Data 609 Module 6 Homework
Don Padmaperuma
Ex.1
Use a dataset such as the PlantGrowth in R to calculate three different distance metrics and discuss the results.
PlantGrowth data set which pertains to Results from an Experiment on Plant Growth.
Euclidean Distance
This represents the shortest distance between two points.
PlantGrowth_euclidean <- dist(PlantGrowth, method = "euclidean")## Warning in dist(PlantGrowth, method = "euclidean"): NAs introduced by coercionas.matrix(PlantGrowth_euclidean)## 1 2 3 4 5 6 7
## 1 0.0000000 1.99404112 1.42835570 2.74357431 0.46669048 0.6222540 1.41421356
## 2 1.9940411 0.00000000 0.56568542 0.74953319 1.52735065 1.3717872 0.57982756
## 3 1.4283557 0.56568542 0.00000000 1.31521861 0.96166522 0.8061017 0.01414214
## 4 2.7435743 0.74953319 1.31521861 0.00000000 2.27688384 2.1213203 1.32936075
## 5 0.4666905 1.52735065 0.96166522 2.27688384 0.00000000 0.1555635 0.94752309
## 6 0.6222540 1.37178716 0.80610173 2.12132034 0.15556349 0.0000000 0.79195959
## 7 1.4142136 0.57982756 0.01414214 1.32936075 0.94752309 0.7919596 0.00000000
## 8 0.5091169 1.48492424 0.91923882 2.23445743 0.04242641 0.1131371 0.90509668
## 9 1.6404877 0.35355339 0.21213203 1.10308658 1.17379726 1.0182338 0.22627417
## 10 1.3717872 0.62225397 0.05656854 1.37178716 0.90509668 0.7495332 0.04242641
## 11 0.9050967 1.08894444 0.52325902 1.83847763 0.43840620 0.2828427 0.50911688
## 12 0.0000000 1.99404112 1.42835570 2.74357431 0.46669048 0.6222540 1.41421356
## 13 0.3394113 1.65462987 1.08894444 2.40416306 0.12727922 0.2828427 1.07480231
## 14 0.8202439 2.81428499 2.24859956 3.56381818 1.28693434 1.4424978 2.23445743
## 15 2.4041631 0.41012193 0.97580736 0.33941125 1.93747258 1.7819091 0.98994949
## 16 0.4808326 2.47487373 1.90918831 3.22440692 0.94752309 1.1030866 1.89504617
## 17 2.6304372 0.63639610 1.20208153 0.11313708 2.16374675 2.0081833 1.21622366
## 18 1.0182338 0.97580736 0.41012193 1.72534055 0.55154329 0.3959798 0.39597980
## 19 0.2121320 1.78190909 1.21622366 2.53144228 0.25455844 0.4101219 1.20208153
## 20 0.7353911 1.25865007 0.69296465 2.00818326 0.26870058 0.1131371 0.67882251
## 21 3.0264170 1.03237590 1.59806133 0.28284271 2.55972655 2.4041631 1.61220346
## 22 1.3435029 0.65053824 0.08485281 1.40007143 0.87681241 0.7212489 0.07071068
## 23 1.9374726 0.05656854 0.50911688 0.80610173 1.47078210 1.3152186 0.52325902
## 24 1.8809040 0.11313708 0.45254834 0.86267027 1.41421356 1.2586501 0.46669048
## 25 1.6970563 0.29698485 0.26870058 1.04651804 1.23036580 1.0748023 0.28284271
## 26 1.5839192 0.41012193 0.15556349 1.15965512 1.11722871 0.9616652 0.16970563
## 27 1.0606602 0.93338095 0.36769553 1.68291414 0.59396970 0.4384062 0.35355339
## 28 2.8001429 0.80610173 1.37178716 0.05656854 2.33345238 2.1778889 1.38592929
## 29 2.3051681 0.31112698 0.87681241 0.43840620 1.83847763 1.6829141 0.89095454
## 30 1.5414928 0.45254834 0.11313708 1.20208153 1.07480231 0.9192388 0.12727922
## 8 9 10 11 12 13 14
## 1 0.50911688 1.64048773 1.37178716 0.9050967 