1969496 3.63424226
#> 12_3608 2.59742494 0.340943237 2.4145894 0.40190618
#> 12_3609 0.90454053 3.598751574 1.9359229 0.47483522
#> 12_3612 2.53194683 0.469509639 1.7134244 3.41350829
#> 12_3618 2.47864766 0.224154424 2.4366971 0.23403850
#> 12_3619 1.04825440 2.823492776 1.8857949 0.19368463
#> 12_3634 1.96516379 0.142263140 1.0288571 3.70439146
#> 12_3639 1.19310778 3.251711226 1.7880693 2.13621233
#> 12_3651 2.84580850 0.272278732 3.1416376 1.42504813
#> 12_3658 1.69852725 0.216581855 1.6817878 0.26516653
#> 12_3671 2.88579820 0.122439049 0.9036057 3.59605949
#> 12_3674 1.22311421 0.202178412 0.8107090 0.31090399
#> 12_3679 2.06213202 0.038637127 2.0742838 0.09848215
#> 12_3691 2.22971786 0.154199215 2.4040590 0.26158344
#> 12_3699 2.62265982 0.301319227 1.3301235 4.05378407
#> 12_3701 0.27659434 0.126975555 1.5238851 0.11297058
#> 12_3702 0.42630026 0.112413728 1.1579355 0.10642281
#> 12_3705 2.66165438 0.216186180 1.4851726 4.39375422
#> 12_3723 1.22998673 0.246919057 2.4051184 0.41937597
#> 12_3731 1.80879676 0.492240729 1.4897330 3.74350071
#> 12_3737 2.45553473 0.279393784 1.0898573 4.11036206
#> 12_3738 2.40425399 0.261065257 2.0446328 3.87665049
#> 12_3741 2.53869381 0.302371987 2.8860962 0.18349954
#> 12_3755 2.20301339 0.420225043 1.7238101 3.65426223
#> 12_3761 0.30945727 2.688756945 1.4358974 0.21030418
#> 12_3766 2.35459599 0.218760235 1.1099428 3.34875980
#> 12_3774 2.78481050 0.688984180 2.0441677 4.19973394
#> 12_3779 2.02996518 0.159467220 2.2538211 0.45807596
#> 12_3782 0.97621785 2.931959300 2.2493001 1.51021242
#> 12_3784 2.40069010 0.500653846 1.4472614 4.16657625
#> 12_3785 0.58079514 2.376290238 1.3138921 1.04370164
#> 12_3789 0.76178056 0.222209351 1.8776329 0.31409160
#> 12_3794 0.13582601 0.323145134 0.8823789 0.36687514
#> 12_3795 0.53986880 2.662897289 1.6628448 1.16901926
#> 12_3799 0.46008189 1.860819458 1.0669980 0.23380084
#> 12_3807 2.42983821 0.454590136 2.1408690 3.75652493
#> 12_3812 0.22714516 0.244184198 1.7519630 0.20870036
#> 12_3815 2.60123995 3.039202059 2.7535611 1.97492263
#> 12_3833 2.39535270 0.387426089 1.9023863 3.21787194
#> 12_3845 1.18550125 0.225399343 1.0301441 2.70612439
#> 12_3846 2.78433061 0.342239417 1.9222407 4.03531277
#> 12_3850 2.65065561 0.304607627 2.8244253 0.32938117
#> 12_3853 1.11818151 3.925592253 0.9467433 2.45444777
#> 12_3858 2.07538027 0.176305309 1.7480182 2.80613518
#> 12_3868 2.41160740 0.439353087 1.3563043 3.95559844
#> 12_3869 0.43370139 0.463672295 1.9633592 0.42877647
#> 12_3874 0.33412608 3.444269173 0.5697548 0.17327407
#> 12_3881 2.32031722 0.149965535 2.5327947 0.22882343
#> 12_3887 2.10345909 0.053756692 1.6124190 3.86172069
#> 12_3894 1.25709304 0.283184186 2.1252781 1.31443685
