cmeans: Fuzzy C-Means Clustering

Description Usage Arguments Details Value Author(s) References Examples

View source: R/cmeans.R

Description

The fuzzy version of the known kmeans clustering algorithm as well as an on-line variant (Unsupervised Fuzzy Competitive learning).

Usage

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cmeans(x, centers, iter.max = 100, verbose = FALSE,
       dist = "euclidean", method = "cmeans", m = 2,
       rate.par = NULL, weights = 1, control = list())

Arguments

x

The data matrix where columns correspond to variables and rows to observations.

centers

Number of clusters or initial values for cluster centers.

iter.max

Maximum number of iterations.

verbose

If TRUE, make some output during learning.

dist

Must be one of the following: If "euclidean", the mean square error, if "manhattan", the mean absolute error is computed. Abbreviations are also accepted.

method

If "cmeans", then we have the c-means fuzzy clustering method, if "ufcl" we have the on-line update. Abbreviations are also accepted.

m

A number greater than 1 giving the degree of fuzzification.

rate.par

A number between 0 and 1 giving the parameter of the learning rate for the on-line variant. The default corresponds to 0.3.

weights

a numeric vector with non-negative case weights. Recycled to the number of observations in x if necessary.

control

a list of control parameters. See Details.

Details

The data given by x is clustered by generalized versions of the fuzzy c-means algorithm, which use either a fixed-point or an on-line heuristic for minimizing the objective function

∑_i ∑_j w_i u_{ij}^m d_{ij},

where w_i is the weight of observation i, u_{ij} is the membership of observation i in cluster j, and d_{ij} is the distance (dissimilarity) between observation i and center j. The dissimilarities used are the sums of squares ("euclidean") or absolute values ("manhattan") of the element-wise differences.

If centers is a matrix, its rows are taken as the initial cluster centers. If centers is an integer, centers rows of x are randomly chosen as initial values.

The algorithm stops when the maximum number of iterations (given by iter.max) is reached, or when the algorithm is unable to reduce the current value val of the objective function by reltol * (abs(val) * reltol) at a step. The relative convergence tolerance reltol can be specified as the reltol component of the list of control parameters, and defaults to sqrt(.Machine$double.eps).

If verbose is TRUE, each iteration displays its number and the value of the objective function.

If method is "cmeans", then we have the c-means fuzzy clustering method, see for example Bezdek (1981). If "ufcl", we have the On-line Update (Unsupervised Fuzzy Competitive Learning) method due to Chung and Lee (1992), see also Pal et al (1996). This method works by performing an update directly after each input signal (i.e., for each single observation).

The parameters m defines the degree of fuzzification. It is defined for real values greater than 1 and the bigger it is the more fuzzy the membership values of the clustered data points are.

Value

An object of class "fclust" which is a list with components:

centers

the final cluster centers.

size

the number of data points in each cluster of the closest hard clustering.

cluster

a vector of integers containing the indices of the clusters where the data points are assigned to for the closest hard clustering, as obtained by assigning points to the (first) class with maximal membership.

iter

the number of iterations performed.

membership

a matrix with the membership values of the data points to the clusters.

withinerror

the value of the objective function.

call

the call used to create the object.

Author(s)

Evgenia Dimitriadou and Kurt Hornik

References

J. C. Bezdek (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum.

Fu Lai Chung and Tong Lee (1992). Fuzzy competitive learning. Neural Networks, 7(3), 539–551.

Nikhil R. Pal, James C. Bezdek, and Richard J. Hathaway (1996). Sequential competitive learning and the fuzzy c-means clustering algorithms. Neural Networks, 9(5), 787–796.