0.0000000 0.3394113 0.8202439
## 2 1.48492424 0.35355339 0.62225397 1.0889444 1.9940411 1.6546299 2.8142850
## 3 0.91923882 0.21213203 0.05656854 0.5232590 1.4283557 1.0889444 2.2485996
## 4 2.23445743 1.10308658 1.37178716 1.8384776 2.7435743 2.4041631 3.5638182
## 5 0.04242641 1.17379726 0.90509668 0.4384062 0.4666905 0.1272792 1.2869343
## 6 0.11313708 1.01823376 0.74953319 0.2828427 0.6222540 0.2828427 1.4424978
## 7 0.90509668 0.22627417 0.04242641 0.5091169 1.4142136 1.0748023 2.2344574
## 8 0.00000000 1.13137085 0.86267027 0.3959798 0.5091169 0.1697056 1.3293607
## 9 1.13137085 0.00000000 0.26870058 0.7353911 1.6404877 1.3010765 2.4607316
## 10 0.86267027 0.26870058 0.00000000 0.4666905 1.3717872 1.0323759 2.1920310
## 11 0.39597980 0.73539105 0.46669048 0.0000000 0.9050967 0.5656854 1.7253405
## 12 0.50911688 1.64048773 1.37178716 0.9050967 0.0000000 0.3394113 0.8202439
## 13 0.16970563 1.30107648 1.03237590 0.5656854 0.3394113 0.0000000 1.1596551
## 14 1.32936075 2.46073160 2.19203102 1.7253405 0.8202439 1.1596551 0.0000000
## 15 1.89504617 0.76367532 1.03237590 1.4990664 2.4041631 2.0647518 3.2244069
## 16 0.98994949 2.12132034 1.85261977 1.3859293 0.4808326 0.8202439 0.3394113
## 17 2.12132034 0.98994949 1.25865007 1.7253405 2.6304372 2.2910260 3.4506811
## 18 0.50911688 0.62225397 0.35355339 0.1131371 1.0182338 0.6788225 1.8384776
## 19 0.29698485 1.42835570 1.15965512 0.6929646 0.2121320 0.1272792 1.0323759
## 20 0.22627417 0.90509668 0.63639610 0.1697056 0.7353911 0.3959798 1.5556349
## 21 2.51730014 1.38592929 1.65462987 2.1213203 3.0264170 2.6870058 3.8466609
## 22 0.83438600 0.29698485 0.02828427 0.4384062 1.3435029 1.0040916 2.1637468
## 23 1.42835570 0.29698485 0.56568542 1.0323759 1.9374726 1.5980613 2.7577164
## 24 1.37178716 0.24041631 0.50911688 0.9758074 1.8809040 1.5414928 2.7011479
## 25 1.18793939 0.05656854 0.32526912 0.7919596 1.6970563 1.3576450 2.5173001
## 26 1.07480231 0.05656854 0.21213203 0.6788225 1.5839192 1.2445079 2.4041631
## 27 0.55154329 0.57982756 0.31112698 0.1555635 1.0606602 0.7212489 1.8809040
## 28 2.29102597 1.15965512 1.42835570 1.8950462 2.8001429 2.4607316 3.6203867
## 29 1.79605122 0.66468037 0.93338095 1.4000714 2.3051681 1.9657569 3.1254120
## 30 1.03237590 0.09899495 0.16970563 0.6363961 1.5414928 1.2020815 2.3617366
## 15 16 17 18 19 20 21
## 1 2.40416306 0.4808326 2.6304372 1.01823376 0.2121320 0.7353911 3.0264170
## 2 0.41012193 2.4748737 0.6363961 0.97580736 1.7819091 1.2586501 1.0323759
## 3 0.97580736 1.9091883 1.2020815 0.41012193 1.2162237 0.6929646 1.5980613
## 4 0.33941125 3.2244069 0.1131371 1.72534055 2.5314423 2.0081833 0.2828427
## 5 1.93747258 0.9475231 2.1637468 0.55154329 0.2545584 0.2687006 2.5597265
## 6 1.78190909 1.1030866 2.0081833 0.39597980 0.4101219 0.1131371 2.4041631
## 7 0.98994949 1.8950462 1.2162237 0.39597980 1.2020815 0.6788225 1.6122035
## 8 1.89504617 0.9899495 2.1213203 0.50911688 0.2969848 0.2262742 2.5173001
## 9 0.76367532 2.1213203 0.9899495 0.62225397 