#> 12_3898 1.97407088 0.267104694 1.9944772 3.62321994
#> 12_3899 2.62391597 0.407386684 1.8991837 4.01785487
#> 12_3901 2.65841137 0.730584859 2.7891902 0.98759877
#> 12_3903 0.47175887 2.458835423 0.5851774 0.23615914
#> 12_3904 3.30264566 0.634290613 3.2008901 3.29604696
#> 12_3905 1.31372109 2.097221307 2.2263486 0.70191892
#> 12_3912 2.19164436 0.212868519 1.2512980 3.54291503
#> 12_3916 0.55477366 2.473579675 1.2242001 0.44306915
#> 12_3918 2.68451974 0.320299942 1.6383548 4.22862679
#> 12_3931 0.83292651 1.763672519 1.6675786 0.29566421
#> 12_3935 0.34730755 0.238397523 0.6403026 0.07040518
#> 12_3936 0.44542657 0.286510760 1.6959237 0.33918666
#> 12_3948 1.96519738 0.073555035 1.3745739 3.16227497
#> 12_3949 0.94758098 0.325371882 1.2838048 2.23713230
#> 12_3950 0.59685605 0.151155071 1.4398578 0.08651630
#> 12_3957 0.97843431 2.965474223 1.1763210 0.32687344
#> 12_3960 1.15883772 2.638531554 2.0470688 1.37448227
#> 12_3961 1.86639622 0.295817252 0.4262592 3.46581086
#> 12_3976 1.91356862 0.536986898 1.1332627 3.12705311
#> 12_3979 2.35058948 0.697532151 2.8722061 0.72044370
#> 12_3994 2.27303393 0.401633812 2.8790936 0.98190483
#> 12_4008 0.34714827 3.202158284 1.8643362 0.44809959
#> 12_4023 1.35974878 2.756721840 2.0723915 1.58242554
#> 12_4025 0.75974437 0.098138532 0.7708707 1.72490313
#> 12_4029 0.43875222 0.194589999 0.9703337 0.37844860
#> 12_4035 1.49089343 0.323131676 2.6946112 0.30759676
#> 12_4038 2.84226995 3.740966168 2.8156926 1.83599638
#> 12_4049 0.93294123 2.488312255 1.6884265 0.92953945
#> 12_4057 1.88807512 0.339486253 2.7964047 0.42768016
#> 12_4062 2.83342902 1.090727371 1.7107142 4.35833897
#> 12_4064 0.99165021 3.897434575 1.0493261 2.10165150
#> 12_4073 2.42155285 0.755636011 0.9670032 3.60220305
#> 12_4074 2.10353619 0.195685378 2.4462742 0.20968767
#> 12_4085 1.31430666 3.370138474 1.7478499 0.74162140
#> 12_4087 2.23855451 0.205388784 2.5213920 0.23477211
#> 12_4092 0.60810759 3.492179620 1.6022236 0.16290690
#> 12_4097 2.84510601 0.524943708 1.6084570 4.21558394
#> 12_4102 1.89055441 0.138521023 2.3482873 0.22161259
#> 12_4106 2.19312502 0.580148536 0.7043942 3.45446065
#> 12_4108 1.69129680 0.473478546 1.6910615 3.09548576
#> 12_4111 2.20063047 0.115532006 1.5945368 3.65096228
#> 12_4118 2.35025258 0.124442639 0.2459261 2.88776491
#> 12_4131 2.96110451 0.613667463 2.6762790 4.03420420
#> 12_4134 1.26724264 3.775135863 1.7080491 2.20490165
#> 12_4136 2.08999740 0.062116773 2.4577631 0.19204210
#> 12_4145 0.86414548 0.328791904 1.7446319 1.89226569
#> 12_4146 2.18323312 0.167899598 2.3132762 0.19218387
#> 12_4158 0.40195928 1.912309611 1.6982393 0.25694525
#> 12_4169 0.91906763 2.122398491 2.4103039 0.93817554
#> 12_4171 0.98164840 0.226912170 0.6689186 2.48629028