Examples

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# a 2-dimensional example
x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=1,sd=0.3),ncol=2))
cl<-cmeans(x,2,20,verbose=TRUE,method="cmeans",m=2)
print(cl)

# a 3-dimensional example
x<-rbind(matrix(rnorm(150,sd=0.3),ncol=3),
         matrix(rnorm(150,mean=1,sd=0.3),ncol=3),
         matrix(rnorm(150,mean=2,sd=0.3),ncol=3))
cl<-cmeans(x,6,20,verbose=TRUE,method="cmeans")
print(cl)

Example output

Iteration:   1, Error:  0.1646046972
Iteration:   2, Error:  0.1543607452
Iteration:   3, Error:  0.1542090708
Iteration:   4, Error:  0.1542074436
Iteration:   5, Error:  0.1542074251
Iteration:   6 converged, Error:  0.1542074248
Fuzzy c-means clustering with 2 clusters

Cluster centers:
        [,1]        [,2]
1 -0.1263853 -0.08036624
2  0.9699374  1.13365887

Memberships:
                  1           2
  [1,] 0.8041721115 0.195827889
  [2,] 0.9624985570 0.037501443
  [3,] 0.9422326865 0.057767313
  [4,] 0.9358055047 0.064194495
  [5,] 0.9494495198 0.050550480
  [6,] 0.8087931231 0.191206877
  [7,] 0.9833660711 0.016633929
  [8,] 0.9819309179 0.018069082
  [9,] 0.9894646400 0.010535360
 [10,] 0.9715390275 0.028460973
 [11,] 0.9311442900 0.068855710
 [12,] 0.9375432876 0.062456712
 [13,] 0.9130738829 0.086926117
 [14,] 0.9192294617 0.080770538
 [15,] 0.9724676099 0.027532390
 [16,] 0.9317887302 0.068211270
 [17,] 0.9820251726 0.017974827
 [18,] 0.9853295839 0.014670416
 [19,] 0.8442704429 0.155729557
 [20,] 0.9441364738 0.055863526
 [21,] 0.9153389923 0.084661008
 [22,] 0.9826214149 0.017378585
 [23,] 0.9892078061 0.010792194
 [24,] 0.8759832492 0.124016751
 [25,] 0.9540134279 0.045986572
 [26,] 0.9347523673 0.065247633
 [27,] 0.9973578267 0.002642173
 [28,] 0.8199341875 0.180065812
 [29,] 0.9360137796 0.063986220
 [30,] 0.9361926486 0.063807351
 [31,] 0.9446261582 0.055373842
 [32,] 0.9912608295 0.008739171
 [33,] 0.6940101181 0.305989882
 [34,] 0.6148928515 0.385107149
 [35,] 0.7882044852 0.211795515
 [36,] 0.9814336729 0.018566327
 [37,] 0.9323308133 0.067669187
 [38,] 0.9723538916 0.027646108
 [39,] 0.5611358982 0.438864102
 [40,] 0.9506471475 0.049352853
 [41,] 0.9420410152 0.057958985
 [42,] 0.9475289679 0.052471032
 [43,] 0.9380632237 0.061936776
 [44,] 0.9928575856 0.007142414
 [45,] 0.9790199311 0.020980069
 [46,] 0.9217313557 0.078268644
 [47,] 0.8883284811 0.111671519
 [48,] 0.9816556987 0.018344301
 [49,] 0.9549250997 0.045074900
 [50,] 0.8871454670 0.112854533
 [51,] 0.2114530375 0.788546962
 [52,] 0.0862448751 0.913755125
 [53,] 0.0510784637 0.948921536
 [54,] 0.0004877015 0.999512298
 [55,] 0.0414776249 0.958522375
 [56,] 0.0259554941 0.974044506
 [57,] 0.0014311945 0.998568806
 [58,] 0.0516033727 0.948396627
 [59,] 0.0688317563 0.931168244
 [60,] 0.0352494627 0.964750537
 [61,] 0.0129179845 0.987082016
 [62,] 0.1849344045 0.815065595
 [63,] 0.0100294106 0.989970589
 [64,] 0.0003615129 0.999638487
 [65,] 0.0271209451 0.972879055
 [66,] 0.0169744698 0.983025530
 [67,] 0.0623126968 0.937687303
 [68,] 0.0183115960 0.981688404
 [69,] 0.0212901927 0.978709807
 [70,] 0.1699873547 0.830012645
 [71,] 0.0762438670 0.923756133
 [72,] 0.0274513011 0.972548699
 [73,] 0.0346728814 0.965327119
 [74,] 0.0165709526 0.983429047
 [75,] 0.1757232598 0.824276740
 [76,] 0.0137118788 0.986288121
 [77,] 0.1526938167 0.847306183
 [78,] 0.0094204114 0.990579589
 [79,] 0.0679097455 0.932090254
 [80,] 0.0586380314 0.941361969
 [81,] 0.1199307203 0.880069280
 [82,] 0.0321827248 0.967817275
 [83,] 0.0456242573 0.954375743
 [84,] 0.0047418541 0.995258146
 [85,] 0.0470258756 0.952974124
 [86,] 0.0436314118 0.956368588
 [87,] 0.0091670303 0.990832970
 [88,] 0.0529815880 0.947018412
 [89,] 0.0454349758 0.954565024
 [90,] 0.0292213963 0.970778604
 [91,] 0.0298330734 0.970166927
 [92,] 0.0353835883 0.964616412
 [93,] 0.0278109131 0.972189087
 [94,] 0.0810262427 0.918973757
 [95,] 0.0348255780 0.965174422
 [96,] 0.0444705016 0.955529498
 [97,] 0.1344526231 0.865547377
 [98,] 0.0021772383 0.997822762
 [99,] 0.0000134157 0.999986584
[100,] 0.0145777392 0.985422261

