Chapter 18 K Means
Now that we have our data, let us proceed with the k-means analysis! First, we’ll want to set the seed of our analysis (setting our seed makes it possible to replicate the data in the future). Then, we’ll use the kmeans() function. kmeans() takes at least 2 arguments: the data and the number of clusters (centers).
The goal of a k-means analysis is to minimize intra-cluster variation while maximizing inter-cluster variation. In other words, you want the observations in a cluster to be more similar with one another than they are similar to observations in other clusters.
set.seed(381)
k3 <- kmeans(survey_data, centers = 3)
print(k3) #this will also print out the results per observation too## K-means clustering with 3 clusters of sizes 400, 545, 61
##
## Cluster means:
## issue_econ issue_race issue_covid trumpapprove
## 1 3.822500 2.747500 2.650000 3.822500
## 2 3.552294 3.825688 3.858716 1.157798
## 3 3.491803 1.442623 2.737705 1.786885
##
## Clustering vector:
## 1 2 3 4 6 7 8 9 10 11 12 13 14 16 18 19
## 2 2 2 2 2 2 1 1 2 2 1 2 1 1 1 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## 1 2 1 2 2 2 2 1 2 2 1 1 1 3 2 1
## 37 38 39 40 41 42 43 44 46 47 48 49 50 51 53 55
## 1 2 1 2 1 2 2 1 1 2 2 2 1 2 2 1
## 56 57 58 59 60 61 62 63 64 66 67 69 72 73 74 75
## 2 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2
## 76 77 78 79 80 81 82 83 86 87 88 89 90 91 92 93
## 3 3 2 1 3 2 2 2 2 1 1 2 1 1 1 1
## 94 95 96 97 98 99 100 101 102 103 104 106 107 108 109 110
## 2 2 1 1 2 1 1 1 1 2 2 1 2 1 1 1
## 111 112 113 115 116 117 118 119 120 122 123 125 126 127 128 129
## 2 1 2 3 3 2 2 1 2 2 1 2 2 1 2 2
## 130 131 132 133 134 136 137 139 140 142 143 144 145 146 150 151
## 2 1 2 2 2 1 1 1 1 2 2 2 1 1 1 2
## 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167
## 1 1 2 2 2 1 1 1 2 2 1 1 2 1 1 2
## 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183
## 2 1 2 3 1 1 1 2 2 1 1 1 2 1 2 2
## 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199
## 2 2 3 2 1 1 1 1 1 2 1 2 2 2 2 2
## 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
## 1 1 1 2 1 2 1 2 3 3 2 1 1 1 1 2
## 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231
## 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1
## 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247
## 2 2 2 2 1 2 1 2 2 2 1 2 2 1 2 2
## 248 249 250 251 252 253 254 255 256 258 259 260 261 262 263 264
## 1 2 1 1 2 2 2 1 2 2 2 2 1 1 2 1
## 265 266 267 270 271 274 275 276 278 280 281 282 283 284 285 287
## 1 1 2 2 2 2 1 1 2 3 2 1 2 2 2 2
## 289 290 291 294 296 298 300 301 302 303 304 305 306 307 308 309
## 2 1 1 3 3 2 2 2 2 1 2 2 1 2 1 2
## 311 312 313 314 315 316 317 318 319 320 321 323 324 325 326 327
## 1 2 1 2 1 1 2 2 2 1 1 2 2 2 2 2
## 328 329 330 331 332 333 334 335 336 337 338 339 340 341 344 345
## 2 3 2 2 2 1 2 2 1 1 2 1 2 1 1 2
## 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 362
## 2 2 3 2 2 3 1 2 2 3 2 1 1 2 1 1
## 363 364 365 366 367 368 369 370 371 372 373 376 377 378 379 