1.4283557 0.9050967 1.3859293
## 10 1.03237590 1.8526198 1.2586501 0.35355339 1.1596551 0.6363961 1.6546299
## 11 1.49906638 1.3859293 1.7253405 0.11313708 0.6929646 0.1697056 2.1213203
## 12 2.40416306 0.4808326 2.6304372 1.01823376 0.2121320 0.7353911 3.0264170
## 13 2.06475180 0.8202439 2.2910260 0.67882251 0.1272792 0.3959798 2.6870058
## 14 3.22440692 0.3394113 3.4506811 1.83847763 1.0323759 1.5556349 3.8466609
## 15 0.00000000 2.8849957 0.2262742 1.38592929 2.1920310 1.6687720 0.6222540
## 16 2.88499567 0.0000000 3.1112698 1.49906638 0.6929646 1.2162237 3.5072496
## 17 0.22627417 3.1112698 0.0000000 1.61220346 2.4183052 1.8950462 0.3959798
## 18 1.38592929 1.4990664 1.6122035 0.00000000 0.8061017 0.2828427 2.0081833
## 19 2.19203102 0.6929646 2.4183052 0.80610173 0.0000000 0.5232590 2.8142850
## 20 1.66877200 1.2162237 1.8950462 0.28284271 0.5232590 0.0000000 2.2910260
## 21 0.62225397 3.5072496 0.3959798 2.00818326 2.8142850 2.2910260 0.0000000
## 22 1.06066017 1.8243355 1.2869343 0.32526912 1.1313708 0.6081118 1.6829141
## 23 0.46669048 2.4183052 0.6929646 0.91923882 1.7253405 1.2020815 1.0889444
## 24 0.52325902 2.3617366 0.7495332 0.86267027 1.6687720 1.1455130 1.1455130
## 25 0.70710678 2.1778889 0.9333810 0.67882251 1.4849242 0.9616652 1.3293607
## 26 0.82024387 2.0647518 1.0465180 0.56568542 1.3717872 0.8485281 1.4424978
## 27 1.34350288 1.5414928 1.5697771 0.04242641 0.8485281 0.3252691 1.9657569
## 28 0.39597980 3.2809755 0.1697056 1.78190909 2.5880108 2.0647518 0.2262742
## 29 0.09899495 2.7860007 0.3252691 1.28693434 2.0930361 1.5697771 0.7212489
## 30 0.86267027 2.0223254 1.0889444 0.52325902 1.3293607 0.8061017 1.4849242
## 22 23 24 25 26 27 28
## 1 1.34350288 1.93747258 1.88090404 1.69705627 1.58391919 1.06066017 2.80014285
## 2 0.65053824 0.05656854 0.11313708 0.29698485 0.41012193 0.93338095 0.80610173
## 3 0.08485281 0.50911688 0.45254834 0.26870058 0.15556349 0.36769553 1.37178716
## 4 1.40007143 0.80610173 0.86267027 1.04651804 1.15965512 1.68291414 0.05656854
## 5 0.87681241 1.47078210 1.41421356 1.23036580 1.11722871 0.59396970 2.33345238
## 6 0.72124892 1.31521861 1.25865007 1.07480231 0.96166522 0.43840620 2.17788889
## 7 0.07071068 0.52325902 0.46669048 0.28284271 0.16970563 0.35355339 1.38592929
## 8 0.83438600 1.42835570 1.37178716 1.18793939 1.07480231 0.55154329 2.29102597
## 9 0.29698485 0.29698485 0.24041631 0.05656854 0.05656854 0.57982756 1.15965512
## 10 0.02828427 0.56568542 0.50911688 0.32526912 0.21213203 0.31112698 1.42835570
## 11 0.43840620 1.03237590 0.97580736 0.79195959 0.67882251 0.15556349 1.89504617
## 12 1.34350288 1.93747258 1.88090404 1.69705627 1.58391919 1.06066017 2.80014285
## 13 1.00409163 1.59806133 1.54149278 1.35764502 1.24450793 0.72124892 2.46073160
## 14 2.16374675 2.75771645 2.70114790 2.51730014 2.40416306 1.88090404 3.62038672
## 15 1.06066017 0.46669048 0.52325902 0.70710678 0.82024387 1.34350288 0.39597980
## 16 1.82433550 2.41830519 2.36173665 2.17788889 2.06475180 1.54149278 3.28097546
