#Loading packages needed for this assignment
library(tidyverse)
library(cluster)
library(factoextra)
library(patchwork)Activity 4.1 - Hierarchical clustering
SUBMISSION INSTRUCTIONS
- Render to html
- Publish your html to RPubs
- Submit a link to your published solutions
Question 1
Consider three data sets below. Each data set contains three “clusters” in two dimensions. In the first, the clusters are three convex spheres. (A convex cluster is one where all points in the cluster can be connected with a straight line that does not leave the cluster.) In the second, one cluster is a sphere; one is a ring; and one is a half-moon. In the third, two clusters are spirals and one is a sphere. Our goal is to compare the performance of various hierarchical methods in clustering different cluster shapes.
getwd()[1] "C:/Users/wi7536ul/OneDrive - Minnesota State/DSCI 415/notes"setwd("C:/Users/wi7536ul/OneDrive - Minnesota State/DSCI 415/Notes")three_spheres <- read.csv('Data/cluster_data1.csv')
ring_moon_sphere <- read.csv('Data/cluster_data2.csv')
two_spirals_sphere <- read.csv('Data/cluster_data3.csv')three_spheres_scaled <- scale(three_spheres)
ring_moon_sphere_scaled <- scale(ring_moon_sphere)
two_spirals_sphere_scaled <- scale(two_spirals_sphere)#scale data
three_spheres_scaled x y
[1,] -1.411334052 0.805032889
[2,] -1.127257595 1.441319079
[3,] -1.338252155 0.378070758
[4,] -1.018211868 0.135813907
[5,] -0.832121890 1.314227035
[6,] -1.060560073 0.287741076
[7,] -1.423269150 0.301487068
[8,] -1.318410610 -0.069372930
[9,] -1.308836374 0.331022336
[10,] -1.107870845 0.880431352
[11,] -0.959095921 0.507387617
[12,] -1.320732235 1.187631841
[13,] -0.904145839 -0.200098151
[14,] -1.463636086 1.820694760
[15,] -1.159600219 0.478830024
[16,] -1.443270595 -0.262490581
[17,] -1.285536570 0.985090571
[18,] -1.214477321 0.401923230
[19,] -1.146911086 1.090064454
[20,] -0.737357278 1.235936920
[21,] -1.434077385 0.372288976
[22,] -1.177641621 0.315578785
[23,] -1.148414403 0.981379186
[24,] -1.570104024 0.914766961
[25,] -0.965585300 0.633124418
[26,] -1.660606193 0.767502235
[27,] -1.274295837 0.821214083
[28,] -1.168515378 1.525537323
[29,] -0.743765844 0.204100082
[30,] -1.055675408 1.049565122
[31,] -1.212582455 0.462076360
[32,] -1.213084907 0.500922264
[33,] -1.457371374 0.800179329
[34,] -1.343987578 0.576688584
[35,] -1.277128574 -0.546937597
[36,] -1.230933309 0.552644568
[37,] -1.034898904 0.432132434
[38,] -1.030639952 0.697709318
[39,] -1.010870725 0.780243671
[40,] -1.409393894 0.793732674
[41,] -1.125321394 0.657786376
[42,] -1.080786924 0.437805876
[43,] -0.989196688 0.141595943
[44,] -0.928451689 0.599442908
[45,] -1.296687421 0.508185892
[46,] -0.795681913 0.631750513
[47,] -1.168380373 0.316703193
[48,] -0.949127007 1.038905553
[49,] -1.259757602 1.336575636
[50,] -1.229998573 0.995429002
[51,] -1.349950449 0.108737325
[52,] -1.492328571 0.229934556
[53,] -1.136693738 1.249479629
[54,] -1.065444614 0.420312294
[55,] -1.435278649 0.991925807
[56,] -1.139911083 1.058138586
[57,] -1.272984539 1.063478719
[58,] -1.193654338 1.395617496
[59,] -1.130471748 -0.063418825
[60,] -1.326250079 0.783662033
[61,] -1.149694829 0.929367023
[62,] -0.774529422 0.253398214
[63,] -1.286210640 -0.193155004
[64,] -1.021504525 0.085826155
[65,] -0.762843640 1.264056988
[66,] -1.362263182 0.326100345
[67,] -1.139693736 0.262204566
[68,] -1.102982696 0.393852619
[69,] -1.387761744 0.182581255
[70,] -1.208356446 0.652893456
[71,] -1.434304438 0.380085869
[72,] -1.304908432 0.425992896
[73,] -1.224950568 0.011395061
[74,] -0.919124515 0.670200623
[75,] -0.933503626 0.377688983
[76,] -1.214467871 0.112034009
[77,] -1.175375870 0.378071541
[78,] -1.038026634 1.010222479
[79,] -1.525834636 0.302197316
[80,] -1.497698027 0.376002663
[81,] -1.311701537 0.988160993
[82,] -1.375658062 1.130771159
[83,] -1.484651321 -0.407079922
[84,] -0.978065433 0.529387010
[85,] -1.242475907 0.112858733
[86,] -1.640657425 1.076660686
[87,] -1.164383151 0.850416106
[88,] -1.014346685 0.459098455
[89,] -1.098861772 0.140854394
[90,] -1.265844850 0.872692561
[91,] -0.679899558 1.020280573
[92,] -1.048489655 0.361556491
[93,] -1.486777837 0.667180540
[94,] -1.059538990 0.859952727
[95,] -0.872772350 1.477486214
[96,] -1.554952923 0.673623186
[97,] -1.222876911 0.537936279
[98,] -1.115395962 0.425231007
[99,] -0.985368133 0.299560920
[100,] -1.305022013 0.937047000
[101,] -0.252000999 -0.968729051
[102,] 0.144858339 -1.567044631
[103,] -0.343154884 -1.288396899
[104,] 0.103352784 -1.934997793
[105,] -0.153720810 -1.276659043
[106,] -0.276785186 -1.365252714
[107,] -0.221847263 -0.971129745
[108,] -0.130406673 -1.205511925
[109,] 0.075499712 -1.786756833
[110,] 0.176128434 -0.805285871
[111,] -0.060680395 -0.787419745
[112,] 0.184773093 -1.571174248
[113,] -0.003591957 -1.431314280
[114,] -0.598965297 -1.263674977
[115,] -0.018092694 -1.238987184
[116,] 0.217675811 -0.594634558
[117,] 0.101955569 -1.166352434
[118,] -0.382734400 -1.613163986
[119,] 0.097004053 -1.467711695
[120,] 0.310379715 -1.609401660
[121,] -0.322003089 -1.105162315
[122,] 0.169625898 -1.108802946
[123,] 0.054021763 -1.548691553
[124,] 0.060111910 -1.618222030
[125,] 0.072418524 -1.119889862
[126,] 0.021006611 -1.354630737
[127,] -0.184547337 -1.902596024
[128,] -0.121125447 -1.053370892
[129,] -0.225281610 -1.932555926
[130,] -0.061562395 -1.331162211
[131,] 0.090079947 -1.425461689
[132,] 0.074410453 -1.334539298
[133,] 0.371545862 -1.122321978
[134,] 0.069406509 -1.875057324
[135,] 0.502342408 -2.322166405
[136,] -0.393737823 -1.273931254
[137,] -0.011929727 -1.175007936
[138,] 0.180917148 -2.174331832
[139,] -0.340554792 -0.691093569
[140,] -0.265289990 -1.616915663
[141,] -0.139862376 -0.997495684
[142,] -0.186999615 -0.891117709
[143,] -0.071294844 -0.419246027
[144,] 0.089649871 -1.370441473
[145,] -0.037077038 -1.150818580
[146,] -0.212717930 -0.487534233
[147,] -0.252181538 -1.622021731
[148,] 0.198196353 -1.320158105
[149,] -0.222582135 -1.012236547
[150,] 0.250062286 -1.375066995
[151,] -0.370411244 -1.591503281
[152,] 0.147614477 -0.928518793
[153,] 0.443362910 -1.226703183
[154,] -0.332171084 -1.072841423
[155,] 0.095000756 -1.307685426
[156,] -0.135964480 -1.303852134
[157,] 0.300263111 -0.794556394
[158,] 0.639715203 -0.406912162
[159,] -0.027601187 -1.427406553
[160,] -0.226603801 -1.231538968
[161,] -0.522471189 -0.881428858
[162,] -0.416212875 -1.532887118
[163,] -0.100512523 -1.533617295
[164,] -0.282766415 -1.864571263
[165,] 0.119623318 -1.198932187
[166,] 0.479155857 -2.141936495
[167,] 0.419649882 -0.580424802
[168,] -0.108382824 -1.979670925
[169,] 0.031469582 -0.674620483
[170,] -0.202292564 -0.656673276
[171,] -0.007553065 -1.716269172
[172,] 0.143240290 -0.822512317
[173,] -0.089287238 -1.337411976
[174,] 0.357221789 -1.970531025
[175,] -0.158483826 -0.876328021
[176,] -0.107808147 -1.909868330
[177,] -0.034709542 -0.880202025
[178,] 0.262720503 -1.235676612
[179,] -0.089241811 -1.515715747
[180,] -0.169402820 -1.343961028
[181,] -0.302366518 -0.639275109
[182,] 0.257644809 -1.150420111
[183,] -0.099387392 -1.005148541
[184,] 0.413508078 -1.052597478
[185,] 0.119178280 -0.734289926
[186,] -0.186772512 -1.349168040
[187,] 0.386155959 -0.820885204
[188,] -0.102647302 -0.894348159
[189,] 0.065899531 -1.482424777
[190,] 0.193202318 -1.559690403
[191,] 0.316140879 -1.416040997
[192,] -0.076597243 -1.521457315
[193,] 0.330787690 -0.923502217
[194,] 0.182303195 -1.538317800
[195,] 0.349922549 -1.215419621
[196,] -0.023460214 -0.787265273
[197,] -0.231642828 -1.430270514
[198,] -0.062664983 -0.889113799
[199,] 0.406150959 -2.229077798
[200,] -0.223173283 -1.657654775
[201,] 1.007631829 0.219343929
[202,] 1.198731664 0.578656578
[203,] 0.614601122 0.704806258
[204,] 1.261798246 0.464081734
[205,] 1.177115191 0.891151414
[206,] 1.605950469 1.613361738
[207,] 1.294270880 0.805669074
[208,] 1.045808260 0.221639559
[209,] 0.913102817 0.293109773
[210,] 1.044056920 -0.169906184
[211,] 1.145240937 0.274159648
[212,] 1.315436232 0.904016983
[213,] 1.310155624 0.470787822
[214,] 1.038682681 0.898286994
[215,] 1.059676358 0.910460842
[216,] 1.641968636 1.002385986
[217,] 1.471561806 0.639679018
[218,] 1.103185765 0.978989575
[219,] 1.181321855 0.328557571
[220,] 1.227193177 0.905481741
[221,] 0.745108226 0.940911997
[222,] 1.158123130 0.598872214
[223,] 1.253634106 0.431784449
[224,] 0.881587734 0.796582968
[225,] 1.172216106 0.639182304
[226,] 1.644792489 1.103989707
[227,] 1.142013453 1.216358995
[228,] 1.289972940 0.489368699
[229,] 1.571771595 0.725985755
[230,] 1.293379349 0.112039644
[231,] 0.817010004 0.216391891
[232,] 1.348564113 1.400400468
[233,] 1.244766754 0.374068331
[234,] 1.409756572 0.318862829
[235,] 0.969866291 0.611274002
[236,] 0.983717514 0.423892868
[237,] 1.157724604 0.802097782
[238,] 1.283345051 0.844359091
[239,] 1.465806637 1.102689195
[240,] 1.194812161 1.261467584
[241,] 1.054850646 0.715311853
[242,] 0.970821603 -0.026027598
[243,] 1.116015710 0.590801799
[244,] 1.355150936 0.476861680
[245,] 1.391340084 0.905425959
[246,] 1.309577029 0.889800916
[247,] 0.925198552 -0.023888055
[248,] 1.489590299 0.838573509
[249,] 1.333541031 0.338378634
[250,] 1.409121590 0.696612651
[251,] 1.289351172 1.008402587
[252,] 1.168281721 0.704377989
[253,] 1.479188160 0.300078481
[254,] 1.384324710 1.026572842
[255,] 1.221590442 0.147970731
[256,] 1.170107228 0.535392100
[257,] 1.236911810 0.639172274
[258,] 0.905783809 0.084234680
[259,] 1.250517108 0.392236396
[260,] 1.236998153 0.851264341
[261,] 0.997657837 1.002874851
[262,] 0.345776532 0.635943069
[263,] 0.946780707 0.720191962
[264,] 1.501588421 0.472869936
[265,] 0.872904138 1.166638578
[266,] 0.740354056 1.343485457
[267,] 0.902563416 1.775666581
[268,] 1.484517618 0.592374875
[269,] 1.493350966 0.151900108
[270,] 1.329263874 0.618014693
[271,] 0.887249076 -0.029790788
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[273,] 1.520720520 0.992410431
[274,] 1.308163413 1.449703520
[275,] 1.349584953 0.304817165
[276,] 1.001356752 1.046770967
[277,] 1.331810664 1.732025420
[278,] 0.839206393 0.381771173
