From a3458401c541b0f253741d403713a63b8a010655 Mon Sep 17 00:00:00 2001
From: criscuol <alexis.criscuolo@pasteur.fr>
Date: Wed, 3 Jun 2020 18:43:49 +0200
Subject: [PATCH] 0.21b

---
 README.md         |  31 +-
 example/clust.txt | 840 +++++++++++++++++++++++-----------------------
 example/plot.png  | Bin 36651 -> 29263 bytes
 3 files changed, 446 insertions(+), 425 deletions(-)

diff --git a/README.md b/README.md
index 37bcb85..f75ef97 100644
--- a/README.md
+++ b/README.md
@@ -172,7 +172,7 @@ nAUC aWallace2          0.999118  [0.996141 , 1.000000]
 The clustering based on the cutoff 0.007 seems robust to data subsampling, as the three estimated nAUC are quite high (e.g. > 0.75).
 However, the same clustering seems less robust to data perturbation, as the 2.5% CI are quite small for the silhouette and the first Wallace coefficient, e.g. < 0.4.
 
-**Searching for optimal clustering**
+**Searching for optimal clustering(s)**
 
 An optimal MST-based clustering can be defined by the cutoff value that maximizes the different estimated statistics.
 By considering every branch length from the minimum spanning tree in _data.graphml_ (see above) as a putative cutoff, _MSTclust_ can be used to display in standard output these statistics in a convenient tab-delimited format (option `-t`):
@@ -180,18 +180,37 @@ By considering every branch length from the minimum spanning tree in _data.graph
 grep "data" data.graphml | awk -F '[<>]' '{print$3}' | sort -g | uniq | 
   while read c ; do  MSTclust  -i data.d  -o out  -c $c  -L 2038  -B 9  -t ; done  2>/dev/null
 ```
-After observing the different outputted statistics (not shown), it seems that an optimal clustering can be obtained using 
-0.016691213 as cutoff. 
+After observing the different outputted statistics (not shown), it seems that an optimal clustering can be obtained using a cutoff between 0.010060363 (approx. 20/2038) and 0.048804782 (approx. 100/2038).
+_MSTclust_ can be used again to display the statistics associated to the clustering built from each of these cutoff:
+```bash
+for i in {20..100}
+do
+  c=0$(bc<<<"scale=9;$i/2038");  MSTclust  -i data.d  -o out  -c $c  -L 2038  -B 9  -t ; 
+done 2>/dev/null
+```
+This second set of tab-delimited statistics (not shown) demonstrates that using 0.03581943 as cutoff yields an optimal MST-based clustering (i.e. that maximizes all statistics derived from data perturbation and subsampling analyses).
 This can be summarized using the following command line:
 ```bash
-MSTclust  -i data.d  -o clust  -c 0.016691213  -L 2038  -B 9  -t  2>&1  |  tail -2
+MSTclust  -i data.d  -o clust  -c 0.03581943  -L 2038  -B 9  -t  2>&1  |  tail -2
+```
+This will output:
+```
+n   c           k  silhouette  noise silhouette [low avg up]  noise aWallace1 [low avg up]  noise aWallace2 [low avg up]  nAUC silhouette [low avg up]  nAUC aWallace1 [low avg up]  nAUC aWallace2 [low avg up]
+413 0.035819430 2  0.889605    0.851100 0.892771 0.923340     1.000000 1.000000 1.000000    1.000000 1.000000 1.000000    0.747542 0.894428 0.952076    1.000000 1.000000 1.000000   1.000000 0.997500 1.000000
+```
+
+Of note, previous analyses also show that the cutoff value 0.016192345 leads to a clear local optimum between 0.009813542 (20/2038) and 0.049067713 (100/2048).
+In consequence, the corresponding MST-based clustering can be also considered if the number of classes obtained from the optimal one (i.e. _k_ = 2, see above) is found to be too small.