## 17 1.28693434 0.69296465 0.74953319 0.93338095 1.04651804 1.56977705 0.16970563
## 18 0.32526912 0.91923882 0.86267027 0.67882251 0.56568542 0.04242641 1.78190909
## 19 1.13137085 1.72534055 1.66877200 1.48492424 1.37178716 0.84852814 2.58801082
## 20 0.60811183 1.20208153 1.14551299 0.96166522 0.84852814 0.32526912 2.06475180
## 21 1.68291414 1.08894444 1.14551299 1.32936075 1.44249783 1.96575685 0.22627417
## 22 0.00000000 0.59396970 0.53740115 0.35355339 0.24041631 0.28284271 1.45663997
## 23 0.59396970 0.00000000 0.05656854 0.24041631 0.35355339 0.87681241 0.86267027
## 24 0.53740115 0.05656854 0.00000000 0.18384776 0.29698485 0.82024387 0.91923882
## 25 0.35355339 0.24041631 0.18384776 0.00000000 0.11313708 0.63639610 1.10308658
## 26 0.24041631 0.35355339 0.29698485 0.11313708 0.00000000 0.52325902 1.21622366
## 27 0.28284271 0.87681241 0.82024387 0.63639610 0.52325902 0.00000000 1.73948268
## 28 1.45663997 0.86267027 0.91923882 1.10308658 1.21622366 1.73948268 0.00000000
## 29 0.96166522 0.36769553 0.42426407 0.60811183 0.72124892 1.24450793 0.49497475
## 30 0.19798990 0.39597980 0.33941125 0.15556349 0.04242641 0.48083261 1.25865007
## 29 30
## 1 2.30516811 1.54149278
## 2 0.31112698 0.45254834
## 3 0.87681241 0.11313708
## 4 0.43840620 1.20208153
## 5 1.83847763 1.07480231
## 6 1.68291414 0.91923882
## 7 0.89095454 0.12727922
## 8 1.79605122 1.03237590
## 9 0.66468037 0.09899495
## 10 0.93338095 0.16970563
## 11 1.40007143 0.63639610
## 12 2.30516811 1.54149278
## 13 1.96575685 1.20208153
## 14 3.12541197 2.36173665
## 15 0.09899495 0.86267027
## 16 2.78600072 2.02232539
## 17 0.32526912 1.08894444
## 18 1.28693434 0.52325902
## 19 2.09303607 1.32936075
## 20 1.56977705 0.80610173
## 21 0.72124892 1.48492424
## 22 0.96166522 0.19798990
## 23 0.36769553 0.39597980
## 24 0.42426407 0.33941125
## 25 0.60811183 0.15556349
## 26 0.72124892 0.04242641
## 27 1.24450793 0.48083261
## 28 0.49497475 1.25865007
## 29 0.00000000 0.76367532
## 30 0.76367532 0.00000000Manhattan Distance
Manhattan distance is the sum of absolute differences between points across all dimensions.
PlantGrowth_manhattan <- dist(PlantGrowth, method = "manhattan")## Warning in dist(PlantGrowth, method = "manhattan"): NAs introduced by coercionas.matrix(PlantGrowth_manhattan)## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
## 1 0.00 2.82 2.02 3.88 0.66 0.88 2.00 0.72 2.32 1.94 1.28 0.00 0.48 1.16 3.40
## 2 2.82 0.00 0.80 1.06 2.16 1.94 0.82 2.10 0.50 0.88 1.54 2.82 2.34 3.98 0.58
## 3 2.02 0.80 0.00 1.86 1.36 1.14 0.02 1.30 0.30 0.08 0.74 2.02 1.54 3.18 1.38
## 4 3.88 1.06 1.86 0.00 3.22 3.00 1.88 3.16 1.56 1.94 2.60 3.88 3.40 5.04 0.48
## 5 0.66 2.16 1.36 3.22 0.00 0.22 1.34 0.06 1.66 1.28 0.62 0.66 0.18 1.82 2.74
## 6 0.88 1.94 1.14 3.00 0.22 0.00 1.12 0.16 1.44 1.06 0.40 0.88 0.40 2.04 2.52
## 7 2.00 0.82 0.02 1.88 1.34 1.12 0.00 1.28 0.32 0.06 0.72 2.00 1.52 3.16 1.40
## 8 0.72 2.10 1.30 3.16 0.06 0.16 1.28 0.00 1.60 1.22 0.56 0.72 0.24 1.88 2.68
## 9 2.32 0.50 0.30 