#> 12_4191 0.91168110 0.178407039 1.7544910 0.21844513
#> 12_4195 0.84965799 2.187264165 1.8210990 1.08411341
#> 12_4196 1.65981668 0.096495381 1.9360401 0.20623295
#> 12_4197 2.73989775 0.144522676 2.5502419 0.32360119
#> 12_4198 2.65373646 0.559899927 1.3732416 3.85680462
#> 12_4203 2.11444190 0.454565108 2.3491841 0.56393569
#> 12_4205 2.39847111 0.115691989 2.7795739 0.22396531
#> 12_4208 0.80748200 2.784986962 1.9051554 0.38643962
#> 12_4215 1.17040176 0.646713606 1.3881374 2.10034024
#> 12_4227 2.81714911 3.533239544 3.0213273 1.47156381
#> 12_4228 2.48219352 1.117199445 1.4549568 3.71507958
#> 12_4242 0.86507451 0.475847896 1.5698565 0.57188261
#> 12_4258 3.28235976 3.014737280 3.2369107 0.72174001
#> 12_4272 0.32962778 1.108367007 1.9163940 0.26997313
#> 12_4275 2.94809444 3.128059959 3.1787084 3.06139857
#> 12_4277 2.54236076 0.051228374 1.4173419 3.88876095
#> 12_4283 0.10441834 0.335908091 0.4223475 0.26810865
#> 12_4285 3.21486598 0.602866445 3.1884038 0.48130739
#> 12_4295 0.25258876 2.780168868 1.1416978 0.39114186
#> 12_4296 2.77663525 3.513747880 3.1697817 0.67204576
#> 12_4298 2.70148796 0.359175614 3.0042472 1.21354587
#> 12_4299 0.85770720 0.050943796 0.6464345 1.89659923
#> 12_4303 3.03468495 0.259765225 2.4797700 3.74194820
#> 12_4309 0.28493048 0.058850276 1.9158733 0.28919125
#> 12_4310 2.58977409 0.197137695 2.7941478 0.15440266
#> 12_4311 0.61492236 2.490996628 1.9293615 0.73671577
#> 12_4312 2.47381271 0.057781124 2.6037676 0.33128647
#> 12_4323 0.92552673 0.294921823 1.7931547 2.28582356
#> 12_4326 1.22568568 2.715484396 1.1359372 2.31304629
#> 12_4332 0.99485409 0.163079403 0.5905375 2.10452083
#> 12_4339 2.54523895 3.590922288 2.8854741 1.74984663
#> 12_4341 0.18563219 0.059480933 1.4753756 0.17937350
#> 12_4343 0.60951171 3.196333869 2.2810551 0.58540244
#> 12_4344 0.36225394 1.802414318 0.8129301 0.42034617
#> 12_4350 2.72270278 0.302960937 2.7390172 1.35625000
#> 12_4353 1.57679073 3.416303993 2.1366347 1.13033774
#> 12_4356 1.23061296 3.606902355 1.6366368 0.26385491
#> 12_4357 0.47066805 2.586623369 2.1123380 0.33091301
#> 12_4363 2.11188436 0.131748355 1.2148484 3.73844685
#> 12_4371 2.23392250 0.170388188 1.0677254 3.75709886
#> 12_4372 0.26946259 2.168018446 2.0440562 0.00000000
#>
#> $reference_labels
#> [1] BnTcell BnTcell CD4 BnTcell Bcell BnTcell
#> [7] BnTcell Treg BnTcell Bcell BnTcell BnTcell
#> [13] BnTcell Bcell BnTcell BnTcell BnTcell CD4
#> [19] BnTcell CD8 BnTcell Bcell CD8 BnTcell
#> [25] BnTcell Bcell CD8 Bcell BnTcell CD4
#> [31] CD8 Bcell CD8 BnTcell Bcell BnTcell
#> [37] BnTcell CD4 CD4 CD8 Bcell CD8
#> [43] Plasma_cell Bcell BnTcell CD8 BnTcell BnTcell
#> [49] CD8 CD8 Bcell CD8 CD4 CD8