Closest hard clustering:
  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 [75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Available components:
[1] "centers"     "size"        "cluster"     "membership"  "iter"       
[6] "withinerror" "call"       
Iteration:   1, Error:  0.1298456810
Iteration:   2, Error:  0.1229062610
Iteration:   3, Error:  0.1212776711
Iteration:   4, Error:  0.1206833559
Iteration:   5, Error:  0.1204243043
Iteration:   6, Error:  0.1202854412
Iteration:   7, Error:  0.1201900100
Iteration:   8, Error:  0.1201088417
Iteration:   9, Error:  0.1200290587
Iteration:  10, Error:  0.1199452623
Iteration:  11, Error:  0.1198574450
Iteration:  12, Error:  0.1197696703
Iteration:  13, Error:  0.1196878506
Iteration:  14, Error:  0.1196170832
Iteration:  15, Error:  0.1195598756
Iteration:  16, Error:  0.1195160069
Iteration:  17, Error:  0.1194835469
Iteration:  18, Error:  0.1194600296
Iteration:  19, Error:  0.1194431820
Iteration:  20, Error:  0.1194311862
Fuzzy c-means clustering with 6 clusters

Cluster centers:
        [,1]        [,2]        [,3]
1 2.02713891  2.06187217  1.60006313
2 1.85480130  1.87632883  2.17935541
3 2.22873211  1.95218615  2.13934215
4 0.01608874 -0.04380011 -0.04180612
5 0.89331264  0.86158238  0.73616487
6 1.02580340  1.10541890  1.07396566