1.56 1.66 1.44 0.32 1.60 0.00 0.38 1.04 2.32 1.84 3.48 1.08
## 10 1.94 0.88 0.08 1.94 1.28 1.06 0.06 1.22 0.38 0.00 0.66 1.94 1.46 3.10 1.46
## 11 1.28 1.54 0.74 2.60 0.62 0.40 0.72 0.56 1.04 0.66 0.00 1.28 0.80 2.44 2.12
## 12 0.00 2.82 2.02 3.88 0.66 0.88 2.00 0.72 2.32 1.94 1.28 0.00 0.48 1.16 3.40
## 13 0.48 2.34 1.54 3.40 0.18 0.40 1.52 0.24 1.84 1.46 0.80 0.48 0.00 1.64 2.92
## 14 1.16 3.98 3.18 5.04 1.82 2.04 3.16 1.88 3.48 3.10 2.44 1.16 1.64 0.00 4.56
## 15 3.40 0.58 1.38 0.48 2.74 2.52 1.40 2.68 1.08 1.46 2.12 3.40 2.92 4.56 0.00
## 16 0.68 3.50 2.70 4.56 1.34 1.56 2.68 1.40 3.00 2.62 1.96 0.68 1.16 0.48 4.08
## 17 3.72 0.90 1.70 0.16 3.06 2.84 1.72 3.00 1.40 1.78 2.44 3.72 3.24 4.88 0.32
## 18 1.44 1.38 0.58 2.44 0.78 0.56 0.56 0.72 0.88 0.50 0.16 1.44 0.96 2.60 1.96
## 19 0.30 2.52 1.72 3.58 0.36 0.58 1.70 0.42 2.02 1.64 0.98 0.30 0.18 1.46 3.10
## 20 1.04 1.78 0.98 2.84 0.38 0.16 0.96 0.32 1.28 0.90 0.24 1.04 0.56 2.20 2.36
## 21 4.28 1.46 2.26 0.40 3.62 3.40 2.28 3.56 1.96 2.34 3.00 4.28 3.80 5.44 0.88
## 22 1.90 0.92 0.12 1.98 1.24 1.02 0.10 1.18 0.42 0.04 0.62 1.90 1.42 3.06 1.50
## 23 2.74 0.08 0.72 1.14 2.08 1.86 0.74 2.02 0.42 0.80 1.46 2.74 2.26 3.90 0.66
## 24 2.66 0.16 0.64 1.22 2.00 1.78 0.66 1.94 0.34 0.72 1.38 2.66 2.18 3.82 0.74
## 25 2.40 0.42 0.38 1.48 1.74 1.52 0.40 1.68 0.08 0.46 1.12 2.40 1.92 3.56 1.00
## 26 2.24 0.58 0.22 1.64 1.58 1.36 0.24 1.52 0.08 0.30 0.96 2.24 1.76 3.40 1.16
## 27 1.50 1.32 0.52 2.38 0.84 0.62 0.50 0.78 0.82 0.44 0.22 1.50 1.02 2.66 1.90
## 28 3.96 1.14 1.94 0.08 3.30 3.08 1.96 3.24 1.64 2.02 2.68 3.96 3.48 5.12 0.56
## 29 3.26 0.44 1.24 0.62 2.60 2.38 1.26 2.54 0.94 1.32 1.98 3.26 2.78 4.42 0.14
## 30 2.18 0.64 0.16 1.70 1.52 1.30 0.18 1.46 0.14 0.24 0.90 2.18 1.70 3.34 1.22
## 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
## 1 0.68 3.72 1.44 0.30 1.04 4.28 1.90 2.74 2.66 2.40 2.24 1.50 3.96 3.26 2.18
## 2 3.50 0.90 1.38 2.52 1.78 1.46 0.92 0.08 0.16 0.42 0.58 1.32 1.14 0.44 0.64
## 3 2.70 1.70 0.58 1.72 0.98 2.26 0.12 0.72 0.64 0.38 0.22 0.52 1.94 1.24 0.16
## 4 4.56 0.16 2.44 3.58 2.84 0.40 1.98 1.14 1.22 1.48 1.64 2.38 0.08 0.62 1.70
## 5 1.34 3.06 0.78 0.36 0.38 3.62 1.24 2.08 2.00 1.74 1.58 0.84 3.30 2.60 1.52
## 6 1.56 2.84 0.56 0.58 0.16 3.40 1.02 1.86 1.78 1.52 1.36 0.62 3.08 2.38 1.30
## 7 2.68 1.72 0.56 1.70 0.96 2.28 0.10 0.74 0.66 0.40 0.24 0.50 1.96 1.26 0.18
## 8 1.40 3.00 0.72 0.42 0.32 3.56 1.18 2.02 1.94 1.68 1.52 0.78 3.24 2.54 1.46
## 9 3.00 1.40 0.88 2.02 1.28 1.96 0.42 0.42 0.34 0.08 0.08 0.82 1.64 0.94 0.14
## 10 2.62 1.78 0.50 1.64 0.90 2.34 0.04 0.80 0.72 0.46 0.30 0.44 2.02 1.32 0.24
## 11 1.96 2.44 0.16 0.98 0.24 3.00 0.62 1.46 1.38 1.12 0.96 0.22 2.68 1.98 0.90
## 12 0.68 3.72 1.44 0.30 1.04 4.28 1.90 2.74 2.66 2.40 2.24 1.50 3.96 3.26 2.18
## 13 1.16 3.24 0.96 0.18 0.56 3.80 1.42 2.26 2.18 1.92 1.76 1.02 3.48 2.78 1.70
## 14 0.48 4.88 2.60 1.46 2.20 5.44 3.06 3.90 3.82 3.56 3.40 2.66 5.12 4.42 3.34
## 15 4.08 0.32 1.96 3.10 2.36 0.88 1.50 0.66 0.74 1.00 1.16 