380
## 2 2 2 1 1 1 1 3 2 2 1 2 1 1 2 2
## 381 382 384 385 386 387 388 389 390 391 392 393 394 395 396 397
## 2 2 2 1 1 1 3 1 1 1 1 1 2 2 1 2
## 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413
## 2 2 2 2 1 3 1 2 1 1 2 2 1 2 1 1
## 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429
## 3 2 1 1 2 2 2 2 1 1 2 2 1 1 1 1
## 430 431 432 433 435 437 438 440 441 442 443 444 445 447 448 449
## 2 2 1 2 1 1 1 1 1 1 3 1 2 2 2 1
## 450 453 454 455 456 457 459 462 463 465 466 468 469 470 471 472
## 3 1 1 2 1 2 1 2 2 2 1 1 2 2 1 1
## 474 475 476 477 478 479 480 481 482 483 485 486 487 488 489 490
## 3 1 1 2 2 1 1 2 1 1 2 1 1 2 2 1
## 491 493 494 495 499 501 503 504 505 506 507 508 509 510 511 512
## 2 1 1 1 2 2 2 1 2 1 1 2 2 2 2 2
## 513 514 515 516 518 519 523 524 526 527 528 529 530 532 533 534
## 2 3 2 2 1 1 2 1 2 1 2 1 2 1 2 2
## 535 536 537 539 541 542 543 545 546 547 548 549 550 551 552 553
## 2 1 2 3 2 2 1 1 3 1 3 2 2 2 1 1
## 554 555 557 558 560 561 562 563 564 565 566 567 568 569 570 572
## 2 2 2 1 2 2 1 3 1 3 1 1 2 2 2 1
## 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588
## 3 2 2 1 2 2 1 1 2 1 1 1 1 1 1 2
## 589 590 593 594 597 600 603 605 606 607 608 610 612 613 615 617
## 2 1 1 2 2 1 1 2 1 1 2 2 2 3 2 3
## 618 619 620 621 622 623 624 625 626 627 629 630 631 633 635 637
## 2 1 2 1 2 1 1 1 2 2 2 2 1 3 1 2
## 639 640 641 643 644 645 646 648 649 650 651 652 653 654 655 657
## 3 1 2 2 2 2 2 1 2 2 2 1 1 1 2 3
## 658 659 660 662 663 664 665 666 667 668 669 671 672 673 674 675
## 2 2 1 1 1 3 2 1 2 1 2 2 2 2 1 1
## 677 678 680 681 682 683 684 686 687 688 689 691 692 693 694 695
## 3 1 3 2 1 3 1 1 1 2 2 1 2 2 1 2
## 696 697 698 699 700 701 702 703 704 705 707 708 709 711 712 713
## 2 1 2 2 2 2 2 2 3 1 2 2 2 1 2 2
## 714 715 716 717 718 719 720 722 723 724 725 726 727 728 729 730
## 2 2 2 2 3 1 1 2 1 1 2 2 2 2 2 3
## 731 732 734 735 736 737 738 739 740 741 742 743 744 745 746 747
## 2 2 1 1 2 2 1 2 2 2 1 1 1 2 1 2
## 748 749 750 751 752 754 755 756 757 758 761 762 764 765 766 767
## 1 2 2 1 2 2 1 2 2 2 2 1 1 2 2 2
## 768 769 771 772 773 775 776 778 779 780 783 784 787 788 789 790
## 2 3 2 2 2 3 2 1 2 1 1 2 2 2 1 2
## 791 792 793 794 795 798 799 800 804 805 806 807 808 809 810 811
## 1 2 1 2 1 1 2 2 2 1 1 2 2 2 1 1
## 812 813 815 816 817 818 819 820 821 822 823 824 825 826 827 828
## 2 1 1 2 2 2 2 2 2 2 1 1 2 2 2 2
## 829 830 832 834 835 836 837 840 841 843 844 845 846 847 849 850
## 2 2 2 1 1 1 2 2 2 2 1 1 2 2 2 2
## 851 852 856 857 858 859 860 862 863 864 866 867 868 869 870 871
## 3 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2
## 872 873 874 876 877 879 880 881 882 883 884 885 888 889 890 891
## 3 2 1 2 1 2 1 1 1 2 2 2 2 2 2 2
## 892 894 895 896 897 898 900 902 903 904 905 906 907 908 909 910
## 2 2 2 1 1 2 2 2 1 1 2 1 1 1 2 1
## 912 913 914 916 917 918 919 920 921 922 923 924 925 926 928 930
## 2 1 1 1 2 2 2 1 2 1 1 1 1 1 2 3
## 931 932 933 934 935 936 937 939 941 943 945 946 947 948 949 950
## 2 2 3 2 2 2 3 2 1 1 2 3 1 1 