[279,] 1.144347501 0.650505835
[280,] 1.529586427 0.600955159
[281,] 1.680315705 0.814657494
[282,] 1.054157460 1.537768370
[283,] 1.213312168 0.657211564
[284,] 1.075201948 0.340567793
[285,] 1.367064974 0.837915855
[286,] 0.855138223 0.605091142
[287,] 1.516783738 0.569582586
[288,] 1.300136350 0.426842834
[289,] 1.536339452 0.402040991
[290,] 1.689460306 0.413954848
[291,] 1.098995359 0.308433873
[292,] 1.067691672 1.025685731
[293,] 0.956178271 0.768165796
[294,] 0.967785831 1.493028680
[295,] 1.281162938 0.152935840
[296,] 1.320755400 0.497173988
[297,] 0.516491265 0.141958597
[298,] 1.132294050 0.660774757
[299,] 1.078624692 -0.005884354
[300,] 1.228482493 0.320439966
attr(,"scaled:center")
x y
1.999322 3.673370
attr(,"scaled:scale")
x y
0.8404729 0.5111479 ring_moon_sphere_scaled x y
[1,] -0.0820430376 0.3524628761
[2,] -1.0362391860 0.3347140326
[3,] -0.3780018454 0.7331806618
[4,] -0.3144549278 0.7215695800
[5,] -0.7164977140 0.9166999991
[6,] -0.7340515883 0.7728938063
[7,] -0.0201078204 0.1102329545
[8,] -0.1697089677 0.6045398567
[9,] -0.7548899323 0.7972152996
[10,] -0.7962178792 0.7714065086
[11,] -0.6581908489 0.8519788552
[12,] -0.5326493805 0.8368526410
[13,] -0.6539402617 0.7369631364
[14,] -0.7087296219 0.7973564793
[15,] -1.1273964770 0.1071425174
[16,] -1.1036722962 0.2971230754
[17,] -0.0735640436 0.0897845054
[18,] -0.9444282787 0.6279114364
[19,] -1.1257409841 0.0864163852
[20,] -0.1652378955 0.6527438023
[21,] -0.1122175298 0.4149469137
[22,] -0.0170305242 -0.2355802365
[23,] -0.0462259422 0.1364840209
[24,] 0.0515315797 0.0610744398
[25,] -0.1228048202 0.5159922851
[26,] -1.0676106419 0.5443796104
[27,] -0.6690496762 0.8517367832
[28,] -1.1139660796 0.0846610469
[29,] -0.6512052120 0.8431183005
[30,] -0.9553379365 0.5015976902
[31,] -0.3420393808 0.8207845539
[32,] -0.3366306947 0.8882344706
[33,] -0.0906526325 0.3435839284
[34,] -0.5184707758 0.9299725642
[35,] -0.0904549584 0.6449023629
[36,] -0.2970058684 0.6868591278
[37,] -1.0897897370 0.1043331186
[38,] -0.0656980557 0.3765139809
[39,] -0.6628115110 0.8447786576
[40,] -0.0464738609 0.4035303376
[41,] -0.1738547389 0.5676346572
[42,] -0.9886095873 0.5282533032
[43,] -0.0972970065 0.2833865118
[44,] -0.6752321740 0.8122615094
[45,] -0.3831282906 0.7859403391
[46,] -0.1682080165 0.6094567216
[47,] 0.0011709216 -0.0849692205
[48,] -0.0036831821 0.1146267372
[49,] -0.2587552822 0.6592772813
[50,] -1.0549020459 0.3992015247
[51,] -0.0914309632 0.4104313785
[52,] -0.0431582449 0.3688730498
[53,] -1.1583481357 0.1805332980
[54,] -1.1981602978 -0.1327919815
[55,] -1.1130959827 0.2099718988
[56,] -1.1189161478 0.0493714841
[57,] -0.5389283134 0.8166917252
[58,] -0.1080841240 0.5186931076
[59,] -0.0196338403 0.2876259643
[60,] -0.2044995741 0.5458547562
[61,] -1.0724018409 0.3837869621
[62,] -0.0282640880 -0.0507756812
[63,] -1.0226135699 0.3741482135
[64,] 0.0521515557 0.1209589477
[65,] -1.0130943028 0.4709543632
[66,] -0.2683656936 0.6612843506
[67,] -1.0238359707 0.5131998318
[68,] -0.6212656732 0.9113206622
[69,] -0.2976707068 0.6835871486
[70,] 0.0738273967 0.1167015655
[71,] -1.0325020177 0.4606942678
[72,] -0.9920030174 0.4261958291
[73,] -1.1303405343 -0.0682229615
[74,] -1.1850733174 -0.0887329004
[75,] -0.6131552399 0.9874943299
[76,] -0.6953940832 0.8443104789
[77,] -0.0476332543 0.2027825532
[78,] -0.0247599312 0.3231512218
[79,] -1.0724432478 0.3810594956
[80,] -0.9946933776 0.5897582859
[81,] -0.9791085925 0.3801522800
[82,] -0.8876997904 0.7281568155
[83,] -0.3011169783 0.7930654723
[84,] -0.0239197485 -0.0449656262
[85,] -1.1802824087 -0.0922211294
[86,] -1.0881732809 0.3179405153
[87,] -0.1335878685 0.4662456438
[88,] -0.5310870402 0.8323042249
[89,] -0.8231475157 0.7195294172
[90,] -1.1121864059 0.1393262985
[91,] 0.0014913829 -0.1784744355
[92,] -0.1647106270 0.5524109434
[93,] -0.3948329680 0.8741868168
[94,] -1.0267863428 0.4086571879
[95,] -1.0918478761 0.2448169350
[96,] -0.1470041778 0.5777693181
[97,] -0.2093206665 0.6951782790
[98,] -0.2590223028 0.5975649722
[99,] -0.0560276896 0.3540860479
[100,] -0.8957063366 0.7968987821
[101,] -0.9289801922 0.4290022482
[102,] -0.8917632648 0.7433616679
[103,] -0.1053418057 0.3910336978
[104,] -0.8991124102 0.4983172224
[105,] -0.7386296082 0.7293451960
[106,] -0.3198273640 0.7181287719
[107,] 0.0062925067 -0.0205840212
[108,] -0.3760132877 0.8559350778
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[532,] 1.576904e-02 4.450306e-02
[533,] -9.804173e-02 4.813376e-02
[534,] -3.931965e-02 -4.896267e-02
[535,] -4.871705e-02 9.388329e-02
[536,] -8.203016e-03 1.158681e-02
[537,] -1.860946e-03 1.766311e-03
[538,] -7.107501e-02 -9.917441e-03
[539,] -2.317141e-03 3.739826e-02
[540,] -9.821109e-02 3.385678e-02
[541,] 9.503201e-03 5.145106e-02
[542,] 1.058925e-02 -6.687111e-02
[543,] 3.757320e-02 -1.036352e-01
[544,] -5.660393e-02 -4.813797e-03
[545,] 9.474846e-02 4.921491e-02
[546,] -1.512039e-03 8.519504e-04
[547,] -1.741892e-02 5.028443e-02
[548,] -3.751749e-02 6.816151e-03
[549,] -2.620624e-03 -1.549555e-03
[550,] 1.931385e-02 2.742436e-02
[551,] 7.190791e-02 -2.054689e-02
[552,] 3.008452e-02 5.573690e-02
[553,] -2.337687e-02 -6.486011e-03
[554,] -1.927548e-02 7.705669e-02
[555,] 4.003775e-02 -8.833271e-02
[556,] 1.542291e-02 -3.337565e-02
[557,] -1.066900e-02 -6.651622e-03
[558,] 8.950651e-02 6.690417e-02
[559,] 1.992461e-02 2.619470e-05
[560,] 7.936724e-03 -3.596092e-02
[561,] -4.132273e-02 1.434767e-02
[562,] 2.730323e-02 6.633084e-02
[563,] 5.963317e-03 -1.683732e-02
[564,] 1.000567e-02 -2.381841e-02
[565,] 7.252968e-02 2.463045e-02
[566,] -3.021491e-02 -2.526360e-03
[567,] 1.464802e-05 -1.092048e-01
[568,] -3.496269e-02 -8.175050e-02
[569,] 5.841810e-02 -9.328294e-02
[570,] -6.000198e-02 3.321319e-02
[571,] 6.119414e-02 -5.756231e-02
[572,] -2.578070e-02 -5.614920e-02
[573,] -1.790194e-02 5.690789e-03
[574,] -1.755824e-02 -3.184519e-02
[575,] 6.076143e-02 4.407522e-03
[576,] -6.698204e-02 -7.828374e-02
[577,] -4.656020e-02 -4.562118e-02
[578,] 1.695939e-02 3.230006e-03
[579,] -3.382131e-02 1.966450e-02
[580,] -3.064510e-02 3.155727e-02
[581,] 6.911255e-02 2.528251e-02
[582,] -3.954235e-04 2.815618e-03
[583,] 5.128235e-02 -7.461119e-02
[584,] -1.147671e-02 -6.374840e-03
[585,] 8.730005e-02 -6.951489e-02
[586,] -4.646723e-03 2.674081e-04
[587,] 4.268862e-03 -8.541280e-02
[588,] -7.656913e-03 8.199179e-03
[589,] 1.486619e-02 -1.703818e-03
[590,] 4.307933e-02 -3.069982e-02
[591,] 5.655659e-03 -9.299674e-04
[592,] 9.394055e-03 -7.776415e-02
[593,] -7.718565e-03 6.375479e-02
[594,] 6.433854e-02 2.895034e-02
[595,] -1.152564e-02 -1.019520e-01
[596,] -2.470195e-02 -4.904435e-06
[597,] 2.651708e-02 -9.127244e-02
[598,] 8.340948e-02 2.505252e-02
[599,] -5.881320e-02 -2.725833e-03
[600,] 5.318950e-02 -6.968009e-02
[601,] 8.017335e-02 6.472301e-02
[602,] 5.425766e-02 -8.915430e-02
[603,] -2.310145e-03 -1.003155e-02
[604,] -3.057683e-02 4.912211e-02
[605,] 5.497726e-03 5.008656e-02
[606,] -6.885464e-02 7.280230e-02
[607,] 5.284728e-03 -5.494716e-03
[608,] 9.045318e-02 1.179564e-02
[609,] -1.504605e-02 -1.328855e-02
[610,] 4.512000e-02 -9.246636e-02
[611,] 3.269305e-02 -8.847793e-03
[612,] 7.079726e-02 -2.896512e-02
[613,] -9.759737e-02 -5.004250e-02
[614,] 9.135609e-03 1.178370e-02
[615,] -1.168634e-02 3.171227e-02
[616,] 2.727967e-02 9.634585e-02
[617,] 1.439143e-02 1.108369e-02
[618,] 6.611220e-02 8.872196e-02
[619,] 1.134110e-02 7.516105e-02
[620,] 3.948844e-02 2.381637e-02
[621,] -2.204128e-02 -3.386684e-03
[622,] 1.311927e-02 -2.758286e-03
[623,] -8.601378e-04 -6.589271e-03
[624,] -2.181890e-02 -6.864693e-02
[625,] -8.226898e-02 -3.273482e-02
[626,] -1.627568e-03 8.446293e-03
[627,] 7.313721e-02 -3.586696e-02
[628,] 1.036122e-01 3.048614e-02
[629,] -2.494388e-02 -1.280585e-02
[630,] -9.138568e-04 1.232059e-02
[631,] 4.531081e-02 5.479521e-03
[632,] -2.068977e-02 -4.635090e-02
[633,] 6.202878e-02 2.699763e-02
[634,] 3.223283e-02 4.261864e-02
[635,] -2.429050e-02 1.825251e-02
[636,] -1.955264e-02 -4.630349e-02
[637,] -7.629113e-02 -7.473761e-02
[638,] 3.858484e-02 -8.871039e-02
[639,] 7.043596e-02 -2.628561e-02
[640,] -1.128718e-02 3.020504e-02
[641,] 6.464897e-03 7.233972e-02
[642,] 8.182253e-02 -1.156486e-02
[643,] 1.518581e-02 5.566806e-02
[644,] 2.181251e-02 -5.163846e-02
[645,] 1.078048e-02 6.690840e-02
[646,] 6.221712e-02 3.654171e-02
[647,] 4.779883e-02 2.629173e-02
[648,] 5.613674e-03 -4.663740e-02
[649,] -7.220886e-02 -1.828911e-02
[650,] -8.785107e-02 -7.242672e-02
[651,] -2.598004e-02 -2.810081e-02
[652,] -7.971175e-02 4.718372e-02
[653,] 5.265843e-05 9.876092e-02
[654,] -2.177326e-02 -1.113191e-01
[655,] -4.359390e-02 1.008602e-01
[656,] -5.605309e-03 4.097655e-03
[657,] -8.183747e-03 -7.742299e-03
[658,] -7.275119e-02 -2.467377e-02
[659,] -2.088351e-02 -6.099322e-02
[660,] -2.704929e-02 2.939132e-03
[661,] -1.518617e-02 7.484215e-02
[662,] -4.350730e-02 3.780873e-02
[663,] -3.768370e-02 -3.903507e-02
[664,] 2.743458e-02 -4.337411e-03
[665,] -4.650767e-02 -9.837690e-02
[666,] -1.621260e-03 -8.599995e-02
[667,] 4.997079e-03 -5.695095e-02
[668,] -3.389695e-02 -1.771791e-02
[669,] -2.969106e-02 2.694498e-02
[670,] -9.578316e-03 -8.134085e-02
[671,] 3.763465e-03 -6.057323e-02
[672,] -2.116959e-02 -4.592015e-02
[673,] 2.763235e-02 9.167711e-03
[674,] -2.239901e-02 1.194510e-02
[675,] -3.393777e-02 -3.315653e-02
[676,] 5.840061e-03 -5.795212e-02
[677,] -4.134587e-02 -7.627555e-02
[678,] -5.556057e-02 -1.524073e-02
[679,] -3.563655e-02 -7.649532e-03
[680,] 9.018553e-02 -4.205837e-03
[681,] -9.571136e-02 1.685900e-02
[682,] -7.598006e-03 5.270347e-02
[683,] -7.311286e-02 6.274068e-02
[684,] 3.504369e-02 -9.484858e-02
[685,] -1.550075e-02 1.983286e-03
[686,] -8.285046e-03 -2.257215e-02
[687,] -1.021603e-01 2.027647e-02
[688,] 2.128483e-02 3.082042e-02
[689,] 8.694506e-02 -5.239242e-02
[690,] -6.681066e-03 1.896820e-02
[691,] 5.631129e-02 2.648218e-02
[692,] 1.862126e-02 1.057166e-01
[693,] -6.204060e-04 9.924534e-02
[694,] -2.968530e-03 -6.794861e-02
[695,] -2.696220e-04 -5.761377e-03
[696,] -2.768524e-02 -8.095802e-02
[697,] 1.230357e-03 -8.312844e-02