1.90 0.56 0.14 1.22
## 16 0.00 4.40 2.12 0.98 1.72 4.96 2.58 3.42 3.34 3.08 2.92 2.18 4.64 3.94 2.86
## 17 4.40 0.00 2.28 3.42 2.68 0.56 1.82 0.98 1.06 1.32 1.48 2.22 0.24 0.46 1.54
## 18 2.12 2.28 0.00 1.14 0.40 2.84 0.46 1.30 1.22 0.96 0.80 0.06 2.52 1.82 0.74
## 19 0.98 3.42 1.14 0.00 0.74 3.98 1.60 2.44 2.36 2.10 1.94 1.20 3.66 2.96 1.88
## 20 1.72 2.68 0.40 0.74 0.00 3.24 0.86 1.70 1.62 1.36 1.20 0.46 2.92 2.22 1.14
## 21 4.96 0.56 2.84 3.98 3.24 0.00 2.38 1.54 1.62 1.88 2.04 2.78 0.32 1.02 2.10
## 22 2.58 1.82 0.46 1.60 0.86 2.38 0.00 0.84 0.76 0.50 0.34 0.40 2.06 1.36 0.28
## 23 3.42 0.98 1.30 2.44 1.70 1.54 0.84 0.00 0.08 0.34 0.50 1.24 1.22 0.52 0.56
## 24 3.34 1.06 1.22 2.36 1.62 1.62 0.76 0.08 0.00 0.26 0.42 1.16 1.30 0.60 0.48
## 25 3.08 1.32 0.96 2.10 1.36 1.88 0.50 0.34 0.26 0.00 0.16 0.90 1.56 0.86 0.22
## 26 2.92 1.48 0.80 1.94 1.20 2.04 0.34 0.50 0.42 0.16 0.00 0.74 1.72 1.02 0.06
## 27 2.18 2.22 0.06 1.20 0.46 2.78 0.40 1.24 1.16 0.90 0.74 0.00 2.46 1.76 0.68
## 28 4.64 0.24 2.52 3.66 2.92 0.32 2.06 1.22 1.30 1.56 1.72 2.46 0.00 0.70 1.78
## 29 3.94 0.46 1.82 2.96 2.22 1.02 1.36 0.52 0.60 0.86 1.02 1.76 0.70 0.00 1.08
## 30 2.86 1.54 0.74 1.88 1.14 2.10 0.28 0.56 0.48 0.22 0.06 0.68 1.78 1.08 0.00Minkowski Distance
Minkowski is the generalized form of manhattand and euclidean distance.
PlantGrowth_minkowski <- dist(PlantGrowth, method = "minkowski")## Warning in dist(PlantGrowth, method = "minkowski"): NAs introduced by coercionas.matrix(PlantGrowth_minkowski)## 1 2 3 4 5 6 7
## 1 0.0000000 1.99404112 1.42835570 2.74357431 0.46669048 0.6222540 1.41421356
## 2 1.9940411 0.00000000 0.56568542 0.74953319 1.52735065 1.3717872 0.57982756
## 3 1.4283557 0.56568542 0.00000000 1.31521861 0.96166522 0.8061017 0.01414214
## 4 2.7435743 0.74953319 1.31521861 0.00000000 2.27688384 2.1213203 1.32936075
## 5 0.4666905 1.52735065 0.96166522 2.27688384 0.00000000 0.1555635 0.94752309
## 6 0.6222540 1.37178716 0.80610173 2.12132034 0.15556349 0.0000000 0.79195959
## 7 1.4142136 0.57982756 0.01414214 1.32936075 0.94752309 0.7919596 0.00000000
## 8 0.5091169 1.48492424 0.91923882 2.23445743 0.04242641 0.1131371 0.90509668
## 9 1.6404877 0.35355339 0.21213203 1.10308658 1.17379726 1.0182338 0.22627417
## 10 1.3717872 0.62225397 0.05656854 1.37178716 0.90509668 0.7495332 0.04242641
## 11 0.9050967 1.08894444 0.52325902 1.83847763 0.43840620 0.2828427 0.50911688
## 12 0.0000000 1.99404112 1.42835570 2.74357431 0.46669048 0.6222540 1.41421356
## 13 0.3394113 1.65462987 1.08894444 2.40416306 0.12727922 0.2828427 1.07480231
## 14 0.8202439 2.81428499 2.24859956 3.56381818 1.28693434 1.4424978 2.23445743
## 15 2.4041631 0.41012193 0.97580736 0.33941125 1.93747258 1.7819091 0.98994949
## 16 0.4808326 2.47487373 1.90918831 3.22440692 0.94752309 1.1030866 1.89504617
## 17 2.6304372 0.63639610 1.20208153 0.11313708 2.16374675 2.0081833 1.21622366
## 18 1.0182338 0.97580736 0.41012193 1.72534055 0.55154329 0.3959798 0.39597980
## 19 0.2121320 1.78190909 1.21622366 