Memberships:
                 1           2           3            4           5           6
  [1,] 0.031182129 0.029894678 0.026495493 0.7332621295 0.103531727 0.075633843
  [2,] 0.006293163 0.005924999 0.005132503 0.9267356727 0.034798201 0.021115462
  [3,] 0.043602468 0.044905678 0.038483940 0.5466457597 0.190425146 0.135937009
  [4,] 0.005105510 0.004863401 0.004261589 0.9474284213 0.023209348 0.015131730
  [5,] 0.006103718 0.005809667 0.005036668 0.9285204463 0.033923423 0.020606077
  [6,] 0.017003813 0.016006522 0.014390295 0.8440141699 0.064673464 0.043911736
  [7,] 0.017438711 0.015493820 0.013659739 0.7791045373 0.113410722 0.060892471
  [8,] 0.009643208 0.009098969 0.008049831 0.9079532465 0.038988411 0.026266335
  [9,] 0.019550633 0.018918679 0.016756501 0.8041357613 0.084502979 0.056135446
 [10,] 0.008592215 0.008217756 0.007259424 0.9145936237 0.036898237 0.024438745
 [11,] 0.010661819 0.010161943 0.009022874 0.8973319686 0.043582275 0.029239120
 [12,] 0.001968249 0.001818769 0.001604215 0.9791992418 0.009492673 0.005916853
 [13,] 0.026868012 0.023393047 0.021126600 0.7166762073 0.133365085 0.078571048
 [14,] 0.009109111 0.008750079 0.007705480 0.9087687621 0.039475392 0.026191175
 [15,] 0.023057138 0.021472378 0.019119586 0.7355531097 0.126344937 0.074452851
 [16,] 0.002633931 0.002495302 0.002193376 0.9723208433 0.012427799 0.007928748
 [17,] 0.017499578 0.015893572 0.013951170 0.7607045624 0.126489801 0.065461317
 [18,] 0.006475889 0.006130995 0.005419997 0.9313758000 0.031038764 0.019558555
 [19,] 0.004021132 0.003698344 0.003293002 0.9572521600 0.019695333 0.012040028
 [20,] 0.021167789 0.018747250 0.016454449 0.7207328912 0.146194038 0.076703582
 [21,] 0.015191664 0.014569793 0.012755628 0.8249640223 0.082278444 0.050240450
 [22,] 0.015278086 0.014108936 0.012372400 0.8464962886 0.067589863 0.044154426
 [23,] 0.023409303 0.021243179 0.018460081 0.7389067068 0.122648950 0.075331780
 [24,] 0.018354571 0.017716551 0.015746596 0.8285614700 0.070790536 0.048830275
 [25,] 0.024683662 0.023130683 0.020729744 0.7395746142 0.118277428 0.073603869
 [26,] 0.012717975 0.012298906 0.010731588 0.8732647680 0.054257537 0.036729226
 [27,] 0.007258978 0.006708534 0.005834637 0.9077472281 0.046453562 0.025997061
 [28,] 0.002594901 0.002440015 0.002133353 0.9720402621 0.012760208 0.008031261
 [29,] 0.018890251 0.017666928 0.015280866 0.7292689892 0.143614355 0.075278611
 [30,] 0.012900199 0.011729916 0.010331469 0.8658674451 0.060899950 0.038271021
 [31,] 0.036466119 0.031517850 0.028223149 0.6386216233 0.163231814 0.101939443
 [32,] 0.013800337 0.012723795 0.011434194 0.8592258262 0.063277270 0.039538578
 [33,] 0.024344525 0.021375481 0.018844778 0.6782372377 0.169436053 0.087761925
 [34,] 0.031996321 0.030473882 0.026652136 0.5827042994 0.209588630 0.118584732
 [35,] 0.029479272 0.026669067 0.023793585 0.7355012190 0.109599015 0.074957842
 [36,] 0.018746110 0.016965205 0.015329572 0.8280458258 0.072794177 0.048119110
 [37,] 0.014597778 0.013593325 0.011946801 0.8578010470 0.061215787 0.040845263
 [38,] 0.028993857 0.026464929 0.023837538 0.6799064993 0.151392293 0.089404883