[698,] 6.909285e-02 4.481512e-05
[699,] 2.577097e-02 -1.453825e-02
[700,] 5.017606e-02 -9.040178e-03
[701,] -5.169084e-02 -1.509938e-02
[702,] -1.337604e-02 -3.874500e-03
[703,] -3.403585e-02 -3.133055e-02
[704,] 1.200003e-02 3.337625e-02
[705,] 2.911679e-02 -5.371244e-02
[706,] 4.793051e-02 8.089718e-02
[707,] 6.820563e-03 -1.001547e-01
[708,] 6.629002e-02 -1.253356e-02
[709,] -3.546976e-02 6.207883e-04
[710,] 2.653831e-02 2.679405e-02
[711,] -2.133763e-02 4.020497e-02
[712,] -4.652953e-02 5.782701e-02
[713,] 4.439986e-02 -3.324583e-02
[714,] -4.387122e-02 3.951696e-02
[715,] 1.155923e-02 -9.262329e-02
[716,] 6.245666e-02 2.366827e-02
[717,] -5.351712e-03 -1.530952e-02
[718,] -3.236225e-02 -5.393639e-02
[719,] 3.751291e-02 -6.054890e-02
[720,] 4.965627e-02 -8.114384e-02
[721,] 5.234589e-02 -8.048411e-02
[722,] -3.733527e-02 -1.752074e-02
[723,] -3.389213e-02 -8.877666e-02
[724,] 6.383049e-02 3.781322e-02
[725,] -8.227903e-02 -5.279346e-02
[726,] 1.617827e-02 -1.405316e-02
[727,] -2.128723e-04 1.668688e-03
[728,] 2.901334e-02 7.029609e-02
[729,] 3.742011e-02 -6.432343e-02
[730,] -2.946017e-02 3.927809e-02
[731,] 2.770264e-02 -2.116775e-02
[732,] 9.618335e-03 -1.064364e-02
[733,] 1.019948e-02 6.424905e-02
[734,] -1.610360e-02 -4.854723e-02
[735,] 8.914172e-02 -2.142043e-02
[736,] 1.444997e-02 1.564199e-02
[737,] -1.787477e-02 -1.406242e-02
[738,] 9.336194e-02 -4.071147e-02
[739,] 2.395427e-04 6.625841e-03
[740,] -1.267740e-02 3.577363e-02
[741,] -7.917968e-02 1.103549e-02
[742,] -9.130414e-03 5.001062e-02
[743,] -4.451171e-03 1.476681e-02
[744,] -4.719151e-02 -1.632858e-02
[745,] 6.529527e-02 6.954440e-03
[746,] -1.845277e-02 -1.793308e-02
[747,] 2.319125e-02 -2.174103e-02
[748,] -3.397265e-02 6.751096e-02
[749,] 6.418199e-02 -1.622983e-02
[750,] 5.188596e-02 -2.301740e-02
[751,] 1.828507e-02 -3.250967e-02
[752,] -5.716122e-04 -6.471143e-02
[753,] -6.696936e-02 8.290005e-02
[754,] -1.184405e-02 7.250895e-02
[755,] 7.991398e-02 -3.836381e-02
[756,] -5.516533e-02 -9.294419e-03
[757,] 5.578891e-02 9.612605e-03
[758,] -2.580387e-03 -1.132005e-02
[759,] -4.840010e-02 8.225236e-02
[760,] -7.644359e-03 -5.460263e-02
[761,] -5.953758e-02 -1.842407e-03
[762,] -7.350091e-03 -2.482272e-02
[763,] 4.139197e-02 8.007318e-02
[764,] -1.705842e-02 -1.791921e-02
[765,] 1.811498e-02 8.896391e-03
[766,] 7.965428e-04 -1.133085e-01
[767,] -1.735586e-02 6.489684e-02
[768,] -2.323496e-02 1.189134e-02
[769,] -6.408770e-02 -8.774021e-02
[770,] -6.258626e-03 -8.877741e-02
[771,] 5.402936e-03 -9.637091e-04
[772,] 8.663598e-03 1.259484e-02
[773,] -2.259598e-03 -6.794488e-03
[774,] -2.493353e-02 4.707787e-02
[775,] 1.021113e-01 -3.873976e-02
[776,] -9.601582e-04 -9.107193e-03
[777,] 6.915431e-02 -4.117236e-02
[778,] -8.071214e-02 -1.303457e-02
[779,] -4.817715e-02 2.315403e-02
[780,] 3.973054e-02 -4.057686e-02
[781,] 6.077900e-02 -5.879726e-02
[782,] -7.857383e-02 -2.210735e-03
[783,] 2.021609e-03 -1.449581e-02
[784,] 3.752406e-02 6.366500e-02
[785,] 2.656104e-02 3.025401e-02
[786,] 1.191862e-02 -4.673579e-02
[787,] -2.087202e-02 7.063007e-02
[788,] 8.393491e-02 3.815260e-02
[789,] 1.358088e-03 7.105294e-02
[790,] -8.471077e-02 -1.961990e-02
[791,] 1.900730e-02 1.241708e-02
[792,] -1.430925e-02 -3.194717e-03
[793,] 4.308473e-04 -9.298310e-03
[794,] 4.330827e-02 3.670326e-02
[795,] 2.465641e-02 7.188631e-02
[796,] -7.464754e-02 -6.746937e-02
[797,] -6.921999e-02 -6.745324e-02
[798,] -6.834644e-02 -1.570755e-02
[799,] -1.776666e-02 1.032747e-01
[800,] 8.700378e-02 2.669507e-02
[801,] -2.923628e-02 6.684520e-02
[802,] -4.136915e-02 5.114102e-02
[803,] 2.591093e-02 -5.779768e-02
[804,] 4.741458e-02 -4.283423e-02
[805,] 5.168422e-02 5.066737e-02
[806,] -5.656081e-03 1.835145e-02
[807,] -1.078897e-01 7.216991e-03
[808,] -4.303416e-02 4.979131e-02
[809,] -4.005429e-02 -2.999687e-02
[810,] 1.426170e-02 2.879422e-03
[811,] -1.176876e-02 9.206613e-02
[812,] 8.673907e-02 -5.405650e-02
[813,] -9.145230e-02 3.281554e-02
[814,] -1.275330e-02 7.277216e-02
[815,] 7.581885e-03 -1.267000e-03
attr(,"scaled:center")
x y
0.006450501 -0.002022356
attr(,"scaled:scale")
x y
4.439757 4.362468 #agglomerative clustering
cluster_three_s_single <- agnes(three_spheres_scaled, metric='euclidean', method='single')
cluster_three_s_complete <- agnes(three_spheres_scaled, metric='euclidean', method='complete')
cluster_three_s_average <- agnes(three_spheres_scaled, metric='euclidean', method='average')
cluster_three_s_ward <- agnes(three_spheres_scaled, metric='euclidean', method='ward')#agglomerative clustering
cluster_ring_m_single <- agnes(ring_moon_sphere_scaled, metric='euclidean', method='single')
cluster_ring_m_complete <- agnes(ring_moon_sphere_scaled, metric='euclidean', method='complete')
cluster_ring_m_average <- agnes(ring_moon_sphere_scaled, metric='euclidean', method='average')
cluster_ring_m_ward <- agnes(ring_moon_sphere_scaled, metric='euclidean', method='ward')#agglomerative clustering
cluster_two_s_single <- agnes(two_spirals_sphere_scaled, metric='euclidean', method='single')
cluster_two_s_complete <- agnes(two_spirals_sphere_scaled, metric='euclidean', method='complete')
cluster_two_s_average <- agnes(two_spirals_sphere_scaled, metric='euclidean', method='average')
cluster_two_s_ward <- agnes(two_spirals_sphere_scaled, metric='euclidean', method='ward')#cut tree
single_clusters_three_s <- cutree(cluster_three_s_single, k = 3)
complete_clusters_three_s <- cutree(cluster_three_s_complete, k = 3)
average_clusters_three_s <- cutree(cluster_three_s_average, k = 3)
ward_clusters_three_s <- cutree(cluster_three_s_ward, k = 3)#cut tree
single_clusters_ring_m <- cutree(cluster_ring_m_single, k = 3)
complete_clusters_ring_m <- cutree(cluster_ring_m_complete, k = 3)
average_clusters_ring_m <- cutree(cluster_ring_m_average, k = 3)
ward_clusters_ring_m <- cutree(cluster_ring_m_ward, k = 3)#cut tree
single_clusters_two_s <- cutree(cluster_two_s_single, k = 3)
complete_clusters_two_s <- cutree(cluster_two_s_complete, k = 3)
average_clusters_two_s <- cutree(cluster_two_s_average, k = 3)
ward_clusters_two_s <- cutree(cluster_two_s_ward, k = 3)three_spheres_with_clusters <- bind_cols(
three_spheres,
sing_clust = factor(single_clusters_three_s),
comp_clust = factor(complete_clusters_three_s),
ave_clust = factor(average_clusters_three_s),
ward_clust = factor(ward_clusters_three_s)
)ring_moon_with_clusters <- bind_cols(
ring_moon_sphere,
sing_clust = factor(single_clusters_ring_m),
comp_clust = factor(complete_clusters_ring_m),
ave_clust = factor(average_clusters_ring_m),
ward_clust = factor(ward_clusters_ring_m)
)two_spirals_with_clusters <- bind_cols(
two_spirals_sphere,
sing_clust = factor(single_clusters_two_s),
comp_clust = factor(complete_clusters_two_s),
ave_clust = factor(average_clusters_two_s),
ward_clust = factor(ward_clusters_two_s)
)(three_s_single_sils <- silhouette(
x = single_clusters_three_s,
dist = dist(three_spheres_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.79551757
[2,] 1 3 0.64028913
[3,] 1 2 0.77362112
[4,] 1 2 0.65191128
[5,] 1 3 0.60057057
[6,] 1 2 0.73082387
[7,] 1 2 0.74420373
[8,] 1 2 0.58242564
[9,] 1 2 0.76366387
[10,] 1 3 0.78509079
[11,] 1 2 0.76022170
[12,] 1 3 0.73250182
[13,] 1 2 0.36493927
[14,] 1 3 0.56058046
[15,] 1 2 0.79440474
[16,] 1 2 0.46884733
[17,] 1 3 0.78120347
[18,] 1 2 0.78327018
[19,] 1 3 0.74658443
[20,] 1 3 0.58230187
[21,] 1 2 0.76072052
[22,] 1 2 0.75811315
[23,] 1 3 0.77247879
[24,] 1 2 0.76292648
[25,] 1 2 0.77435993
[26,] 1 2 0.75080836
[27,] 1 2 0.80526870
[28,] 1 3 0.61999927
[29,] 1 2 0.57262743
[30,] 1 3 0.74062817
[31,] 1 2 0.79464839
[32,] 1 2 0.80005986
[33,] 1 2 0.78922854
[34,] 1 2 0.80070130
[35,] 1 2 0.21458653
[36,] 1 2 0.80520709
[37,] 1 2 0.76719074
[38,] 1 2 0.79038318
[39,] 1 3 0.77817505
[40,] 1 2 0.79625818
[41,] 1 2 0.80385686
[42,] 1 2 0.77777204
[43,] 1 2 0.64588992
[44,] 1 2 0.76173535
[45,] 1 2 0.79871994
[46,] 1 3 0.70972474
[47,] 1 2 0.75773082
[48,] 1 3 0.71445897
[49,] 1 3 0.68783004
[50,] 1 3 0.77713596
[51,] 1 2 0.67775607
[52,] 1 2 0.71140185
[53,] 1 3 0.70031224
[54,] 1 2 0.77134985
[55,] 1 3 0.77327161
[56,] 1 3 0.75375729
[57,] 1 3 0.76339273
[58,] 1 3 0.66391770
[59,] 1 2 0.55908394
[60,] 1 2 0.80461227
[61,] 1 3 0.78286825
[62,] 1 2 0.61163566
[63,] 1 2 0.49868317
[64,] 1 2 0.62499701
[65,] 1 3 0.58644327
[66,] 1 2 0.75832706
[67,] 1 2 0.73515419
[68,] 1 2 0.77179649
[69,] 1 2 0.70718280
[70,] 1 2 0.80906659
[71,] 1 2 0.76234916
[72,] 1 2 0.78600798
[73,] 1 2 0.62273966
[74,] 1 3 0.76015511
[75,] 1 2 0.72356889
[76,] 1 2 0.67646283
[77,] 1 2 0.77586895
[78,] 1 3 0.74577229
[79,] 1 2 0.72714844
[80,] 1 2 0.75023429
[81,] 1 3 0.78051559
[82,] 1 3 0.74659519
[83,] 1 2 0.37629749
[84,] 1 2 0.76864088
[85,] 1 2 0.67889310
[86,] 1 2 0.73443991
[87,] 1 3 0.79729831
[88,] 1 2 0.76738705
[89,] 1 2 0.67436405
[90,] 1 3 0.80044535
[91,] 1 3 0.60233274
[92,] 1 2 0.75259713
[93,] 1 2 0.78502132
[94,] 1 3 0.77899481
[95,] 1 3 0.56533183
[96,] 1 2 0.77225675
[97,] 1 2 0.80401416
[98,] 1 2 0.78061687
[99,] 1 2 0.71516034
[100,] 1 3 0.79021249
[101,] 2 1 0.70241863
[102,] 2 3 0.79209368
[103,] 2 1 0.74503066
[104,] 2 3 0.73515231
[105,] 2 1 0.79580152
[106,] 2 1 0.77093764
[107,] 2 1 0.71275378
[108,] 2 1 0.79146235
[109,] 2 3 0.76595557
[110,] 2 3 0.65526459
[111,] 2 1 0.66672349
[112,] 2 3 0.78471899
[113,] 2 1 0.81453890
[114,] 2 1 0.63349974
[115,] 2 1 0.80800928
[116,] 2 3 0.51101276
[117,] 2 3 0.79176700
[118,] 2 1 0.73079320
[119,] 2 3 0.80804877
[120,] 2 3 0.75145419
[121,] 2 1 0.72051648
[122,] 2 3 0.76675333
[123,] 2 1 0.80515564
[124,] 2 3 0.79544740
[125,] 2 3 0.78706710
[126,] 2 1 0.81639207
[127,] 2 1 0.72828110
[128,] 2 1 0.76164969
[129,] 2 1 0.71654387
[130,] 2 1 0.81166818
[131,] 2 3 0.81102545
[132,] 2 3 0.81313187
[133,] 2 3 0.70714215
[134,] 2 3 0.74989199
[135,] 2 3 0.60943573
[136,] 2 1 0.72484975
[137,] 2 1 0.79968338
[138,] 2 3 0.68009135
[139,] 2 1 0.51972224
[140,] 2 1 0.76110701
[141,] 2 1 0.74186342
[142,] 2 1 0.69002973
[143,] 2 1 0.41335011
[144,] 2 3 0.81188394
[145,] 2 1 0.79387586
[146,] 2 1 0.41823384
[147,] 2 1 0.76335646
[148,] 2 3 0.78984467