2.53144228 0.25455844 0.4101219 1.20208153
## 20 0.7353911 1.25865007 0.69296465 2.00818326 0.26870058 0.1131371 0.67882251
## 21 3.0264170 1.03237590 1.59806133 0.28284271 2.55972655 2.4041631 1.61220346
## 22 1.3435029 0.65053824 0.08485281 1.40007143 0.87681241 0.7212489 0.07071068
## 23 1.9374726 0.05656854 0.50911688 0.80610173 1.47078210 1.3152186 0.52325902
## 24 1.8809040 0.11313708 0.45254834 0.86267027 1.41421356 1.2586501 0.46669048
## 25 1.6970563 0.29698485 0.26870058 1.04651804 1.23036580 1.0748023 0.28284271
## 26 1.5839192 0.41012193 0.15556349 1.15965512 1.11722871 0.9616652 0.16970563
## 27 1.0606602 0.93338095 0.36769553 1.68291414 0.59396970 0.4384062 0.35355339
## 28 2.8001429 0.80610173 1.37178716 0.05656854 2.33345238 2.1778889 1.38592929
## 29 2.3051681 0.31112698 0.87681241 0.43840620 1.83847763 1.6829141 0.89095454
## 30 1.5414928 0.45254834 0.11313708 1.20208153 1.07480231 0.9192388 0.12727922
## 8 9 10 11 12 13 14
## 1 0.50911688 1.64048773 1.37178716 0.9050967 0.0000000 0.3394113 0.8202439
## 2 1.48492424 0.35355339 0.62225397 1.0889444 1.9940411 1.6546299 2.8142850
## 3 0.91923882 0.21213203 0.05656854 0.5232590 1.4283557 1.0889444 2.2485996
## 4 2.23445743 1.10308658 1.37178716 1.8384776 2.7435743 2.4041631 3.5638182
## 5 0.04242641 1.17379726 0.90509668 0.4384062 0.4666905 0.1272792 1.2869343
## 6 0.11313708 1.01823376 0.74953319 0.2828427 0.6222540 0.2828427 1.4424978
## 7 0.90509668 0.22627417 0.04242641 0.5091169 1.4142136 1.0748023 2.2344574
## 8 0.00000000 1.13137085 0.86267027 0.3959798 0.5091169 0.1697056 1.3293607
## 9 1.13137085 0.00000000 0.26870058 0.7353911 1.6404877 1.3010765 2.4607316
## 10 0.86267027 0.26870058 0.00000000 0.4666905 1.3717872 1.0323759 2.1920310
## 11 0.39597980 0.73539105 0.46669048 0.0000000 0.9050967 0.5656854 1.7253405
## 12 0.50911688 1.64048773 1.37178716 0.9050967 0.0000000 0.3394113 0.8202439
## 13 0.16970563 1.30107648 1.03237590 0.5656854 0.3394113 0.0000000 1.1596551
## 14 1.32936075 2.46073160 2.19203102 1.7253405 0.8202439 1.1596551 0.0000000
## 15 1.89504617 0.76367532 1.03237590 1.4990664 2.4041631 2.0647518 3.2244069
## 16 0.98994949 2.12132034 1.85261977 1.3859293 0.4808326 0.8202439 0.3394113
## 17 2.12132034 0.98994949 1.25865007 1.7253405 2.6304372 2.2910260 3.4506811
## 18 0.50911688 0.62225397 0.35355339 0.1131371 1.0182338 0.6788225 1.8384776
## 19 0.29698485 1.42835570 1.15965512 0.6929646 0.2121320 0.1272792 1.0323759
## 20 0.22627417 0.90509668 0.63639610 0.1697056 0.7353911 0.3959798 1.5556349
## 21 2.51730014 1.38592929 1.65462987 2.1213203 3.0264170 2.6870058 3.8466609
## 22 0.83438600 0.29698485 0.02828427 0.4384062 1.3435029 1.0040916 2.1637468
## 23 1.42835570 0.29698485 0.56568542 1.0323759 1.9374726 1.5980613 2.7577164
## 24 1.37178716 0.24041631 0.50911688 0.9758074 1.8809040 1.5414928 2.7011479
## 25 1.18793939 0.05656854 0.32526912 0.7919596 1.6970563 1.3576450 2.5173001
## 26 1.07480231 0.05656854 0.21213203 0.6788225 1.5839192 1.2445079 2.4041631
## 27 