 [39,] 0.019117446 0.016924331 0.014915445 0.7699441256 0.114953979 0.064144674
 [40,] 0.043404573 0.039525829 0.034318994 0.5822910602 0.178034902 0.122424641
 [41,] 0.018387567 0.018017805 0.015745729 0.8208723040 0.075066183 0.051910412
 [42,] 0.016013662 0.014533084 0.012831873 0.7933206646 0.106384945 0.056915772
 [43,] 0.007152092 0.006691343 0.005924854 0.9208292207 0.036990924 0.022411566
 [44,] 0.018980023 0.017737290 0.015171784 0.7434440337 0.131246443 0.073420427
 [45,] 0.016660708 0.015102723 0.013237562 0.7712993488 0.121146931 0.062552727
 [46,] 0.009072265 0.008438969 0.007326118 0.8971035266 0.048420388 0.029638733
 [47,] 0.016143132 0.014837984 0.013174850 0.8480377614 0.064598381 0.043207892
 [48,] 0.001461545 0.001360121 0.001205122 0.9846420968 0.006976088 0.004355027
 [49,] 0.003889862 0.003598323 0.003166631 0.9539975364 0.022397091 0.012950557
 [50,] 0.025546153 0.022666226 0.020104830 0.7425877245 0.115955351 0.073139716
 [51,] 0.046264481 0.050020174 0.038122189 0.0723822558 0.390034039 0.403176861
 [52,] 0.022398404 0.017378263 0.014055030 0.0175561146 0.437933695 0.490678494
 [53,] 0.040790104 0.030126180 0.024672268 0.0193174308 0.274042849 0.611051169
 [54,] 0.097090861 0.061930822 0.053121560 0.0456466324 0.338853080 0.403357045
 [55,] 0.013621711 0.011874554 0.009281567 0.0083909430 0.154631275 0.802199951
 [56,] 0.017984481 0.015808344 0.012618935 0.0315904960 0.674298401 0.247699344
 [57,] 0.007982512 0.007389885 0.005570039 0.0049027593 0.077041243 0.897113561
 [58,] 0.014716581 0.012567412 0.009718921 0.0074140747 0.112520288 0.843062723
 [59,] 0.066330058 0.072011936 0.049381434 0.0395576960 0.231980534 0.540738342
 [60,] 0.016148092 0.015325914 0.011932409 0.0231989244 0.566017593 0.367377068
 [61,] 0.094702673 0.066800197 0.053067531 0.0436193056 0.292140958 0.449669335
 [62,] 0.043883182 0.046166458 0.036418800 0.0899405331 0.440064743 0.343526283
 [63,] 0.074616152 0.077718776 0.053477323 0.0417847577 0.234382055 0.518020935
 [64,] 0.031491957 0.030752342 0.021609401 0.0154976154 0.142536975 0.758111709
 [65,] 0.025892384 0.023118021 0.017329297 0.0107491390 0.122030374 0.800880784
 [66,] 0.025239407 0.024829620 0.019145749 0.0402951378 0.497912538 0.392577547
 [67,] 0.039712733 0.029560393 0.025523199 0.0498948665 0.586087027 0.269221782
 [68,] 0.010469482 0.008953223 0.007382476 0.0238647208 0.833637009 0.115693089
 [69,] 0.006065325 0.005311596 0.004297732 0.0113591210 0.879046751 0.093919474
 [70,] 0.077607075 0.072613887 0.062556569 0.0637461983 0.357279910 0.366196361
 [71,] 0.032702798 0.033256389 0.024121076 0.0270331962 0.250930364 0.631956177
 [72,] 0.088320777 0.060600439 0.051776052 0.0312208199 0.282433843 0.485648069
 [73,] 0.132549617 0.080261986 0.064696239 0.0300207410 0.218810550 0.473660867
 [74,] 0.095507479 0.066312074 0.051209043 0.0316726056 0.237560329 0.517738470
 [75,] 0.036015320 0.035384359 0.028546497 0.0479844869 0.473256481 0.378812857
 [76,] 0.007424191 0.006646909 0.004880437 0.0037358645 0.048664587 0.928648012
 [77,] 0.016145154 0.013076890 0.011167018 0.0288478359 0.783289205 0.147473896
 [78,] 0.164385878 0.114526695 0.080918552 0.0269426317 0.165999574 0.447226669