1 2
## 951 952 953 954 955 956 957 958 959 960 961 962 963 964 966 968
## 2 1 1 1 1 2 2 1 2 1 2 2 1 2 2 2
## 969 971 972 974 975 976 977 978 982 983 984 986 988 990 991 994
## 2 2 2 2 2 1 2 2 3 1 1 2 1 1 2 2
## 996 997 998 1000 1001 1002 1003 1004 1005 1007 1008 1009 1010 1011 1012 1014
## 3 1 1 2 2 1 2 1 1 1 3 2 2 2 1 1
## 1015 1018 1021 1022 1023 1024 1025 1026 1028 1029 1030 1031 1032 1033 1034 1038
## 1 1 1 1 1 2 2 1 2 2 2 2 2 2 2 1
## 1039 1040 1041 1042 1044 1045 1046 1047 1048 1049 1050 1051 1054 1055 1056 1057
## 1 2 1 2 2 2 1 1 2 2 1 2 1 2 1 1
## 1058 1059 1061 1063 1064 1065 1066 1068 1069 1070 1072 1075 1076 1077 1078 1079
## 1 2 3 2 2 1 3 3 3 2 1 2 2 2 2 1
## 1080 1081 1082 1083 1084 1085 1087 1088 1089 1090 1091 1093 1094 1095 1096 1097
## 2 2 1 2 1 2 2 2 2 2 2 2 3 1 1 3
## 1098 1099 1100 1103 1104 1106 1107 1108 1110 1111 1112 1113 1114 1115 1116 1118
## 1 2 2 1 2 1 2 2 2 2 2 2 2 2 1 1
## 1119 1120 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135
## 1 2 1 2 1 2 2 1 2 2 2 2 1 2 1 2
## 1136 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1152 1153
## 1 1 2 2 1 1 1 2 1 2 2 1 1 1 1 2
## 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169
## 2 2 1 2 1 2 1 2 2 2 2 2 2 1 2 1
## 1170 1171 1172 1173 1174 1175 1176 1177 1178 1180 1183 1185 1187 1188 1190 1191
## 2 2 2 1 1 1 2 2 2 2 1 1 1 2 2 2
## 1192 1193 1194 1195 1196 1198 1199 1201 1202 1203 1204 1205 1206 1207
## 2 3 1 2 2 2 1 1 1 2 1 1 2 2
##
## Within cluster sum of squares by cluster:
## [1] 1049.2925 497.7505 214.3279
## (between_SS / total_SS = 58.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"K-means is a single-cluster assignment, so each observation will be automatically assigned to one cluster. You can extract the cluster results (per observation) from the data by extracting the $cluster atomic.
Below, we extract the clusters per each observation and then attach it to the survey data.
survey_data$cluster <- k3$cluster18.1 Visualization
Another useful thing to do is to visualize the results of the k-means analysis. To do so, we can use the fviz_cluster() function, which is from factoextra. Let us do this now with our 3-cluster analysis.
fviz_cluster(k3, data = survey_data,
#palette = c("#2E9FDF", "#00AFBB", "#E7B800"), #change the colors of the clusters
geom = "point", ggtheme = theme_minimal())
We could obviously do this with analyses including larger clusters. This can be especially useful to determine the optimal number of clusters.
k2 <- kmeans(survey_data, centers = 2, nstart = 25)
fviz_cluster(k2, data = survey_data,
geom = "point", ggtheme = theme_minimal())
k4 <- kmeans(survey_data, centers = 4, nstart = 25)
fviz_cluster(k4, data = survey_data,
geom = "point", ggtheme = theme_minimal())
k5 <- kmeans(survey_data, centers = 5, nstart = 25)
fviz_cluster(k5, data = survey_data,
geom = "point", ggtheme = theme_minimal())
k9 <- kmeans(survey_data, centers = 9, nstart = 25)
fviz_cluster(k9, data = survey_data,
geom = "point", ggtheme = theme_minimal())