#> [55] Myeloid BnTcell Bcell Bcell Bcell BnTcell
#> [61] CD8 CD8 Bcell CD4 Bcell Treg
#> [67] CD4 Bcell CD4 CD4 CD8 BnTcell
#> [73] Bcell CD8 CD8 Bcell CD4 Bcell
#> [79] CD4 Bcell CD8 Bcell Myeloid CD4
#> [85] CD8 CD4 BnTcell Bcell Bcell Stroma
#> [91] CD8 Bcell BnTcell BnTcell CD4 Myeloid
#> [97] CD4 CD4 CD8 CD8 Bcell Bcell
#> [103] Bcell CD4 CD8 BnTcell CD8 CD8
#> [109] CD4 CD8 CD4 Treg Bcell CD8
#> [115] BnTcell CD8 CD8 CD8 BnTcell Treg
#> [121] CD4 BnTcell BnTcell CD4 Bcell CD4
#> [127] CD4 CD4 CD4 BnTcell Myeloid CD4
#> [133] Bcell Bcell BnTcell CD4 CD8 Myeloid
#> [139] BnTcell CD4 Bcell BnTcell CD4 Treg
#> [145] Bcell CD4 Bcell Myeloid Bcell BnTcell
#> [151] Bcell CD8 CD4 CD8 Myeloid CD4
#> [157] CD4 BnTcell Bcell CD4 Myeloid Bcell
#> [163] CD4 CD8 CD8 CD8 Myeloid BnTcell
#> [169] BnTcell Bcell BnTcell Bcell Bcell Myeloid
#> [175] Myeloid CD4 CD4 Bcell BnTcell CD8
#> [181] BnTcell Bcell Bcell CD4 CD4 BnTcell
#> [187] CD8 CD8 Myeloid CD4 Bcell CD4
#> [193] CD4 Bcell CD4 CD4 Myeloid CD8
#> [199] CD8 CD8 CD8 CD4 Bcell BnTcell
#> [205] BnTcell CD4 BnTcell BnTcell CD8 CD4
#> [211] Bcell BnTcell CD4 CD8 Bcell CD4
#> [217] Bcell CD4 CD4 Treg CD4 CD4
#> [223] Bcell CD8 CD4 CD4 CD4 CD4
#> [229] CD8 CD4 CD4 Bcell CD4 BnTcell
#> [235] CD4 CD8 CD4 CD4 Bcell CD8
#> [241] BnTcell CD8 BnTcell Bcell CD4 BnTcell
#> [247] CD8 BnTcell BnTcell BnTcell BnTcell CD8
#> [253] BnTcell CD8 Bcell BnTcell BnTcell Treg
#> [259] Bcell Myeloid Treg CD8 BnTcell Bcell
#> [265] BnTcell BnTcell Treg CD4 BnTcell CD8
#> [271] BnTcell BnTcell CD8 Bcell BnTcell BnTcell
#> [277] BnTcell BnTcell BnTcell Bcell CD8 CD8
#> [283] CD4 BnTcell BnTcell CD4 CD8 CD8
#> [289] Treg CD4 BnTcell CD4 CD4 CD8
#> [295] CD4 CD4 BnTcell BnTcell BnTcell BnTcell
#> [301] BnTcell CD8 BnTcell CD4 Treg Bcell
#> [307] CD4 Treg CD4 Bcell BnTcell Myeloid
#> [313] BnTcell Myeloid BnTcell Bcell BnTcell BnTcell
#> [319] CD8 CD4 BnTcell BnTcell BnTcell BnTcell
#> [325] BnTcell CD8 BnTcell CD8 BnTcell BnTcell
#> [331] BnTcell Stroma BnTcell BnTcell BnTcell CD4
#> [337] CD4 BnTcell BnTcell BnTcell BnTcell BnTcell
#> [343] CD8 BnTcell BnTcell CD4 BnTcell BnTcell
#> [349] BnTcell CD4 BnTcell Treg BnTcell BnTcell
#> [355] CD4 CD8 BnTcell BnTcell Stroma BnTcell
#> [361] BnTcell BnTcell BnTcell Bcell Myeloid Bcell
#> [367] CD8 BnTcell Bcell CD4 BnTcell BnTcell
#> [373] Bcell CD8 BnTcell BnTcell CD4 CD8
#> [379] BnTcell BnTcell CD4 CD4 BnTcell BnTcell
#> [385] Bcell CD8 Bcell BnTcell CD4 CD8
#> [391] Bcell Myeloid Bcell Bcell CD4 BnTcell
#> [397] Bcell Bcell BnTcell Bcell CD8 BnTcell
#> [403] Bcell Bcell CD4 Bcell CD8 BnTcell
#> [409] BnTcell BnTcell Tumor Bcell Myeloid BnTcell
#> [415] BnTcell Myeloid BnTcell Bcell Bcell Bcell
#> [421] CD8 CD8 Bcell CD8 BnTcell BnTcell