[149,] 2 1 0.72659013
[150,] 2 3 0.77865737
[151,] 2 1 0.73633869
[152,] 2 3 0.71662619
[153,] 2 3 0.69898726
[154,] 2 1 0.70807297
[155,] 2 3 0.80906809
[156,] 2 1 0.80098373
[157,] 2 3 0.60785899
[158,] 2 3 0.08084134
[159,] 2 1 0.81356375
[160,] 2 1 0.77427892
[161,] 2 1 0.54201728
[162,] 2 1 0.72538485
[163,] 2 1 0.79889436
[164,] 2 1 0.71924211
[165,] 2 3 0.79400058
[166,] 2 3 0.64121389
[167,] 2 3 0.40638228
[168,] 2 1 0.72091454
[169,] 2 3 0.61509587
[170,] 2 1 0.55233740
[171,] 2 1 0.77868993
[172,] 2 3 0.67236472
[173,] 2 1 0.80900825
[174,] 2 3 0.69148898
[175,] 2 1 0.69073856
[176,] 2 1 0.73541163
[177,] 2 1 0.71374740
[178,] 2 3 0.76505946
[179,] 2 1 0.80205179
[180,] 2 1 0.79667770
[181,] 2 1 0.50039393
[182,] 2 3 0.75252769
[183,] 2 1 0.75120088
[184,] 2 3 0.67076875
[185,] 2 3 0.63184125
[186,] 2 1 0.79324075
[187,] 2 3 0.58571027
[188,] 2 1 0.71034423
[189,] 2 3 0.81063828
[190,] 2 3 0.78431123
[191,] 2 3 0.75983939
[192,] 2 1 0.80276685
[193,] 2 3 0.65764867
[194,] 2 3 0.78851683
[195,] 2 3 0.73360707
[196,] 2 1 0.67185902
[197,] 2 1 0.78266498
[198,] 2 1 0.71426480
[199,] 2 3 0.64064766
[200,] 2 1 0.76428626
[201,] 3 2 0.67295947
[202,] 3 2 0.81305089
[203,] 3 1 0.61358141
[204,] 3 2 0.79602984
[205,] 3 1 0.80677129
[206,] 3 1 0.63756924
[207,] 3 2 0.81970669
[208,] 3 2 0.68410217
[209,] 3 2 0.67562869
[210,] 3 2 0.42230627
[211,] 3 2 0.72677658
[212,] 3 1 0.81082149
[213,] 3 2 0.79637691
[214,] 3 1 0.78218701
[215,] 3 1 0.78498992
[216,] 3 2 0.75785678
[217,] 3 2 0.79898467
[218,] 3 1 0.78052186
[219,] 3 2 0.75233713
[220,] 3 1 0.80859864
[221,] 3 1 0.66613829
[222,] 3 2 0.81225672
[223,] 3 2 0.78841323
[224,] 3 1 0.74526796
[225,] 3 2 0.81720500
[226,] 3 1 0.74615633
[227,] 3 1 0.72725367
[228,] 3 2 0.80080151
[229,] 3 2 0.78310917
[230,] 3 2 0.66010946
[231,] 3 2 0.60134583
[232,] 3 1 0.69299075
[233,] 3 2 0.77196886
[234,] 3 2 0.74534920
[235,] 3 2 0.77667561
[236,] 3 2 0.74325995
[237,] 3 1 0.81624506
[238,] 3 2 0.81797651
[239,] 3 1 0.76498055
[240,] 3 1 0.72122489
[241,] 3 2 0.80391793
[242,] 3 2 0.51160310
[243,] 3 2 0.80582591
[244,] 3 2 0.79403215
[245,] 3 2 0.80527551
[246,] 3 1 0.81314486
[247,] 3 2 0.49560758
[248,] 3 2 0.79680532
[249,] 3 2 0.75876036
[250,] 3 2 0.81074691
[251,] 3 1 0.79085605
[252,] 3 2 0.81933092
[253,] 3 2 0.72954869
[254,] 3 1 0.78569922
[255,] 3 2 0.67525035
[256,] 3 2 0.80449649
[257,] 3 2 0.81984067
[258,] 3 2 0.56278570
[259,] 3 2 0.77763322
[260,] 3 1 0.81730684
[261,] 3 1 0.75258482
[262,] 3 1 0.40704343
[263,] 3 1 0.77428739
[264,] 3 2 0.77174292
[265,] 3 1 0.67395036
[266,] 3 1 0.57427801
[267,] 3 1 0.50973333
[268,] 3 2 0.79285488
[269,] 3 2 0.66942719
[270,] 3 2 0.81500455
[271,] 3 2 0.47454426
[272,] 3 1 0.73734117
[273,] 3 2 0.77936551
[274,] 3 1 0.67735004
[275,] 3 2 0.74597111
[276,] 3 1 0.74397088
[277,] 3 1 0.59894909
[278,] 3 2 0.68080024
[279,] 3 2 0.81526662
[280,] 3 2 0.78505267
[281,] 3 2 0.75964678
[282,] 3 1 0.61765678
[283,] 3 2 0.82045165
[284,] 3 2 0.73999843
[285,] 3 2 0.81303455
[286,] 3 2 0.73987382
[287,] 3 2 0.78422685
[288,] 3 2 0.78668197
[289,] 3 2 0.74931796
[290,] 3 2 0.71842152
[291,] 3 2 0.73300352
[292,] 3 1 0.76397109
[293,] 3 1 0.77445519
[294,] 3 1 0.61082096
[295,] 3 2 0.68112066
[296,] 3 2 0.80072791
[297,] 3 2 0.39303723
[298,] 3 2 0.81437524
[299,] 3 2 0.55867340
[300,] 3 2 0.75298188
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = single_clusters_three_s, dist = dist(three_spheres_scaled))
attr(,"class")
[1] "silhouette"avg_three_s_single <- mean(three_s_single_sils[, "sil_width"])
(three_s_complete_sils <- silhouette(
x = complete_clusters_three_s,
dist = dist(three_spheres_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.79564151
[2,] 1 3 0.64040841
[3,] 1 2 0.77364736
[4,] 1 2 0.65196172
[5,] 1 3 0.60076331
[6,] 1 2 0.73093611
[7,] 1 2 0.74416723
[8,] 1 2 0.58203934
[9,] 1 2 0.76368067
[10,] 1 3 0.78493486
[11,] 1 2 0.76046504
[12,] 1 3 0.73243304
[13,] 1 2 0.36443216
[14,] 1 3 0.56079735
[15,] 1 2 0.79452320
[16,] 1 2 0.46798837
[17,] 1 3 0.78107344
[18,] 1 2 0.78334650
[19,] 1 3 0.74650414
[20,] 1 3 0.58249447
[21,] 1 2 0.76071463
[22,] 1 2 0.75817428
[23,] 1 3 0.77235721
[24,] 1 2 0.76304955
[25,] 1 2 0.77462111
[26,] 1 2 0.75087560
[27,] 1 2 0.80542730
[28,] 1 3 0.62015760
[29,] 1 2 0.57306601
[30,] 1 3 0.74054210
[31,] 1 2 0.79474232
[32,] 1 2 0.80016342
[33,] 1 2 0.78934263
[34,] 1 2 0.80078586
[35,] 1 2 0.21246097
[36,] 1 2 0.80531712
[37,] 1 2 0.76736297
[38,] 1 2 0.79061345
[39,] 1 3 0.77797225
[40,] 1 2 0.79637979
[41,] 1 2 0.80402981
[42,] 1 2 0.77791807
[43,] 1 2 0.64596902
[44,] 1 2 0.76202064
[45,] 1 2 0.79879942
[46,] 1 3 0.70936376
[47,] 1 2 0.75779655
[48,] 1 3 0.71438293
[49,] 1 3 0.68784038
[50,] 1 3 0.77701353
[51,] 1 2 0.67760347
[52,] 1 2 0.71129614
[53,] 1 3 0.70030993
[54,] 1 2 0.77150033
[55,] 1 3 0.77312680
[56,] 1 3 0.75366498
[57,] 1 3 0.76328741
[58,] 1 3 0.66398108
[59,] 1 2 0.55878978
[60,] 1 2 0.80474925
[61,] 1 3 0.78272896
[62,] 1 2 0.61204056
[63,] 1 2 0.49803334
[64,] 1 2 0.62499680
[65,] 1 3 0.58664322
[66,] 1 2 0.75832348
[67,] 1 2 0.73520964
[68,] 1 2 0.77191938
[69,] 1 2 0.70708133
[70,] 1 2 0.80920681
[71,] 1 2 0.76234654
[72,] 1 2 0.78606135
[73,] 1 2 0.62252423
[74,] 1 3 0.75987608
[75,] 1 2 0.72380905
[76,] 1 2 0.67637314
[77,] 1 2 0.77595336
[78,] 1 3 0.74566981
[79,] 1 2 0.72707713
[80,] 1 2 0.75021034
[81,] 1 3 0.78038397
[82,] 1 3 0.74649802
[83,] 1 2 0.37498886
[84,] 1 2 0.76887329
[85,] 1 2 0.67879113
[86,] 1 3 0.73439192
[87,] 1 3 0.79713394
[88,] 1 2 0.76757913
[89,] 1 2 0.67436290
[90,] 1 3 0.80028604
[91,] 1 3 0.60233083
[92,] 1 2 0.75274257
[93,] 1 2 0.78509684
[94,] 1 3 0.77882923
[95,] 1 3 0.56564964
[96,] 1 2 0.77231982
[97,] 1 2 0.80412332
[98,] 1 2 0.78074181
[99,] 1 2 0.71533176
[100,] 1 3 0.79006769
[101,] 2 1 0.70516592
[102,] 2 3 0.79415038
[103,] 2 1 0.74885997
[104,] 2 3 0.73716273
[105,] 2 1 0.79925293
[106,] 2 1 0.77477406
[107,] 2 1 0.71542069
[108,] 2 1 0.79467109
[109,] 2 3 0.76814480
[110,] 2 3 0.65290794
[111,] 2 1 0.66777712
[112,] 2 3 0.78664039
[113,] 2 1 0.81783794
[114,] 2 1 0.63752664
[115,] 2 1 0.81095095
[116,] 2 3 0.50542419
[117,] 2 3 0.79288842
[118,] 2 1 0.73483414
[119,] 2 3 0.81016895
[120,] 2 3 0.75288952
[121,] 2 1 0.72391019
[122,] 2 3 0.76717400
[123,] 2 3 0.80751716
[124,] 2 3 0.79774435
[125,] 2 3 0.78806050
[126,] 2 1 0.81948435
[127,] 2 1 0.73192255
[128,] 2 1 0.76431284
[129,] 2 1 0.72020780
[130,] 2 1 0.81497789
[131,] 2 3 0.81310254
[132,] 2 3 0.81505160
[133,] 2 3 0.70628316
[134,] 2 3 0.75202152
[135,] 2 3 0.61035640
[136,] 2 1 0.72872039
[137,] 2 1 0.80239938
[138,] 2 3 0.68172563
[139,] 2 1 0.52139611
[140,] 2 1 0.76503031
[141,] 2 1 0.74436453
[142,] 2 1 0.69220632
[143,] 2 1 0.41200878
[144,] 2 3 0.81384646
[145,] 2 1 0.79660060
[146,] 2 1 0.41808839
[147,] 2 1 0.76726160
[148,] 2 3 0.79118922
[149,] 2 1 0.72942553
[150,] 2 3 0.77992083
[151,] 2 1 0.74037578
[152,] 2 3 0.71575791
[153,] 2 3 0.69833864
[154,] 2 1 0.71139210
[155,] 2 3 0.81082871
[156,] 2 1 0.80444694
[157,] 2 3 0.60412793
[158,] 3 2 -0.08084134
[159,] 2 1 0.81692858
[160,] 2 1 0.77779750
[161,] 2 1 0.54507854
[162,] 2 1 0.72945866
[163,] 2 1 0.80252847
[164,] 2 1 0.72302975
[165,] 2 3 0.79520744
[166,] 2 3 0.64223626
[167,] 2 3 0.39738751
[168,] 2 1 0.72437580
[169,] 2 3 0.61251243
[170,] 2 1 0.55323788
[171,] 2 1 0.78211440
[172,] 2 3 0.67048181
[173,] 2 1 0.81240992
[174,] 2 3 0.69286763
[175,] 2 1 0.69273111
[176,] 2 1 0.73893278
[177,] 2 1 0.71522262
[178,] 2 3 0.76567888
[179,] 2 1 0.80565329
[180,] 2 1 0.80029063
[181,] 2 1 0.50162263
[182,] 2 3 0.75267926
[183,] 2 1 0.75358157
[184,] 2 3 0.66896438
[185,] 2 3 0.62917753
[186,] 2 1 0.79689828
[187,] 2 3 0.58139679
[188,] 2 1 0.71220302
[189,] 2 3 0.81286747
[190,] 2 3 0.78619243
[191,] 2 3 0.76087127
[192,] 2 1 0.80634148
[193,] 2 3 0.65521723
[194,] 2 3 0.79041949
[195,] 2 3 0.73354961
[196,] 2 1 0.67272831
[197,] 2 1 0.78649135
[198,] 2 1 0.71591949
[199,] 2 3 0.64181461
[200,] 2 1 0.76813908
[201,] 3 2 0.67425425
[202,] 3 2 0.81078757
[203,] 3 1 0.61146054
[204,] 3 2 0.79420668
[205,] 3 1 0.80290242
[206,] 3 1 0.63372482
[207,] 3 2 0.81675826
[208,] 3 2 0.68512944
[209,] 3 2 0.67673021
[210,] 3 2 0.42911724
[211,] 3 2 0.72673775
[212,] 3 1 0.80694880
[213,] 3 2 0.79445420
[214,] 3 1 0.77839893
[215,] 3 1 0.78115313
[216,] 3 2 0.75512782
[217,] 3 2 0.79644567
[218,] 3 1 0.77652815
[219,] 3 2 0.75166906
[220,] 3 1 0.80469680
[221,] 3 1 0.66274777
[222,] 3 2 0.80999994
[223,] 3 2 0.78679485
[224,] 3 1 0.74203557
[225,] 3 2 0.81476333
[226,] 3 1 0.74245530
[227,] 3 1 0.72303349
[228,] 3 2 0.79880415
[229,] 3 2 0.78051834
[230,] 3 2 0.66112709
[231,] 3 2 0.60408922
[232,] 3 1 0.68884600
[233,] 3 2 0.77075651
[234,] 3 2 0.74430765
[235,] 3 2 0.77505791
[236,] 3 2 0.74273358
[237,] 3 1 0.81258906
[238,] 3 2 0.81498595
[239,] 3 1 0.76103648
[240,] 3 1 0.71699978
[241,] 3 2 0.80157183
[242,] 3 2 0.51672818
[243,] 3 2 0.80372631
[244,] 3 2 0.79205568
[245,] 3 2 0.80226509
[246,] 3 1 0.80929250
[247,] 3 2 0.50117862
[248,] 3 2 0.79393612
[249,] 3 2 0.75764909
[250,] 3 2 0.80801740
[251,] 3 1 0.78683296
[252,] 3 2 0.81670886
[253,] 3 2 0.72861181
[254,] 3 1 0.78172844
[255,] 3 2 0.67617709
[256,] 3 2 0.80250116
[257,] 3 2 0.81729447
[258,] 3 2 0.56671649
[259,] 3 2 0.77627927
[260,] 3 1 0.81350924
[261,] 3 1 0.74863152
[262,] 3 1 0.40618381
[263,] 3 1 0.77119200
[264,] 3 2 0.76984074
[265,] 3 1 0.66990556
[266,] 3 1 0.57020764
[267,] 3 1 0.50557749
[268,] 3 2 0.79046806
[269,] 3 2 0.66958484
[270,] 3 2 0.81246551
[271,] 3 2 0.48065118
[272,] 3 1 0.73328675
[273,] 3 2 0.77646413
[274,] 3 1 0.67317898
[275,] 3 2 0.74508919
[276,] 3 1 0.73994471
[277,] 3 1 0.59489905
[278,] 3 2 0.68150291
[279,] 3 2 0.81285165
[280,] 3 2 0.78269492
[281,] 3 2 0.75711607
[282,] 3 1 0.61340389
[283,] 3 2 0.81788033
[284,] 3 2 0.73968025
[285,] 3 2 0.81005624
[286,] 3 1 0.73762654
[287,] 3 2 0.78195328
[288,] 3 2 0.78501961
[289,] 3 2 0.74779264
[290,] 3 2 0.71700714
[291,] 3 2 0.73285547
[292,] 3 1 0.75992702
[293,] 3 1 0.77116526
[294,] 3 1 0.60656575
[295,] 3 2 0.68175795
[296,] 3 2 0.79866577