+This second clustering can be summarized using the following command line:
+```bash
+MSTclust  -i data.d  -o clust  -c 0.016192345  -L 2038  -B 9  -t  2>&1  |  tail -2
 ```
 This will output:
 ```
 n   c           k  silhouette  noise silhouette [low avg up]  noise aWallace1 [low avg up]  noise aWallace2 [low avg up]  nAUC silhouette [low avg up]  nAUC aWallace1 [low avg up]  nAUC aWallace2 [low avg up]
-413 0.016691213 3  0.829778    0.763112 0.838848 0.918818     0.444911 0.977796 1.000000    0.998107 0.999338 1.000000    0.825384 0.899548 0.938995    1.000000 1.000000 1.000000   0.828055 0.978866 1.000000
+413 0.016192345 4  0.822087    0.739681 0.828704 0.904527     0.998107 0.993513 1.000000    1.000000 1.000000 1.000000    0.869052 0.903598 0.936799    1.000000 1.000000 1.000000   0.775950 0.970570 1.000000
 ```
-Details of the corresponding clustering (3 classes) is written into file _clust.txt_ (available in _example/_).
+Details of the corresponding clustering (_k_ = 4 classes) is written into file _clust.txt_ (available in _example/_).
 A silhouette plot can be easily drawn using the output of the following command line on _clust.txt_:
 ```bash
 grep -F " s=" clust.txt | sed 's/ s=//' | sed 1d
diff --git a/example/clust.txt b/example/clust.txt
index b50479b..c3d9320 100644
--- a/example/clust.txt
+++ b/example/clust.txt
@@ -1,423 +1,425 @@
 # n=413
-# c=0.01669121
-# k=3
-# s=0.82977824
+# c=0.01619235
+# k=4
+# s=0.82208711
 
-## cluster_1     n=402   s=0.83278240
-143  s=0.89825432
-85   s=0.89815314
-37   s=0.89815145
-74   s=0.89811303
-343  s=0.89792441
-86   s=0.89785800
-396  s=0.89541756
-298  s=0.89456357
-124  s=0.89423503
-378  s=0.89408981
-98   s=0.89394730
-170  s=0.89390835
-41   s=0.89390809
-334  s=0.88770005
-322  s=0.88763977
-336  s=0.88760053
-169  s=0.88760047
-401  s=0.88760031
-157  s=0.88759993
-151  s=0.88601817
-235  s=0.88600377
-340  s=0.88598133
-226  s=0.88586892
-144  s=0.88553706
-405  s=0.88528186
-181  s=0.88523413
-191  s=0.88509641
-253  s=0.88508710
-296  s=0.88505816
-16   s=0.88505004
-408  s=0.88498494
-282  s=0.88494903
-7    s=0.88491086
-276  s=0.88491082
-66   s=0.88487400
-208  s=0.88481098
-237  s=0.88480514
-39   s=0.88430297
-153  s=0.88411530
-72   s=0.88264892
-126  s=0.88204060
-140  s=0.88143228
-252  s=0.88136205
-67   s=0.88128918
-158  s=0.88121773
-99   s=0.88118281
-73   s=0.88118281
-163  s=0.88118193
-185  s=0.88114746
-200  s=0.88111037
-15   s=0.88111037
-12   s=0.88111037
-393  s=0.88103797
-115  s=0.87568758
-364  s=0.87532500
-407  s=0.87514509
-338  s=0.87511094
-177  s=0.87507125
-192  s=0.87499870
-283  s=0.87499782
-173  s=0.87485384
-387  s=0.87481860
-374  s=0.87478150
-194  s=0.87478082
-178  s=0.87470751
-161  s=0.87359261
-76   s=0.87357888
-132  s=0.87351307
-345  s=0.87316932
-399  s=0.87313918
-81   s=0.87310261
-375  s=0.87307435
-92   s=0.87303104