 [79,] 0.048046933 0.043204244 0.033150523 0.0560528071 0.391474699 0.428070793
 [80,] 0.037925512 0.028470164 0.024819000 0.0475649521 0.602440899 0.258779473
 [81,] 0.005792613 0.005076313 0.003949968 0.0042043150 0.107842108 0.873134683
 [82,] 0.008604478 0.007148191 0.005605474 0.0051527659 0.108818405 0.864670686
 [83,] 0.014037073 0.011221505 0.009497201 0.0211651253 0.794840427 0.149238669
 [84,] 0.030858002 0.028310640 0.019992563 0.0123610285 0.117437362 0.791040404
 [85,] 0.099485054 0.077760680 0.070865305 0.0579117000 0.341426021 0.352551241
 [86,] 0.025695831 0.022154454 0.016747888 0.0186691063 0.250587469 0.666145251
 [87,] 0.016448974 0.015151108 0.011063205 0.0098768195 0.121020049 0.826439846
 [88,] 0.032185612 0.030158552 0.025423209 0.1915921704 0.521733727 0.198906730
 [89,] 0.151710685 0.092716833 0.072724749 0.0267479691 0.187686144 0.468413620
 [90,] 0.020181706 0.018164711 0.013149027 0.0100196650 0.111300509 0.827184383
 [91,] 0.038405705 0.030084256 0.022509666 0.0147804250 0.156489575 0.737730372
 [92,] 0.019793522 0.017765762 0.014209369 0.0174236781 0.400109736 0.530697934
 [93,] 0.037840481 0.031417104 0.027069307 0.0423520599 0.551231545 0.310089503
 [94,] 0.028563079 0.024413929 0.019354550 0.0391115942 0.535048107 0.353508741
 [95,] 0.041877741 0.038463595 0.031014845 0.0291958238 0.333959546 0.525488450
 [96,] 0.016342248 0.013236416 0.010861752 0.0142389920 0.547523239 0.397797354
 [97,] 0.035345437 0.032474963 0.027517445 0.0686327355 0.569677445 0.266351975
 [98,] 0.015665510 0.015056775 0.011473896 0.0133240788 0.233714114 0.710765627
 [99,] 0.004448651 0.003928881 0.003041295 0.0034666777 0.098064450 0.887050045
[100,] 0.016116657 0.015419471 0.011847780 0.0151503431 0.298191925 0.643273824
[101,] 0.011390208 0.031100197 0.955233303 0.0002895831 0.000794716 0.001191993
[102,] 0.101005309 0.517271049 0.338644478 0.0058379108 0.014971840 0.022269413
[103,] 0.537157317 0.134003561 0.152533581 0.0182200140 0.063919110 0.094166417
[104,] 0.052551293 0.079712038 0.859162408 0.0010488391 0.002994473 0.004530948
[105,] 0.772785916 0.076987015 0.124881941 0.0030583547 0.008943314 0.013343459
[106,] 0.064438785 0.824437771 0.093072961 0.0018840446 0.006016784 0.010149655
[107,] 0.191239837 0.227533527 0.528513330 0.0076855065 0.018750337 0.026277462
[108,] 0.088972659 0.665849646 0.211855031 0.0042052456 0.011445408 0.017672010
[109,] 0.687488273 0.116033595 0.140547595 0.0068438530 0.019821758 0.029264926
[110,] 0.388123884 0.344894932 0.231131561 0.0037046915 0.012094379 0.020050553
[111,] 0.377065992 0.185370621 0.369398209 0.0079728535 0.024143024 0.036049301
[112,] 0.093040707 0.295689574 0.570649531 0.0057146175 0.014305032 0.020600539
[113,] 0.840054746 0.055771664 0.085799030 0.0021694603 0.006463303 0.009741797
[114,] 0.030326654 0.058565984 0.903794644 0.0009509014 0.002573018 0.003788798
[115,] 0.093801211 0.451891363 0.405203728 0.0066627377 0.017134386 0.025306575
[116,] 0.059618474 0.813125846 0.100700933 0.0029746585 0.008904841 0.014675247
[117,] 0.086835359 0.085555088 0.059224372 0.0223276299 0.160343862 0.585713689