[297,] 3 2 0.39929805
[298,] 3 2 0.81195857
[299,] 3 2 0.56246881
[300,] 3 2 0.75222840
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = complete_clusters_three_s, dist = dist(three_spheres_scaled))
attr(,"class")
[1] "silhouette"avg_three_s_complete <- mean(three_s_complete_sils[, "sil_width"])
(three_s_average_sils <- silhouette(
x = average_clusters_three_s,
dist = dist(three_spheres_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.79564151
[2,] 1 3 0.64040841
[3,] 1 2 0.77364736
[4,] 1 2 0.65196172
[5,] 1 3 0.60076331
[6,] 1 2 0.73093611
[7,] 1 2 0.74416723
[8,] 1 2 0.58203934
[9,] 1 2 0.76368067
[10,] 1 3 0.78493486
[11,] 1 2 0.76046504
[12,] 1 3 0.73243304
[13,] 1 2 0.36443216
[14,] 1 3 0.56079735
[15,] 1 2 0.79452320
[16,] 1 2 0.46798837
[17,] 1 3 0.78107344
[18,] 1 2 0.78334650
[19,] 1 3 0.74650414
[20,] 1 3 0.58249447
[21,] 1 2 0.76071463
[22,] 1 2 0.75817428
[23,] 1 3 0.77235721
[24,] 1 2 0.76304955
[25,] 1 2 0.77462111
[26,] 1 2 0.75087560
[27,] 1 2 0.80542730
[28,] 1 3 0.62015760
[29,] 1 2 0.57306601
[30,] 1 3 0.74054210
[31,] 1 2 0.79474232
[32,] 1 2 0.80016342
[33,] 1 2 0.78934263
[34,] 1 2 0.80078586
[35,] 1 2 0.21246097
[36,] 1 2 0.80531712
[37,] 1 2 0.76736297
[38,] 1 2 0.79061345
[39,] 1 3 0.77797225
[40,] 1 2 0.79637979
[41,] 1 2 0.80402981
[42,] 1 2 0.77791807
[43,] 1 2 0.64596902
[44,] 1 2 0.76202064
[45,] 1 2 0.79879942
[46,] 1 3 0.70936376
[47,] 1 2 0.75779655
[48,] 1 3 0.71438293
[49,] 1 3 0.68784038
[50,] 1 3 0.77701353
[51,] 1 2 0.67760347
[52,] 1 2 0.71129614
[53,] 1 3 0.70030993
[54,] 1 2 0.77150033
[55,] 1 3 0.77312680
[56,] 1 3 0.75366498
[57,] 1 3 0.76328741
[58,] 1 3 0.66398108
[59,] 1 2 0.55878978
[60,] 1 2 0.80474925
[61,] 1 3 0.78272896
[62,] 1 2 0.61204056
[63,] 1 2 0.49803334
[64,] 1 2 0.62499680
[65,] 1 3 0.58664322
[66,] 1 2 0.75832348
[67,] 1 2 0.73520964
[68,] 1 2 0.77191938
[69,] 1 2 0.70708133
[70,] 1 2 0.80920681
[71,] 1 2 0.76234654
[72,] 1 2 0.78606135
[73,] 1 2 0.62252423
[74,] 1 3 0.75987608
[75,] 1 2 0.72380905
[76,] 1 2 0.67637314
[77,] 1 2 0.77595336
[78,] 1 3 0.74566981
[79,] 1 2 0.72707713
[80,] 1 2 0.75021034
[81,] 1 3 0.78038397
[82,] 1 3 0.74649802
[83,] 1 2 0.37498886
[84,] 1 2 0.76887329
[85,] 1 2 0.67879113
[86,] 1 3 0.73439192
[87,] 1 3 0.79713394
[88,] 1 2 0.76757913
[89,] 1 2 0.67436290
[90,] 1 3 0.80028604
[91,] 1 3 0.60233083
[92,] 1 2 0.75274257
[93,] 1 2 0.78509684
[94,] 1 3 0.77882923
[95,] 1 3 0.56564964
[96,] 1 2 0.77231982
[97,] 1 2 0.80412332
[98,] 1 2 0.78074181
[99,] 1 2 0.71533176
[100,] 1 3 0.79006769
[101,] 2 1 0.70516592
[102,] 2 3 0.79415038
[103,] 2 1 0.74885997
[104,] 2 3 0.73716273
[105,] 2 1 0.79925293
[106,] 2 1 0.77477406
[107,] 2 1 0.71542069
[108,] 2 1 0.79467109
[109,] 2 3 0.76814480
[110,] 2 3 0.65290794
[111,] 2 1 0.66777712
[112,] 2 3 0.78664039
[113,] 2 1 0.81783794
[114,] 2 1 0.63752664
[115,] 2 1 0.81095095
[116,] 2 3 0.50542419
[117,] 2 3 0.79288842
[118,] 2 1 0.73483414
[119,] 2 3 0.81016895
[120,] 2 3 0.75288952
[121,] 2 1 0.72391019
[122,] 2 3 0.76717400
[123,] 2 3 0.80751716
[124,] 2 3 0.79774435
[125,] 2 3 0.78806050
[126,] 2 1 0.81948435
[127,] 2 1 0.73192255
[128,] 2 1 0.76431284
[129,] 2 1 0.72020780
[130,] 2 1 0.81497789
[131,] 2 3 0.81310254
[132,] 2 3 0.81505160
[133,] 2 3 0.70628316
[134,] 2 3 0.75202152
[135,] 2 3 0.61035640
[136,] 2 1 0.72872039
[137,] 2 1 0.80239938
[138,] 2 3 0.68172563
[139,] 2 1 0.52139611
[140,] 2 1 0.76503031
[141,] 2 1 0.74436453
[142,] 2 1 0.69220632
[143,] 2 1 0.41200878
[144,] 2 3 0.81384646
[145,] 2 1 0.79660060
[146,] 2 1 0.41808839
[147,] 2 1 0.76726160
[148,] 2 3 0.79118922
[149,] 2 1 0.72942553
[150,] 2 3 0.77992083
[151,] 2 1 0.74037578
[152,] 2 3 0.71575791
[153,] 2 3 0.69833864
[154,] 2 1 0.71139210
[155,] 2 3 0.81082871
[156,] 2 1 0.80444694
[157,] 2 3 0.60412793
[158,] 3 2 -0.08084134
[159,] 2 1 0.81692858
[160,] 2 1 0.77779750
[161,] 2 1 0.54507854
[162,] 2 1 0.72945866
[163,] 2 1 0.80252847
[164,] 2 1 0.72302975
[165,] 2 3 0.79520744
[166,] 2 3 0.64223626
[167,] 2 3 0.39738751
[168,] 2 1 0.72437580
[169,] 2 3 0.61251243
[170,] 2 1 0.55323788
[171,] 2 1 0.78211440
[172,] 2 3 0.67048181
[173,] 2 1 0.81240992
[174,] 2 3 0.69286763
[175,] 2 1 0.69273111
[176,] 2 1 0.73893278
[177,] 2 1 0.71522262
[178,] 2 3 0.76567888
[179,] 2 1 0.80565329
[180,] 2 1 0.80029063
[181,] 2 1 0.50162263
[182,] 2 3 0.75267926
[183,] 2 1 0.75358157
[184,] 2 3 0.66896438
[185,] 2 3 0.62917753
[186,] 2 1 0.79689828
[187,] 2 3 0.58139679
[188,] 2 1 0.71220302
[189,] 2 3 0.81286747
[190,] 2 3 0.78619243
[191,] 2 3 0.76087127
[192,] 2 1 0.80634148
[193,] 2 3 0.65521723
[194,] 2 3 0.79041949
[195,] 2 3 0.73354961
[196,] 2 1 0.67272831
[197,] 2 1 0.78649135
[198,] 2 1 0.71591949
[199,] 2 3 0.64181461
[200,] 2 1 0.76813908
[201,] 3 2 0.67425425
[202,] 3 2 0.81078757
[203,] 3 1 0.61146054
[204,] 3 2 0.79420668
[205,] 3 1 0.80290242
[206,] 3 1 0.63372482
[207,] 3 2 0.81675826
[208,] 3 2 0.68512944
[209,] 3 2 0.67673021
[210,] 3 2 0.42911724
[211,] 3 2 0.72673775
[212,] 3 1 0.80694880
[213,] 3 2 0.79445420
[214,] 3 1 0.77839893
[215,] 3 1 0.78115313
[216,] 3 2 0.75512782
[217,] 3 2 0.79644567
[218,] 3 1 0.77652815
[219,] 3 2 0.75166906
[220,] 3 1 0.80469680
[221,] 3 1 0.66274777
[222,] 3 2 0.80999994
[223,] 3 2 0.78679485
[224,] 3 1 0.74203557
[225,] 3 2 0.81476333
[226,] 3 1 0.74245530
[227,] 3 1 0.72303349
[228,] 3 2 0.79880415
[229,] 3 2 0.78051834
[230,] 3 2 0.66112709
[231,] 3 2 0.60408922
[232,] 3 1 0.68884600
[233,] 3 2 0.77075651
[234,] 3 2 0.74430765
[235,] 3 2 0.77505791
[236,] 3 2 0.74273358
[237,] 3 1 0.81258906
[238,] 3 2 0.81498595
[239,] 3 1 0.76103648
[240,] 3 1 0.71699978
[241,] 3 2 0.80157183
[242,] 3 2 0.51672818
[243,] 3 2 0.80372631
[244,] 3 2 0.79205568
[245,] 3 2 0.80226509
[246,] 3 1 0.80929250
[247,] 3 2 0.50117862
[248,] 3 2 0.79393612
[249,] 3 2 0.75764909
[250,] 3 2 0.80801740
[251,] 3 1 0.78683296
[252,] 3 2 0.81670886
[253,] 3 2 0.72861181
[254,] 3 1 0.78172844
[255,] 3 2 0.67617709
[256,] 3 2 0.80250116
[257,] 3 2 0.81729447
[258,] 3 2 0.56671649
[259,] 3 2 0.77627927
[260,] 3 1 0.81350924
[261,] 3 1 0.74863152
[262,] 3 1 0.40618381
[263,] 3 1 0.77119200
[264,] 3 2 0.76984074
[265,] 3 1 0.66990556
[266,] 3 1 0.57020764
[267,] 3 1 0.50557749
[268,] 3 2 0.79046806
[269,] 3 2 0.66958484
[270,] 3 2 0.81246551
[271,] 3 2 0.48065118
[272,] 3 1 0.73328675
[273,] 3 2 0.77646413
[274,] 3 1 0.67317898
[275,] 3 2 0.74508919
[276,] 3 1 0.73994471
[277,] 3 1 0.59489905
[278,] 3 2 0.68150291
[279,] 3 2 0.81285165
[280,] 3 2 0.78269492
[281,] 3 2 0.75711607
[282,] 3 1 0.61340389
[283,] 3 2 0.81788033
[284,] 3 2 0.73968025
[285,] 3 2 0.81005624
[286,] 3 1 0.73762654
[287,] 3 2 0.78195328
[288,] 3 2 0.78501961
[289,] 3 2 0.74779264
[290,] 3 2 0.71700714
[291,] 3 2 0.73285547
[292,] 3 1 0.75992702
[293,] 3 1 0.77116526
[294,] 3 1 0.60656575
[295,] 3 2 0.68175795
[296,] 3 2 0.79866577
[297,] 3 2 0.39929805
[298,] 3 2 0.81195857
[299,] 3 2 0.56246881
[300,] 3 2 0.75222840
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = average_clusters_three_s, dist = dist(three_spheres_scaled))
attr(,"class")
[1] "silhouette"avg_three_s_average <- mean(three_s_average_sils[, "sil_width"])
(three_s_ward_sils <- silhouette(
x = ward_clusters_three_s,
dist = dist(three_spheres_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.79551757
[2,] 1 3 0.64028913
[3,] 1 2 0.77362112
[4,] 1 2 0.65191128
[5,] 1 3 0.60057057
[6,] 1 2 0.73082387
[7,] 1 2 0.74420373
[8,] 1 2 0.58242564
[9,] 1 2 0.76366387
[10,] 1 3 0.78509079
[11,] 1 2 0.76022170
[12,] 1 3 0.73250182
[13,] 1 2 0.36493927
[14,] 1 3 0.56058046
[15,] 1 2 0.79440474
[16,] 1 2 0.46884733
[17,] 1 3 0.78120347
[18,] 1 2 0.78327018
[19,] 1 3 0.74658443
[20,] 1 3 0.58230187
[21,] 1 2 0.76072052
[22,] 1 2 0.75811315
[23,] 1 3 0.77247879
[24,] 1 2 0.76292648
[25,] 1 2 0.77435993
[26,] 1 2 0.75080836
[27,] 1 2 0.80526870
[28,] 1 3 0.61999927
[29,] 1 2 0.57262743
[30,] 1 3 0.74062817
[31,] 1 2 0.79464839
[32,] 1 2 0.80005986
[33,] 1 2 0.78922854
[34,] 1 2 0.80070130
[35,] 1 2 0.21458653
[36,] 1 2 0.80520709
[37,] 1 2 0.76719074
[38,] 1 2 0.79038318
[39,] 1 3 0.77817505
[40,] 1 2 0.79625818
[41,] 1 2 0.80385686
[42,] 1 2 0.77777204
[43,] 1 2 0.64588992
[44,] 1 2 0.76173535
[45,] 1 2 0.79871994
[46,] 1 3 0.70972474
[47,] 1 2 0.75773082
[48,] 1 3 0.71445897
[49,] 1 3 0.68783004
[50,] 1 3 0.77713596
[51,] 1 2 0.67775607
[52,] 1 2 0.71140185
[53,] 1 3 0.70031224
[54,] 1 2 0.77134985
[55,] 1 3 0.77327161
[56,] 1 3 0.75375729
[57,] 1 3 0.76339273
[58,] 1 3 0.66391770
[59,] 1 2 0.55908394
[60,] 1 2 0.80461227
[61,] 1 3 0.78286825
[62,] 1 2 0.61163566
[63,] 1 2 0.49868317
[64,] 1 2 0.62499701
[65,] 1 3 0.58644327
[66,] 1 2 0.75832706
[67,] 1 2 0.73515419
[68,] 1 2 0.77179649
[69,] 1 2 0.70718280
[70,] 1 2 0.80906659
[71,] 1 2 0.76234916
[72,] 1 2 0.78600798
[73,] 1 2 0.62273966
[74,] 1 3 0.76015511
[75,] 1 2 0.72356889
[76,] 1 2 0.67646283
[77,] 1 2 0.77586895
[78,] 1 3 0.74577229
[79,] 1 2 0.72714844
[80,] 1 2 0.75023429
[81,] 1 3 0.78051559
[82,] 1 3 0.74659519
[83,] 1 2 0.37629749
[84,] 1 2 0.76864088
[85,] 1 2 0.67889310
[86,] 1 2 0.73443991
[87,] 1 3 0.79729831
[88,] 1 2 0.76738705
[89,] 1 2 0.67436405
[90,] 1 3 0.80044535
[91,] 1 3 0.60233274
[92,] 1 2 0.75259713
[93,] 1 2 0.78502132
[94,] 1 3 0.77899481
[95,] 1 3 0.56533183
[96,] 1 2 0.77225675
[97,] 1 2 0.80401416
[98,] 1 2 0.78061687
[99,] 1 2 0.71516034
[100,] 1 3 0.79021249
[101,] 2 1 0.70241863
[102,] 2 3 0.79209368
[103,] 2 1 0.74503066
[104,] 2 3 0.73515231
[105,] 2 1 0.79580152
[106,] 2 1 0.77093764
[107,] 2 1 0.71275378
[108,] 2 1 0.79146235
[109,] 2 3 0.76595557
[110,] 2 3 0.65526459
[111,] 2 1 0.66672349
[112,] 2 3 0.78471899
[113,] 2 1 0.81453890
[114,] 2 1 0.63349974
[115,] 2 1 0.80800928
[116,] 2 3 0.51101276
[117,] 2 3 0.79176700
[118,] 2 1 0.73079320
[119,] 2 3 0.80804877
[120,] 2 3 0.75145419
[121,] 2 1 0.72051648
[122,] 2 3 0.76675333
[123,] 2 1 0.80515564
[124,] 2 3 0.79544740
[125,] 2 3 0.78706710
[126,] 2 1 0.81639207
[127,] 2 1 0.72828110
[128,] 2 1 0.76164969
[129,] 2 1 0.71654387
[130,] 2 1 0.81166818
[131,] 2 3 0.81102545
[132,] 2 3 0.81313187