-274  s=0.87255919
-6    s=0.87249452
-230  s=0.87245748
-55   s=0.87244258
-409  s=0.87242326
-406  s=0.87242326
-370  s=0.87241431
-128  s=0.87241266
-206  s=0.87241252
-290  s=0.87238702
-127  s=0.87237623
-391  s=0.87234363
-344  s=0.87231243
-278  s=0.87231170
-272  s=0.87228193
-201  s=0.87227681
-245  s=0.87226769
-295  s=0.87223913
-82   s=0.87223112
-121  s=0.87220443
-137  s=0.87220420
-232  s=0.87220357
-270  s=0.87216656
-52   s=0.87216656
-31   s=0.87215535
-179  s=0.87209883
-10   s=0.87209628
-231  s=0.87209521
-175  s=0.87203458
-47   s=0.87178727
-17   s=0.87163787
-382  s=0.87161931
-347  s=0.87110186
-389  s=0.87105454
-83   s=0.87090626
-164  s=0.86998089
-101  s=0.86978062
-119  s=0.86978012
-404  s=0.86969943
-113  s=0.86969838
-400  s=0.86917035
-380  s=0.86910031
-168  s=0.86902814
-166  s=0.86892374
-381  s=0.86892243
-352  s=0.86888720
-139  s=0.86885197
-155  s=0.86885189
-109  s=0.86878288
-122  s=0.86878133
-183  s=0.86871211
-159  s=0.86871209
-104  s=0.86871080
-216  s=0.86857762
-196  s=0.86823079
-297  s=0.86703724
-330  s=0.86660966
-78   s=0.86657057
-331  s=0.86548614
-266  s=0.86373299
-149  s=0.86322457
-142  s=0.86272856
-49   s=0.86269319
-42   s=0.86262110
-213  s=0.86258008
-280  s=0.86254361
-267  s=0.86241688
-293  s=0.86233045
-165  s=0.86222207
-285  s=0.86195927
-152  s=0.86155977
-138  s=0.86118748
-333  s=0.86111735
-383  s=0.86111599
-277  s=0.86110932
-46   s=0.86079404
-79   s=0.86057596
-148  s=0.86021880
-33   s=0.86019292
-367  s=0.86017428
-281  s=0.86013522
-392  s=0.86011796
-359  s=0.86011254
-243  s=0.86004086
-335  s=0.85996651
-18   s=0.85996132
-105  s=0.85996084
-365  s=0.85993197
-112  s=0.85989825
-372  s=0.85988819
-339  s=0.85988819
-264  s=0.85987062
-90   s=0.85982600
-304  s=0.85976483
-302  s=0.85971821
-180  s=0.85971797
-221  s=0.85968328
-217  s=0.85957884
-204  s=0.85954408
-291  s=0.85950954
-96   s=0.85940198
-107  s=0.85901557
-110  s=0.85876651
-286  s=0.85858493
-244  s=0.85829192
-303  s=0.85822478
-64   s=0.85815688
-68   s=0.85814321
-254  s=0.85806914
-141  s=0.85801638
-354  s=0.85779538
-97   s=0.85777240
-114  s=0.85763390
-398  s=0.85756234
-388  s=0.85750140
-84   s=0.85697218
-203  s=0.85695166
-133  s=0.85679821
-123  s=0.85672995
-265  s=0.85163380
-225  s=0.85161286
-316  s=0.85142122
-25   s=0.85142112
-301  s=0.85139621
-320  s=0.85138558
-269  s=0.85138553
-321  s=0.85137460
-262  s=0.85074922
-260  s=0.85058498
-14   s=0.85051893
-215  s=0.85051385
-70   s=0.85044842
-58   s=0.85044842
-40   s=0.85044412
-385  s=0.85023382
-182  s=0.85012973
-292  s=0.85009299
-284  s=0.84988056
-329  s=0.84984652
-54   s=0.84984591
-8    s=0.84938597
-299  s=0.84929314
-195  s=0.84927013
-59   s=0.84893027
-273  s=0.84882479
-38   s=0.84879064
-75   s=0.84867535
-60   s=0.84864384
-246  s=0.84853303
-50   s=0.84850404
-162  s=0.84836231
-100  s=0.84832772
-44   s=0.84829549