[118,] 0.160627654 0.357077235 0.422861857 0.0085459899 0.020896919 0.029990346
[119,] 0.087621452 0.114171490 0.776713389 0.0028688073 0.007623383 0.011001479
[120,] 0.430101179 0.344888670 0.183804997 0.0043916969 0.013912458 0.022900999
[121,] 0.106490706 0.338872767 0.498837647 0.0078748245 0.019657413 0.028266642
[122,] 0.156810105 0.468170616 0.228891120 0.0197367689 0.050127715 0.076263674
[123,] 0.274972235 0.218162221 0.451941244 0.0063251623 0.019236015 0.029363123
[124,] 0.286068836 0.187813888 0.432238735 0.0135411159 0.034184255 0.046153169
[125,] 0.266304581 0.148908869 0.550297133 0.0042775826 0.012196905 0.018014929
[126,] 0.057602234 0.253785235 0.677191249 0.0013569706 0.003943460 0.006120851
[127,] 0.059954603 0.807677178 0.114266598 0.0019211436 0.006068918 0.010111560
[128,] 0.354755446 0.151574932 0.445309559 0.0063574430 0.017299562 0.024703058
[129,] 0.080631055 0.240388710 0.666645562 0.0014544418 0.004257755 0.006622478
[130,] 0.018413308 0.941551666 0.035077104 0.0005429127 0.001668422 0.002746587
[131,] 0.303469936 0.318632210 0.285883828 0.0125488419 0.032286194 0.047178990
[132,] 0.122789071 0.617211259 0.226059062 0.0035595781 0.011414350 0.018966680
[133,] 0.103812642 0.629297321 0.193707112 0.0080710044 0.024530448 0.040581474
[134,] 0.291390446 0.489524548 0.171465860 0.0047167318 0.015768891 0.027133524
[135,] 0.021089637 0.035384688 0.939366319 0.0005421933 0.001462666 0.002154497
[136,] 0.204182703 0.488294428 0.284340586 0.0025863257 0.007901570 0.012694386
[137,] 0.080933651 0.636295311 0.237090108 0.0055337962 0.015635702 0.024511431
[138,] 0.165862228 0.632985321 0.146749478 0.0055073664 0.017918986 0.030976620
[139,] 0.196280700 0.286170100 0.440995583 0.0117092568 0.027207365 0.037636996
[140,] 0.937566144 0.027773908 0.026312882 0.0008602356 0.002846972 0.004639859
[141,] 0.137257276 0.147575403 0.688903073 0.0035824940 0.009304407 0.013377348
[142,] 0.043607930 0.782426346 0.161654670 0.0015038453 0.004225908 0.006581300
[143,] 0.063169190 0.297391699 0.621846069 0.0021295718 0.006092289 0.009371181
[144,] 0.101205599 0.355274019 0.493763094 0.0070428126 0.017491707 0.025222769
[145,] 0.813353793 0.072735522 0.068523021 0.0044769875 0.015557716 0.025352961
[146,] 0.616823895 0.118588621 0.146667272 0.0134167754 0.042802929 0.061700508
[147,] 0.126145069 0.255696994 0.572723184 0.0056608105 0.015950209 0.023823733
[148,] 0.121478723 0.265004378 0.584640086 0.0038963158 0.010127414 0.014853083
[149,] 0.284671071 0.327601458 0.160945416 0.0190844246 0.071171191 0.136526439
[150,] 0.047253642 0.701891894 0.233753137 0.0020622925 0.005872042 0.009166992

Closest hard clustering:
  [1] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
 [38] 4 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 5 6 6 6 5 6 5 6 6 6 5 5 5 5 6 6 6 6 6
 [75] 5 6 5 6 6 5 6 6 5 6 6 6 6 5 6 6 6 6 5 5 6 5 5 6 6 6 3 2 1 3 1 2 3 2 1 1 1
[112] 3 1 3 2 2 6 3 3 1 3 2 3 3 3 3 2 3 3 2 2 2 2 2 3 2 2 2 3 1 3 2 3 3 1 1 3 3
[149] 2 2

Available components:
[1] "centers"     "size"        "cluster"     "membership"  "iter"       
[6] "withinerror" "call"       

e1071 documentation built on Oct. 23, 2020, 5:13 p.m.