[133,] 2 3 0.70714215
[134,] 2 3 0.74989199
[135,] 2 3 0.60943573
[136,] 2 1 0.72484975
[137,] 2 1 0.79968338
[138,] 2 3 0.68009135
[139,] 2 1 0.51972224
[140,] 2 1 0.76110701
[141,] 2 1 0.74186342
[142,] 2 1 0.69002973
[143,] 2 1 0.41335011
[144,] 2 3 0.81188394
[145,] 2 1 0.79387586
[146,] 2 1 0.41823384
[147,] 2 1 0.76335646
[148,] 2 3 0.78984467
[149,] 2 1 0.72659013
[150,] 2 3 0.77865737
[151,] 2 1 0.73633869
[152,] 2 3 0.71662619
[153,] 2 3 0.69898726
[154,] 2 1 0.70807297
[155,] 2 3 0.80906809
[156,] 2 1 0.80098373
[157,] 2 3 0.60785899
[158,] 2 3 0.08084134
[159,] 2 1 0.81356375
[160,] 2 1 0.77427892
[161,] 2 1 0.54201728
[162,] 2 1 0.72538485
[163,] 2 1 0.79889436
[164,] 2 1 0.71924211
[165,] 2 3 0.79400058
[166,] 2 3 0.64121389
[167,] 2 3 0.40638228
[168,] 2 1 0.72091454
[169,] 2 3 0.61509587
[170,] 2 1 0.55233740
[171,] 2 1 0.77868993
[172,] 2 3 0.67236472
[173,] 2 1 0.80900825
[174,] 2 3 0.69148898
[175,] 2 1 0.69073856
[176,] 2 1 0.73541163
[177,] 2 1 0.71374740
[178,] 2 3 0.76505946
[179,] 2 1 0.80205179
[180,] 2 1 0.79667770
[181,] 2 1 0.50039393
[182,] 2 3 0.75252769
[183,] 2 1 0.75120088
[184,] 2 3 0.67076875
[185,] 2 3 0.63184125
[186,] 2 1 0.79324075
[187,] 2 3 0.58571027
[188,] 2 1 0.71034423
[189,] 2 3 0.81063828
[190,] 2 3 0.78431123
[191,] 2 3 0.75983939
[192,] 2 1 0.80276685
[193,] 2 3 0.65764867
[194,] 2 3 0.78851683
[195,] 2 3 0.73360707
[196,] 2 1 0.67185902
[197,] 2 1 0.78266498
[198,] 2 1 0.71426480
[199,] 2 3 0.64064766
[200,] 2 1 0.76428626
[201,] 3 2 0.67295947
[202,] 3 2 0.81305089
[203,] 3 1 0.61358141
[204,] 3 2 0.79602984
[205,] 3 1 0.80677129
[206,] 3 1 0.63756924
[207,] 3 2 0.81970669
[208,] 3 2 0.68410217
[209,] 3 2 0.67562869
[210,] 3 2 0.42230627
[211,] 3 2 0.72677658
[212,] 3 1 0.81082149
[213,] 3 2 0.79637691
[214,] 3 1 0.78218701
[215,] 3 1 0.78498992
[216,] 3 2 0.75785678
[217,] 3 2 0.79898467
[218,] 3 1 0.78052186
[219,] 3 2 0.75233713
[220,] 3 1 0.80859864
[221,] 3 1 0.66613829
[222,] 3 2 0.81225672
[223,] 3 2 0.78841323
[224,] 3 1 0.74526796
[225,] 3 2 0.81720500
[226,] 3 1 0.74615633
[227,] 3 1 0.72725367
[228,] 3 2 0.80080151
[229,] 3 2 0.78310917
[230,] 3 2 0.66010946
[231,] 3 2 0.60134583
[232,] 3 1 0.69299075
[233,] 3 2 0.77196886
[234,] 3 2 0.74534920
[235,] 3 2 0.77667561
[236,] 3 2 0.74325995
[237,] 3 1 0.81624506
[238,] 3 2 0.81797651
[239,] 3 1 0.76498055
[240,] 3 1 0.72122489
[241,] 3 2 0.80391793
[242,] 3 2 0.51160310
[243,] 3 2 0.80582591
[244,] 3 2 0.79403215
[245,] 3 2 0.80527551
[246,] 3 1 0.81314486
[247,] 3 2 0.49560758
[248,] 3 2 0.79680532
[249,] 3 2 0.75876036
[250,] 3 2 0.81074691
[251,] 3 1 0.79085605
[252,] 3 2 0.81933092
[253,] 3 2 0.72954869
[254,] 3 1 0.78569922
[255,] 3 2 0.67525035
[256,] 3 2 0.80449649
[257,] 3 2 0.81984067
[258,] 3 2 0.56278570
[259,] 3 2 0.77763322
[260,] 3 1 0.81730684
[261,] 3 1 0.75258482
[262,] 3 1 0.40704343
[263,] 3 1 0.77428739
[264,] 3 2 0.77174292
[265,] 3 1 0.67395036
[266,] 3 1 0.57427801
[267,] 3 1 0.50973333
[268,] 3 2 0.79285488
[269,] 3 2 0.66942719
[270,] 3 2 0.81500455
[271,] 3 2 0.47454426
[272,] 3 1 0.73734117
[273,] 3 2 0.77936551
[274,] 3 1 0.67735004
[275,] 3 2 0.74597111
[276,] 3 1 0.74397088
[277,] 3 1 0.59894909
[278,] 3 2 0.68080024
[279,] 3 2 0.81526662
[280,] 3 2 0.78505267
[281,] 3 2 0.75964678
[282,] 3 1 0.61765678
[283,] 3 2 0.82045165
[284,] 3 2 0.73999843
[285,] 3 2 0.81303455
[286,] 3 2 0.73987382
[287,] 3 2 0.78422685
[288,] 3 2 0.78668197
[289,] 3 2 0.74931796
[290,] 3 2 0.71842152
[291,] 3 2 0.73300352
[292,] 3 1 0.76397109
[293,] 3 1 0.77445519
[294,] 3 1 0.61082096
[295,] 3 2 0.68112066
[296,] 3 2 0.80072791
[297,] 3 2 0.39303723
[298,] 3 2 0.81437524
[299,] 3 2 0.55867340
[300,] 3 2 0.75298188
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = ward_clusters_three_s, dist = dist(three_spheres_scaled))
attr(,"class")
[1] "silhouette"avg_three_s_ward <- mean(three_s_ward_sils[, "sil_width"])title_three_single <- paste("Three spheres – single (s =", round(avg_three_s_single, 3), ")")
title_three_complete <- paste("Three spheres – complete (s =", round(avg_three_s_complete, 3), ")")
title_three_average <- paste("Three spheres – average (s =", round(avg_three_s_average, 3), ")")
title_three_ward <- paste("Three spheres – ward (s =", round(avg_three_s_ward, 3), ")")(ring_m_single_sils <- silhouette(
x = single_clusters_ring_m,
dist = dist(ring_moon_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.618402319
[2,] 1 2 0.688924707
[3,] 1 2 0.726520903
[4,] 1 2 0.715908828
[5,] 1 2 0.710009100
[6,] 1 2 0.739316285
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[580,] 2 1 0.212084434
[581,] 2 1 0.204113804
[582,] 2 3 0.103943472
[583,] 2 3 0.232086916
[584,] 2 3 0.282082816
[585,] 2 3 0.215713344
[586,] 2 1 0.280350318
[587,] 2 3 0.251200297
[588,] 2 1 0.250364118
[589,] 2 1 0.291946836
[590,] 2 3 0.254147853
[591,] 2 3 0.257254611
[592,] 2 3 0.274476591
[593,] 2 1 0.232022462
[594,] 2 1 0.282671418
[595,] 2 3 0.083106178
[596,] 2 1 0.255554616
[597,] 2 1 0.278025581
[598,] 2 1 0.302540783
[599,] 2 3 0.152640701
[600,] 2 3 0.240536174
[601,] 2 3 0.209586726
[602,] 2 1 0.287154447
[603,] 2 1 0.158674947
[604,] 2 3 0.162319824
[605,] 2 3 0.290336193
[606,] 2 1 0.252341922
[607,] 2 1 0.294908124
[608,] 2 3 0.173961036
[609,] 2 1 0.231249926
[610,] 2 3 0.173260776
[611,] 2 3 0.249057362
[612,] 2 1 0.249066941
[613,] 2 1 0.239089341
[614,] 2 3 0.214815399
[615,] 2 1 0.296820711
[616,] 2 1 0.251649887
[617,] 2 3 0.309529694
[618,] 2 3 0.289948004
[619,] 2 1 0.302588902
[620,] 2 1 0.298986530
[621,] 2 3 0.026075209
[622,] 2 3 0.237903342
[623,] 2 1 0.303548415
[624,] 2 1 0.127802507
[625,] 2 1 0.288998032
[626,] 2 1 0.219802501
[627,] 2 1 0.288110892
[628,] 2 3 0.288658931
[629,] 2 3 0.292323792
[630,] 2 1 0.225836200
[631,] 2 1 0.285182232
[632,] 2 3 0.255845900
[633,] 2 3 0.308307173
[634,] 2 1 0.289969967
[635,] 2 1 0.195469917
[636,] 2 3 0.281963601
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[639,] 2 3 0.173851895
[640,] 2 1 0.300776132
[641,] 2 1 0.248730859
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[646,] 2 1 0.304649356
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[648,] 2 3 0.232416590
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[650,] 2 3 0.299017236
[651,] 2 3 -0.030659690
[652,] 2 1 0.278961355
[653,] 2 3 0.203453093
[654,] 2 3 0.276650244
[655,] 2 1 0.266560775
[656,] 2 3 0.205001622
[657,] 2 1 0.215015324
[658,] 2 3 0.287297409
[659,] 2 1 0.199958691
[660,] 2 3 0.242739832
[661,] 2 3 0.277941217
[662,] 2 3 0.255677123
[663,] 2 1 0.282575835
[664,] 2 3 0.273625449
[665,] 2 3 0.212564697
[666,] 2 1 0.259656117
[667,] 2 1 0.304534404
[668,] 2 3 0.227813585
[669,] 2 1 0.276340426
[670,] 2 3 0.184858782
[671,] 2 3 0.168130111
[672,] 2 1 0.295806053
[673,] 2 1 0.253975217
[674,] 2 3 0.298428095
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[676,] 2 1 0.256726327
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[678,] 2 3 0.254842048
[679,] 2 3 0.279149331
[680,] 2 3 0.256480749
[681,] 2 3 0.231021823
[682,] 2 1 0.289021136
[683,] 2 1 0.281271812
[684,] 2 1 0.282521102
[685,] 2 3 0.113518453
[686,] 2 3 0.274974088
[687,] 2 3 0.282957998
[688,] 2 3 0.234833947
[689,] 2 3 0.160199155
[690,] 2 3 0.209111074
[691,] 2 1 0.303806169
[692,] 2 1 0.148352118
[693,] 2 3 0.270068125
[694,] 2 3 0.304396709
[695,] 2 1 0.291373545
[696,] 2 1 0.208485139
[697,] 2 1 0.259135411
[698,] 2 3 0.302930948
[699,] 2 3 0.211783066
[700,] 2 3 0.310440433
[701,] 2 3 0.265809982
[702,] 2 1 0.305216031
[703,] 2 1 0.307661498
[704,] 2 3 0.178220492
[705,] 2 1 0.291294268
[706,] 2 3 0.268431050
[707,] 2 1 0.278846821
[708,] 2 1 0.254024452
[709,] 2 1 0.273264123
[710,] 2 3 0.249387924
[711,] 2 3 0.193544318
[712,] 2 1 0.301580225
[713,] 2 3 0.291170993
[714,] 2 3 0.179047098
[715,] 2 1 0.308580969
[716,] 2 3 0.190944103
[717,] 2 1 0.277617098
[718,] 2 1 0.202770439
[719,] 2 1 0.167079170
[720,] 2 1 0.224282438
[721,] 2 3 0.232996728
[722,] 2 3 0.282099313
[723,] 2 3 0.008957763
[724,] 2 3 0.118170788
[725,] 2 1 0.146663450
[726,] 2 1 0.277069700
[727,] 2 1 0.276897458
[728,] 2 3 0.231788230
[729,] 2 3 0.257074258
[730,] 2 1 0.237033461
[731,] 2 1 0.239171899
[732,] 2 3 0.300379984
[733,] 2 3 0.251074938
[734,] 2 1 0.301971056
[735,] 2 3 0.121839903
[736,] 2 1 0.259899919
[737,] 2 1 0.282813813
[738,] 2 1 0.203482852
[739,] 2 3 0.289744552
[740,] 2 3 0.167579812
[741,] 2 1 0.133398515
[742,] 2 1 0.307727310
[743,] 2 1 0.259115296
[744,] 2 3 0.247827786
[745,] 2 1 0.283849260
[746,] 2 1 0.224436866
[747,] 2 1 0.232677131
[748,] 2 1 0.271740535
[749,] 2 1 0.264155040
[750,] 2 3 0.228086814
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = single_clusters_ring_m, dist = dist(ring_moon_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_ring_m_single <- mean(ring_m_single_sils[, "sil_width"])
(ring_m_complete_sils <- silhouette(
x = complete_clusters_ring_m,
dist = dist(ring_moon_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 2 -0.172320718
[2,] 2 3 0.463302128
[3,] 2 1 0.602758201
[4,] 2 1 0.572213385
[5,] 2 1 0.700347770
[6,] 2 1 0.691097972
[7,] 1 2 0.103740047
[8,] 2 1 0.432311025
[9,] 2 1 0.695213893
[10,] 2 1 0.692255225
[11,] 2 1 0.694544896
[12,] 2 1 0.671565877
[13,] 2 1 0.676025605
[14,] 2 1 0.693218651
[15,] 3 2 -0.266137142
[16,] 3 2 -0.420824640
[17,] 1 2 0.060072141
[18,] 2 3 0.640395720
[19,] 3 2 -0.250021516
[20,] 2 1 0.453209515
[21,] 1 2 -0.254851891
[22,] 1 2 0.271707113
[23,] 1 2 0.055354144
[24,] 1 2 0.205503616
[25,] 2 1 0.337885004
[26,] 2 3 0.574071805
[27,] 2 1 0.695606549
[28,] 3 2 -0.251941725
[29,] 2 1 0.693067914
[30,] 2 3 0.585297489
[31,] 2 1 0.607327193
[32,] 2 1 0.613024056
[33,] 1 2 -0.173774696
[34,] 2 1 0.673671298
[35,] 2 1 0.388811335
[36,] 2 1 0.551747942
[37,] 3 2 -0.274853080
[38,] 1 2 -0.175884237
[39,] 2 1 0.694506588
[40,] 1 2 -0.179130163
[41,] 2 1 0.414259802
[42,] 2 3 0.590016775
[43,] 1 2 -0.129719548
[44,] 2 1 0.692375664
[45,] 2 1 0.617751560
[46,] 2 1 0.433825758
[47,] 1 2 0.232977908
[48,] 1 2 0.117882626
[49,] 2 1 0.519547434
[50,] 2 3 0.501296206
[51,] 1 2 -0.230780246
[52,] 1 2 -0.145401882