-186  s=0.84816327
-210  s=0.84803842
-188  s=0.84800315
-56   s=0.84797376
-35   s=0.84794210
-207  s=0.84792141
-348  s=0.84790449
-289  s=0.84788846
-51   s=0.84743654
-11   s=0.84729519
-20   s=0.84675544
-350  s=0.84646689
-271  s=0.84576159
-69   s=0.84552037
-279  s=0.84541764
-361  s=0.84528200
-116  s=0.84524732
-147  s=0.84524613
-351  s=0.84517876
-187  s=0.84516535
-222  s=0.84510934
-288  s=0.84510903
-236  s=0.84489492
-174  s=0.84486905
-341  s=0.84003932
-323  s=0.83997345
-256  s=0.83990112
-318  s=0.83989680
-319  s=0.83986228
-317  s=0.83986228
-314  s=0.83977109
-184  s=0.83976077
-403  s=0.83965524
-229  s=0.83956283
-71   s=0.83955506
-250  s=0.83953735
-197  s=0.83875174
-306  s=0.83872536
-108  s=0.83865536
-263  s=0.83841422
-189  s=0.83824859
-145  s=0.83792224
-275  s=0.83786784
-120  s=0.83756081
-355  s=0.83753576
-287  s=0.83753495
-211  s=0.83750092
-346  s=0.83744383
-369  s=0.83742965
-356  s=0.83729554
-373  s=0.83671387
-62   s=0.83593853
-368  s=0.83589778
-88   s=0.83586696
-223  s=0.83508608
-77   s=0.83481174
-353  s=0.83475770
-357  s=0.83465939
-402  s=0.83458450
-134  s=0.83411138
-363  s=0.83383968
-160  s=0.83380661
-305  s=0.83353679
-255  s=0.83350269
-146  s=0.83343447
-219  s=0.83335839
-309  s=0.82905428
-313  s=0.82894967
-315  s=0.82868625
-308  s=0.82868625
-251  s=0.82852992
-248  s=0.82846167
-247  s=0.82846130
-23   s=0.82844604
-3    s=0.82837868
-257  s=0.82837739
-342  s=0.82833741
-312  s=0.82813618
-130  s=0.82800002
-234  s=0.82799453
-167  s=0.82796398
-36   s=0.82772334
-233  s=0.82765762
-48   s=0.82762442
-95   s=0.82708935
-227  s=0.82667815
-156  s=0.82643620
-61   s=0.82594375
-94   s=0.82594231
-397  s=0.82581265
-242  s=0.82547137
-371  s=0.82508870
-80   s=0.82477636
-193  s=0.82473934
-117  s=0.82429320
-135  s=0.82415146
-240  s=0.82407542
-258  s=0.82407338
-238  s=0.82400528
-205  s=0.82394608
-228  s=0.82362416
-45   s=0.82336730
-202  s=0.82224984
-63   s=0.82126097
-310  s=0.81835772
-307  s=0.81803689
-311  s=0.81792943
-214  s=0.81767199
-199  s=0.81741562
-241  s=0.81567181
-65   s=0.81544331
-172  s=0.81543692
-218  s=0.81543690
-377  s=0.81490001
-220  s=0.81486646
-395  s=0.81479891
-249  s=0.81458737
-13   s=0.81405246
-106  s=0.81374803
-22   s=0.81373053
-360  s=0.81322170
-136  s=0.81288298
-261  s=0.81287908
-102  s=0.81284974
-111  s=0.81275787
-198  s=0.81228949
-358  s=0.81159486
-259  s=0.81098264
-386  s=0.81075611
-24   s=0.80936262
-171  s=0.80639256
-154  s=0.80452136
-93   s=0.80445272
-376  s=0.80415445
-87   s=0.80411933
-190  s=0.80376578
-150  s=0.80154019
-212  s=0.80110144
-294  s=0.79617692
-125  s=0.79520744
-57   s=0.79316846
-89   s=0.79304017
-103  s=0.79234143
-384  s=0.79126037
-129  s=0.79106778
-43   s=0.78935000
-414  s=0.78534625
-91   s=0.78394775
-53   s=0.78361285
-366  s=0.78159332
-394  s=0.78097067
-379  s=0.77968901