#> [427] BnTcell BnTcell BnTcell Stroma Bcell Bcell
#> [433] Bcell BnTcell Treg Bcell Bcell Myeloid
#> [439] BnTcell Myeloid BnTcell BnTcell Bcell BnTcell
#> [445] CD4 Bcell CD4 BnTcell BnTcell CD4
#> [451] CD4 BnTcell BnTcell Bcell BnTcell Bcell
#> [457] Bcell CD4 CD4 BnTcell BnTcell BnTcell
#> [463] BnTcell Bcell BnTcell CD4 CD4 BnTcell
#> [469] CD4 CD8 BnTcell Bcell CD8 Bcell
#> [475] BnTcell CD8 BnTcell Bcell CD4 BnTcell
#> [481] BnTcell CD4 BnTcell Treg Bcell BnTcell
#> [487] BnTcell BnTcell CD8 BnTcell BnTcell CD4
#> [493] BnTcell BnTcell Bcell CD4 Bcell CD4
#> [499] Bcell Stroma CD4 BnTcell CD4 Bcell
#> [505] CD4 Bcell Bcell BnTcell Bcell CD8
#> [511] BnTcell CD4 Bcell Bcell Bcell Bcell
#> [517] Bcell CD8 Bcell Myeloid BnTcell BnTcell
#> [523] CD4 CD8 CD4 CD8 Bcell BnTcell
#> [529] Bcell CD8 CD8 Bcell BnTcell Myeloid
#> [535] BnTcell CD4 CD8 CD8 CD4 CD4
#> [541] Bcell BnTcell BnTcell BnTcell CD4 CD8
#> [547] BnTcell CD8 CD8 CD4 CD4 CD4
#> [553] Myeloid Myeloid CD8 Bcell CD4 BnTcell
#> [559] CD4 Myeloid Stroma Bcell CD4 Bcell
#> [565] CD4 CD4 BnTcell BnTcell CD4 Bcell
#> [571] CD8 CD8 CD4 CD8 Bcell CD8
#> [577] Treg CD8 Bcell CD4 CD8 Treg
#> [583] Treg CD8 Bcell Bcell CD4 CD8
#> [589] CD4 Myeloid CD4 CD4 CD4 CD4
#> [595] Treg Myeloid CD4 CD4 Myeloid Bcell
#> [601] CD8 Bcell Myeloid CD8 CD8 Treg
#> [607] CD4 CD8 CD4 Bcell CD8 Treg
#> [613] CD8 CD8 CD4 Bcell Bcell Bcell
#> [619] CD4 CD8 CD8 CD4 CD8 CD8
#> [625] CD8 CD8 CD4 Myeloid Bcell CD8
#> [631] CD8 Myeloid Bcell Treg Bcell CD8
#> [637] Myeloid Bcell CD8 CD4 CD4 Myeloid
#> [643] Stroma CD4 Bcell CD8 CD4 Bcell
#> [649] CD8 Treg Bcell CD8 Bcell CD4
#> [655] Treg CD8 CD8 CD4 Treg CD8
#> [661] Myeloid Myeloid CD8 Myeloid CD8 CD8
#> [667] CD8 Treg CD8 Bcell CD8 CD8
#> [673] CD4 Bcell CD8 Bcell Myeloid Myeloid
#> [679] Bcell Bcell CD8 Myeloid BnTcell CD8
#> [685] CD8 CD8 CD4 Bcell CD8 CD8
#> [691] Myeloid Bcell Treg CD8 Myeloid CD8
#> [697] CD8 CD4 Bcell BnTcell Bcell CD8
#> [703] Bcell CD8 Bcell Stroma Myeloid CD8
#> [709] CD8 Myeloid Bcell Bcell CD8 CD8
#> [715] CD4 CD4 Bcell Bcell CD8 Myeloid
#> [721] CD4 BnTcell Bcell CD4 CD8 Bcell
#> [727] CD8 CD4 Bcell Treg Bcell CD8
#> [733] CD4 CD8 CD8 CD8 CD8 BnTcell
#> [739] Bcell Treg Bcell CD4 Bcell Bcell
#> [745] CD8 Myeloid Bcell Treg Treg CD8
#> [751] Treg Treg Bcell CD8 BnTcell CD8
#> [757] Tumor BnTcell Bcell BnTcell CD8 Stroma
#> [763] Treg Bcell BnTcell CD4 CD8 CD8
#> [769] Myeloid CD4 Bcell CD4 Myeloid Bcell
#> [775] CD8 BnTcell Myeloid Bcell Bcell CD4
#> [781] Bcell Bcell Bcell CD8 CD8 Bcell
#> 10 Levels: Bcell BnTcell CD4 CD8 Myeloid Neutrophil Plasma_cell Stroma ... Tumor
#>
#> $params
#> $params$k
#> [1] 3
#>
#> $params$method
#> [1] "pearson"
#>
#>
# }