[53,] 3 2 -0.316167990
[54,] 3 2 -0.050861226
[55,] 3 2 -0.351637404
[56,] 3 2 -0.222349788
[57,] 2 1 0.670324627
[58,] 2 1 0.326599006
[59,] 1 2 -0.046244462
[60,] 2 1 0.423344887
[61,] 2 3 0.486016902
[62,] 1 2 0.191117979
[63,] 2 3 0.494472487
[64,] 1 2 0.169537840
[65,] 2 3 0.555063503
[66,] 2 1 0.526031575
[67,] 2 3 0.573266584
[68,] 2 1 0.692107780
[69,] 2 1 0.550840045
[70,] 1 2 0.192968238
[71,] 2 3 0.544010102
[72,] 2 3 0.535390552
[73,] 3 2 -0.122453071
[74,] 3 2 -0.090903592
[75,] 2 1 0.689732685
[76,] 2 1 0.697148249
[77,] 1 2 -0.002369977
[78,] 1 2 -0.084421424
[79,] 2 3 0.484223711
[80,] 2 3 0.613937743
[81,] 2 3 0.509839038
[82,] 2 3 0.681637416
[83,] 2 1 0.583552362
[84,] 1 2 0.192270649
[85,] 3 2 -0.089144642
[86,] 3 2 -0.440801594
[87,] 2 1 0.310516594
[88,] 2 1 0.670658346
[89,] 2 1 0.683890130
[90,] 3 2 -0.296268515
[91,] 1 2 0.268339243
[92,] 2 1 0.397706945
[93,] 2 1 0.634747463
[94,] 2 3 0.515444334
[95,] 3 2 -0.384818989
[96,] 2 1 0.399160731
[97,] 2 1 0.502680918
[98,] 2 1 0.489299967
[99,] 1 2 -0.146225753
[100,] 2 1 0.691825177
[101,] 2 3 0.551442885
[102,] 2 3 0.684099625
[103,] 1 2 -0.228475118
[104,] 2 3 0.594969743
[105,] 2 1 0.683009460
[106,] 2 1 0.573634892
[107,] 1 2 0.207772325
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[109,] 1 2 0.104865031
[110,] 2 1 0.545960894
[111,] 2 1 0.527889785
[112,] 1 2 0.097366990
[113,] 1 2 -0.042752491
[114,] 1 2 0.033071750
[115,] 3 2 -0.202233213
[116,] 2 3 0.675450193
[117,] 3 2 -0.370701470
[118,] 2 1 0.682296025
[119,] 2 1 0.317802563
[120,] 2 1 0.653241624
[121,] 2 3 0.657511037
[122,] 3 2 -0.398964077
[123,] 3 2 -0.423359598
[124,] 1 2 -0.161882429
[125,] 2 1 0.690291795
[126,] 2 1 0.622885431
[127,] 2 1 0.674524981
[128,] 2 1 0.636745284
[129,] 3 2 -0.312249625
[130,] 2 1 0.495207855
[131,] 2 1 0.512314056
[132,] 2 1 0.684333074
[133,] 2 1 0.565634992
[134,] 1 2 -0.277922019
[135,] 3 2 -0.373221563
[136,] 2 1 0.683973385
[137,] 1 2 0.189224214
[138,] 1 2 0.093872259
[139,] 2 1 0.689998176
[140,] 2 1 0.690414762
[141,] 2 1 0.661744731
[142,] 2 1 0.551787415
[143,] 2 3 0.678150708
[144,] 3 2 -0.391980701
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[146,] 2 1 0.395767742
[147,] 2 1 0.695950838
[148,] 3 2 -0.412010328
[149,] 2 1 0.696331986
[150,] 1 2 -0.213554953
[151,] 2 3 0.593865940
[152,] 1 2 0.030863751
[153,] 3 2 -0.283590093
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[157,] 1 2 -0.082115528
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[161,] 3 2 -0.067548452
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[167,] 3 2 -0.326911461
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[169,] 2 3 0.541562701
[170,] 2 1 0.688221838
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[174,] 3 2 -0.267523106
[175,] 1 2 -0.229174466
[176,] 2 1 0.693371011
[177,] 2 1 0.684278686
[178,] 2 3 0.529012006
[179,] 1 2 -0.144086559
[180,] 2 1 0.691281736
[181,] 1 2 -0.142036101
[182,] 2 1 0.543479621
[183,] 1 2 -0.099635645
[184,] 1 2 0.178906473
[185,] 2 1 0.372471509
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[187,] 3 2 -0.407049152
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[189,] 2 1 0.617248422
[190,] 2 1 0.542168306
[191,] 2 1 0.648629074
[192,] 3 2 -0.362335011
[193,] 2 1 0.525963017
[194,] 2 1 0.695217594
[195,] 2 3 0.635734292
[196,] 2 1 0.625557058
[197,] 3 2 -0.405662553
[198,] 3 2 -0.250838786
[199,] 2 1 0.641543188
[200,] 2 1 0.407360515
[201,] 2 3 0.595552640
[202,] 3 2 -0.359292468
[203,] 2 1 0.578293257
[204,] 2 1 0.679957941
[205,] 3 2 -0.383204613
[206,] 2 1 0.626238617
[207,] 2 3 0.646107686
[208,] 2 3 0.667210427
[209,] 3 2 -0.345816530
[210,] 1 2 0.277824983
[211,] 2 3 0.645500942
[212,] 2 1 0.657768568
[213,] 2 1 0.677469412
[214,] 1 2 -0.224315078
[215,] 1 2 0.248713707
[216,] 3 2 0.002685784
[217,] 1 2 -0.237945442
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[219,] 2 3 0.658822817
[220,] 2 3 0.600332943
[221,] 2 1 0.522432691
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[255,] 3 1 -0.419265281
[256,] 2 1 0.431206556
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[259,] 2 1 0.643414610
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[262,] 3 2 -0.233624357
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[264,] 3 1 0.471993479
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[750,] 1 2 0.782407522
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = complete_clusters_ring_m, dist = dist(ring_moon_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_ring_m_complete <- mean(ring_m_complete_sils[, "sil_width"])
(ring_m_average_sils <- silhouette(
x = average_clusters_ring_m,
dist = dist(ring_moon_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 3 0.36933575
[2,] 1 3 0.61593703
[3,] 1 3 0.59860619
[4,] 1 3 0.57843727
[5,] 1 3 0.65400971
[6,] 1 3 0.65985982
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[9,] 1 3 0.66094244
[10,] 1 3 0.66200009
[11,] 1 3 0.65375494
[12,] 1 3 0.63700048
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[18,] 1 3 0.65612433
[19,] 1 2 0.52836523
[20,] 1 3 0.50659892
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[750,] 3 1 0.84349548
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = average_clusters_ring_m, dist = dist(ring_moon_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_ring_m_average <- mean(ring_m_average_sils[, "sil_width"])
(ring_m_ward_sils <- silhouette(
x = ward_clusters_ring_m,
dist = dist(ring_moon_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 3 0.355192168
[2,] 1 3 0.614969376
[3,] 1 3 0.589316591
[4,] 1 3 0.568240839
[5,] 1 3 0.647636711
[6,] 1 3 0.654164424
[7,] 1 3 0.177976230
[8,] 1 3 0.487577108
[9,] 1 3 0.655314153
[10,] 1 3 0.656796246
[11,] 1 3 0.647120939
[12,] 1 3 0.629226810
[13,] 1 3 0.645473344
[14,] 1 3 0.652615944
[15,] 1 2 0.543737754
[16,] 1 3 0.607088242
[17,] 1 3 0.214040518
[18,] 1 3 0.652651755
[19,] 1 2 0.534999346
[20,] 1 3 0.493750816
[21,] 1 3 0.400242524
[22,] 1 3 -0.050025795
[23,] 1 3 0.217503902
[24,] 1 3 0.069633417
[25,] 1 3 0.439270300
[26,] 1 3 0.641735829
[27,] 1 3 0.648193547
[28,] 1 2 0.535984478
[29,] 1 3 0.646689110
[30,] 1 3 0.640902543
[31,] 1 3 0.581400574
[32,] 1 3 0.578256219
[33,] 1 3 0.357510138
[34,] 1 3 0.621942552
[35,] 1 3 0.449003369
[36,] 1 3 0.558469983
[37,] 1 2 0.547984121
[38,] 1 3 0.353226957
[39,] 1 3 0.647861249
[40,] 1 3 0.349381230
[41,] 1 3 0.481824599
[42,] 1 3 0.643781375
[43,] 1 3 0.334973455
[44,] 1 3 0.649714706
[45,] 1 3 0.593529019
[46,] 1 3 0.487743120
[47,] 1 3 0.028102958
[48,] 1 3 0.164503037
[49,] 1 3 0.539684580
[50,] 1 3 0.625663554
[51,] 1 3 0.384812774
[52,] 1 3 0.332679914
[53,] 1 2 0.567428693
[54,] 1 2 0.410846022
[55,] 1 2 0.585789165
[56,] 1 2 0.519051367
[57,] 1 3 0.630522625
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[60,] 1 3 0.492122788
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[62,] 1 3 0.083136251
[63,] 1 3 0.622065279
[64,] 1 3 0.108687212
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[744,] 3 1 0.847908750
[745,] 3 1 0.861585313
[746,] 3 1 0.804005158
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[749,] 3 1 0.838537508
[750,] 3 1 0.864082223
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = ward_clusters_ring_m, dist = dist(ring_moon_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_ring_m_ward <- mean(ring_m_ward_sils[, "sil_width"])title_ring_single <- paste("Ring–moon–sphere – single (s) =", round(avg_ring_m_single, 3), ")")
title_ring_complete <- paste("Ring–moon–sphere – complete (s =", round(avg_ring_m_complete, 3), ")")
title_ring_average <- paste("Ring–moon–sphere – average (s =", round(avg_ring_m_average, 3), ")")
title_ring_ward <- paste("Ring–moon–sphere – ward (s) =", round(avg_ring_m_ward, 3), ")")(two_s_single_sils <- silhouette(
x = single_clusters_two_s,
dist = dist(two_spirals_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 3 -0.74363016
[2,] 1 3 -0.74226653
[3,] 1 3 -0.73561137
[4,] 1 3 -0.74191187
[5,] 1 3 -0.70950994
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[7,] 1 3 -0.69814145
[8,] 1 3 -0.67593905
[9,] 1 3 -0.72036919
[10,] 1 3 -0.70370283
[11,] 1 3 -0.68653183
[12,] 1 3 -0.63752723
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[495,] 2 3 -0.05027262
[496,] 2 3 -0.05579264
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[499,] 2 3 -0.05169692
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[503,] 2 3 -0.06341422
[504,] 2 3 -0.06695771
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[507,] 2 3 -0.07385851
[508,] 2 3 -0.07634239
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[516,] 3 1 0.95484736
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[815,] 3 2 0.96324600
attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = single_clusters_two_s, dist = dist(two_spirals_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_two_s_single <- mean(two_s_single_sils[, "sil_width"])
(two_s_complete_sils <- silhouette(
x = complete_clusters_two_s,
dist = dist(two_spirals_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 3 0.2755327003
[2,] 1 3 0.2862591581
[3,] 1 3 0.2653284905
[4,] 1 3 0.2900805373
[5,] 1 3 0.2342937151
[6,] 1 3 0.2357931253
[7,] 1 3 0.2409674033
[8,] 1 3 0.1980173154
[9,] 1 3 0.2520095059
[10,] 1 2 0.2590912382
[11,] 1 3 0.2095956308
[12,] 1 3 0.1570254484
[13,] 1 2 0.1365947957
[14,] 1 2 0.2118265717
[15,] 1 2 0.2195840405
[16,] 1 2 0.2138148158
[17,] 1 2 0.2268824845
[18,] 1 2 0.0516722006
[19,] 1 2 0.1959073527
[20,] 1 2 0.0816485522
[21,] 1 2 0.1053477759
[22,] 1 2 0.1146564450
[23,] 1 2 0.0224971146
[24,] 1 2 -0.0623618826
[25,] 1 2 -0.0103724737
[26,] 1 2 0.0101588486
[27,] 1 2 -0.0608326387
[28,] 1 2 -0.0776068612
[29,] 1 2 -0.0354349353
[30,] 2 1 0.0544005707
[31,] 1 2 -0.0523378995
[32,] 2 1 0.0755660948
[33,] 2 1 0.1249048886
[34,] 2 1 0.0194722973
[35,] 2 1 0.0632941236
[36,] 2 1 0.0461455404
[37,] 2 1 0.1691205409
[38,] 2 1 0.0499315562
[39,] 2 1 0.1727804458
[40,] 2 1 0.1232010972
[41,] 2 1 0.1485436075
[42,] 2 1 0.1877552944
[43,] 2 1 -0.0278594350
[44,] 2 1 0.0929224210
[45,] 2 1 0.0615964915