-390  s=0.76884389
-26   s=0.74811280
-4    s=0.71702322
-131  s=0.69890047
-328  s=0.68702138
-30   s=0.68701967
-209  s=0.68670817
-2    s=0.66485392
-239  s=0.64841072
-411  s=0.62230583
-337  s=0.61921847
-176  s=0.61921768
-412  s=0.61529783
-325  s=0.51759181
-362  s=0.50438460
-27   s=0.47275294
-413  s=0.38401053
-349  s=0.37688457
-327  s=0.33924291
-332  s=0.31875402
-34   s=0.31348939
-32   s=0.30576043
-224  s=0.30412398
-118  s=0.27288434
+## cluster_1     n=2   s=0.97512282
+28   s=0.97527463
+21   s=0.97497102
 
-## cluster_2     n=5   s=0.82793797
-326  s=0.85681704
-1    s=0.83456644
-19   s=0.82185474
-410  s=0.81560084
-9    s=0.81085080
+## cluster_2     n=5   s=0.82492473
+326  s=0.85318993
+1    s=0.83225636
+19   s=0.81857605
+410  s=0.81212073
+9    s=0.80848059
 
-## cluster_3     n=6   s=0.63003300
-29   s=0.72546691
-324  s=0.72546498
-300  s=0.68082799
-268  s=0.61902163
-28   s=0.51521003
-21   s=0.51420649
+## cluster_3     n=402   s=0.82230651
+343  s=0.89160886
+143  s=0.89140390
+85   s=0.89129591
+37   s=0.89129410
+86   s=0.89125321
+74   s=0.89125309
+396  s=0.88968601
+298  s=0.88767608
+124  s=0.88732608
+378  s=0.88717137
+98   s=0.88701955
+170  s=0.88697805
+41   s=0.88697795
+334  s=0.88026518
+322  s=0.88018911
+169  s=0.88014720
+401  s=0.88014703
+336  s=0.88014689
+157  s=0.88014682
+151  s=0.87845998
+235  s=0.87843625
+340  s=0.87842069
+237  s=0.87838037
+226  s=0.87830083
+144  s=0.87794716
+405  s=0.87767503
+181  s=0.87762414
+208  s=0.87748017
+191  s=0.87747729
+253  s=0.87746736
+296  s=0.87743650
+16   s=0.87742785
+408  s=0.87735842
+282  s=0.87732013
+7    s=0.87727943
+276  s=0.87727939
+66   s=0.87724013
+153  s=0.87665634
+39   s=0.87651322
+72   s=0.87509538
+126  s=0.87444809
+140  s=0.87380062
+252  s=0.87372568
+393  s=0.87368855
+67   s=0.87364831
+158  s=0.87357226
+99   s=0.87353490
+73   s=0.87353490
+163  s=0.87353416
+185  s=0.87349747
+200  s=0.87345800
+15   s=0.87345800
+12   s=0.87345800
+115  s=0.86756724
+364  s=0.86718077
+407  s=0.86698890
+338  s=0.86695252
+177  s=0.86691045
+192  s=0.86683316
+283  s=0.86683242
+173  s=0.86667883
+387  s=0.86664108
+374  s=0.86660156
+194  s=0.86660125
+178  s=0.86652315
+76   s=0.86532017
+132  s=0.86525068
+161  s=0.86521048
+345  s=0.86487452
+399  s=0.86485237
+81   s=0.86481320
+375  s=0.86478331
+92   s=0.86473675
+55   s=0.86444480
+370  s=0.86432039
+272  s=0.86427449
+274  s=0.86423450
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+79   s=0.85160188
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+
+## cluster_4     n=4   s=0.71997276
+29   s=0.77528778
+324  s=0.77528653
+300  s=0.69240573
+268  s=0.63691100
diff --git a/example/plot.png b/example/plot.png
index 52427e8542c7741ec89d1e1ce2137ad5830c9b7e..2bf127400371f30715a7c107b6af6592a745c595 100644
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