[46,] 2 1 0.0614336223
[47,] 2 1 0.0012166020
[48,] 2 1 -0.0811861372
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[199,] 1 2 -0.2348504805
[200,] 1 2 -0.2137737261
[201,] 1 2 -0.2149160197
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attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = complete_clusters_two_s, dist = dist(two_spirals_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_two_s_complete <- mean(two_s_complete_sils[, "sil_width"])
(two_s_average_sils <- silhouette(
x = average_clusters_two_s,
dist = dist(two_spirals_sphere_scaled)
)) cluster neighbor sil_width
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attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = average_clusters_two_s, dist = dist(two_spirals_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_two_s_average <- mean(two_s_average_sils[, "sil_width"])
(two_s_ward_sils <- silhouette(
x = ward_clusters_two_s,
dist = dist(two_spirals_sphere_scaled)
)) cluster neighbor sil_width
[1,] 1 2 0.5041696170
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attr(,"Ordered")
[1] FALSE
attr(,"call")
silhouette.default(x = ward_clusters_two_s, dist = dist(two_spirals_sphere_scaled))
attr(,"class")
[1] "silhouette"avg_two_s_ward <- mean(two_s_ward_sils[, "sil_width"])title_two_single <- paste("Two spirals – single (s =", round(avg_two_s_single, 3), ")")
title_two_complete <- paste("Two spirals – complete (s =", round(avg_two_s_complete, 3), ")")
title_two_average <- paste("Two spirals – average (s =", round(avg_two_s_average, 3), ")")
title_two_ward <- paste("Two spirals – ward (s =", round(avg_two_s_ward, 3), ")")p_ring_single <- ggplot(ring_moon_with_clusters,
aes(x, y, colour = sing_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Single linkage (s =", round(avg_ring_m_single, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_ring_complete <- ggplot(ring_moon_with_clusters,
aes(x, y, colour = comp_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Complete linkage (s =", round(avg_ring_m_complete, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_ring_average <- ggplot(ring_moon_with_clusters,
aes(x, y, colour = ave_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Average linkage (s =", round(avg_ring_m_average, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_ring_ward <- ggplot(ring_moon_with_clusters,
aes(x, y, colour = ward_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Ward linkage (s =", round(avg_ring_m_ward, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")p_three_single <- ggplot(three_spheres_with_clusters,
aes(x, y, colour = sing_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Single linkage (s =", round(avg_three_s_single, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_three_complete <- ggplot(three_spheres_with_clusters,
aes(x, y, colour = comp_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Complete linkage (s =", round(avg_three_s_complete, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_three_average <- ggplot(three_spheres_with_clusters,
aes(x, y, colour = ave_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Average linkage (s =", round(avg_three_s_average, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")
p_three_ward <- ggplot(three_spheres_with_clusters,
aes(x, y, colour = ward_clust)) +
geom_point() +
coord_equal() +
ggtitle(paste("Ward linkage (s =", round(avg_three_s_ward, 3), ")")) +
theme_minimal() +
theme(legend.position = "none")p_two_single <- ggplot(two_spirals_with_clusters,
aes(x, y, colour = sing_clust)) +
geom_point() +
coord_equal() +
labs(title = title_two_single) +
theme_minimal() +
theme(legend.position = "none")
p_two_complete <- ggplot(two_spirals_with_clusters,
aes(x, y, colour = comp_clust)) +
geom_point() +
coord_equal() +
labs(title = title_two_complete) +
theme_minimal() +
theme(legend.position = "none")
p_two_average <- ggplot(two_spirals_with_clusters,
aes(x, y, colour = ave_clust)) +
geom_point() +
coord_equal() +
labs(title = title_two_average) +
theme_minimal() +
theme(legend.position = "none")
p_two_ward <- ggplot(two_spirals_with_clusters,
aes(x, y, colour = ward_clust)) +
geom_point() +
coord_equal() +
labs(title = title_two_ward) +
theme_minimal() +
theme(legend.position = "none")(p_three_single | p_three_complete | p_three_average | p_three_ward) /
(p_ring_single | p_ring_complete | p_ring_average | p_ring_ward) /
(p_two_single | p_two_complete | p_two_average | p_two_ward)
Perform agglomerative clustering with single, complete, average, and Ward linkages. Cut each tree to produce three clusters. Produce 12 scatterplots, one per data set/linkage combination, showing the 3-cluster solution. Title each graph with the linkage used, as well as the average silhouette width (\(\bar s\)) for that clustering solution. Use patchwork to create a nice 4x3 grid of your plots.
Discuss the following:
Which linkage works best for which scenario?
Three spheres: all linkages are 0.72 - which are decently high silhouettes scores - indicates that they performed equally well and it’s hard to pick one or the other
Ring-moon-sphere: average (0.587) ward (0.586) complete (0.488) single (0.145)
Average and ward worked the best here and they did a pretty similar job, while the single and complete linkages performed the worst
Two spirals: average(0.422) ward (0.423) complete (0.386) single (0.158)
Average and ward also performed the best here, but they didn’t do a super great job. Similar to the ring-moon-sphere, the single and complete linkages performed the worst
Does the average silhouette width always do a good job of measuring the quality of the clustering solution?
Using average silhouette width can give a good measure of the overall cluster quality, but it doesn’t necessarily mean it will be entirely accurate. When the clusters are not convex, rather than compact and convex, the estimates will not be as accurate.
(Hint: you have a lot of repetitive code to write. You may find it helpful to write a function that takes a data set and a linkage method as arguments, does the clustering and computes average silhouette width, and produces the desired plot.)
Question 2
Consider the data set below on milk content of 25 mammals. The variables have been pre-scaled to z-scores, hence no additional standardizing is necessary. (Data source: Everitt et al. Cluster analysis 4ed)
mammals <- read.csv('Data/mammal_milk.csv') %>%
column_to_rownames('Mammal')A)
Perform agglomerative clustering with single, complete, average, and Ward linkages. Which has the best agglomerative coefficient?
cluster_mammals <- agnes(mammals, metric='euclidean', method='single')
cluster_mammals <- agnes(mammals, metric='euclidean', method='complete')
cluster_mammals <- agnes(mammals, metric='euclidean', method='average')
cluster_mammals <- agnes(mammals, metric='euclidean', method='ward')(mammals_single <- agnes(mammals, method='single'))$ac[1] 0.7875718(mammals_complete <- agnes(mammals, method='complete'))$ac[1] 0.8985539(mammals_average <- agnes(mammals, method='average'))$ac[1] 0.8706571(mammals_ward <- agnes(mammals, method='ward'))$ac[1] 0.9413994The linkage with the best agglomerative coefficient in this situation is the Ward linkage.
B)
Plot a dendrogram of the method with the highest AC. Which mammals cluster together first?
mammals_ward_tree <- agnes(mammals, method = "ward")
mammals_ward_plot <- fviz_dend(mammals_ward_tree) + ggtitle("Ward linkage dendrogram")Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.
ℹ The deprecated feature was likely used in the factoextra package.
Please report the issue at <https://github.com/kassambara/factoextra/issues>.Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
ℹ The deprecated feature was likely used in the factoextra package.
Please report the issue at <https://github.com/kassambara/factoextra/issues>.Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the factoextra package.
Please report the issue at <https://github.com/kassambara/factoextra/issues>.mammals_ward_plot
The mammals that cluster together first are bison and llama, followed by camel and zebra.
C)
If the tree is cut at a height of 4, how many clusters will form? Which cluster will have the fewest mammals, and which mammals will they be?
fviz_dend(mammals_ward, h = 4) +
labs(title='Ward linkage')
Clusters formed: 4
Fewest mammals: cluster 1, only 5 mammals
Which mammals: bison, llama, camel, zebra, elephant
D)
Use WSS and average silhouette method to suggest the optimal number of clusters. Re-create the dendrogram with the cluster memberships indicated.
fviz_nbclust(mammals,
FUNcluster = hcut,
k.max = 10,
method='wss',
hc_method='ward',
hc_func = 'agnes')
fviz_nbclust(mammals,
FUNcluster = hcut,
k.max = 10,
method='silhouette',
hc_method='ward',
hc_func = 'agnes')
WSS plot: seems to suggest 3 clusters
Average silhouette: also seems to suggest 3 clusters
mammals_clusters_3 <- cutree(as.hclust(mammals_ward_tree), k = 3)
fviz_dend(mammals_ward_tree, k = 3) + labs(title = "Ward linkage dendrogram (k = 3 clusters)")
E)
Use suitable visualizations, including dimension reduction techniques, to explore the different milk characteristics of the assigned clusters. Discuss.
mammals_pca <- prcomp(mammals, center=TRUE, scale. = TRUE)k3_biplot <- fviz_pca(mammals_pca,
habillage = factor(mammals_clusters_3),
repel = TRUE) +
ggtitle("3-cluster solution") +
guides(color = "none", shape = "none")
k3_biplot
mammals_dist <- dist(mammals)
mammals_sils_3 <- silhouette(x = mammals_clusters_3,
dist = mammals_dist)
head(mammals_sils_3) cluster neighbor sil_width
[1,] 1 2 0.6206877
[2,] 1 2 0.5331256
[3,] 1 2 0.6686388
[4,] 1 2 0.1739062
[5,] 2 3 0.6464723
[6,] 2 1 0.3426564fviz_silhouette(mammals_sils_3) cluster size ave.sil.width
1 1 17 0.53
2 2 6 0.54
3 3 2 0.70
Biplot:
-Seal and dolpin milk is high in fat
-Green cluster mammals have milk with more protein and ash
-Red cluster mammals have milk with more water and lactose
- Overall, the mammals can be clearly separated based on their milk types
Silhouette plot:
-Shows an average of 0.55 = decent fit