0.55154329 0.57982756 0.31112698 0.1555635 1.0606602 0.7212489 1.8809040
## 28 2.29102597 1.15965512 1.42835570 1.8950462 2.8001429 2.4607316 3.6203867
## 29 1.79605122 0.66468037 0.93338095 1.4000714 2.3051681 1.9657569 3.1254120
## 30 1.03237590 0.09899495 0.16970563 0.6363961 1.5414928 1.2020815 2.3617366
## 15 16 17 18 19 20 21
## 1 2.40416306 0.4808326 2.6304372 1.01823376 0.2121320 0.7353911 3.0264170
## 2 0.41012193 2.4748737 0.6363961 0.97580736 1.7819091 1.2586501 1.0323759
## 3 0.97580736 1.9091883 1.2020815 0.41012193 1.2162237 0.6929646 1.5980613
## 4 0.33941125 3.2244069 0.1131371 1.72534055 2.5314423 2.0081833 0.2828427
## 5 1.93747258 0.9475231 2.1637468 0.55154329 0.2545584 0.2687006 2.5597265
## 6 1.78190909 1.1030866 2.0081833 0.39597980 0.4101219 0.1131371 2.4041631
## 7 0.98994949 1.8950462 1.2162237 0.39597980 1.2020815 0.6788225 1.6122035
## 8 1.89504617 0.9899495 2.1213203 0.50911688 0.2969848 0.2262742 2.5173001
## 9 0.76367532 2.1213203 0.9899495 0.62225397 1.4283557 0.9050967 1.3859293
## 10 1.03237590 1.8526198 1.2586501 0.35355339 1.1596551 0.6363961 1.6546299
## 11 1.49906638 1.3859293 1.7253405 0.11313708 0.6929646 0.1697056 2.1213203
## 12 2.40416306 0.4808326 2.6304372 1.01823376 0.2121320 0.7353911 3.0264170
## 13 2.06475180 0.8202439 2.2910260 0.67882251 0.1272792 0.3959798 2.6870058
## 14 3.22440692 0.3394113 3.4506811 1.83847763 1.0323759 1.5556349 3.8466609
## 15 0.00000000 2.8849957 0.2262742 1.38592929 2.1920310 1.6687720 0.6222540
## 16 2.88499567 0.0000000 3.1112698 1.49906638 0.6929646 1.2162237 3.5072496
## 17 0.22627417 3.1112698 0.0000000 1.61220346 2.4183052 1.8950462 0.3959798
## 18 1.38592929 1.4990664 1.6122035 0.00000000 0.8061017 0.2828427 2.0081833
## 19 2.19203102 0.6929646 2.4183052 0.80610173 0.0000000 0.5232590 2.8142850
## 20 1.66877200 1.2162237 1.8950462 0.28284271 0.5232590 0.0000000 2.2910260
## 21 0.62225397 3.5072496 0.3959798 2.00818326 2.8142850 2.2910260 0.0000000
## 22 1.06066017 1.8243355 1.2869343 0.32526912 1.1313708 0.6081118 1.6829141
## 23 0.46669048 2.4183052 0.6929646 0.91923882 1.7253405 1.2020815 1.0889444
## 24 0.52325902 2.3617366 0.7495332 0.86267027 1.6687720 1.1455130 1.1455130
## 25 0.70710678 2.1778889 0.9333810 0.67882251 1.4849242 0.9616652 1.3293607
## 26 0.82024387 2.0647518 1.0465180 0.56568542 1.3717872 0.8485281 1.4424978
## 27 1.34350288 1.5414928 1.5697771 0.04242641 0.8485281 0.3252691 1.9657569
## 28 0.39597980 3.2809755 0.1697056 1.78190909 2.5880108 2.0647518 0.2262742
## 29 0.09899495 2.7860007 0.3252691 1.28693434 2.0930361 1.5697771 0.7212489
## 30 0.86267027 2.0223254 1.0889444 0.52325902 1.3293607 0.8061017 1.4849242
## 22 23 24 25 26 27 28
## 1 1.34350288 1.93747258 1.88090404 1.69705627 1.58391919 1.06066017 2.80014285
## 2 0.65053824 0.05656854 0.11313708 0.29698485 0.41012193 0.93338095 0.80610173
## 3 0.08485281 0.50911688 0.45254834 0.26870058 0.15556349 0.36769553 1.37178716
## 4 1.40007143 0.80610173 0.86267027 1.04651804 1.15965512 1.68291414 0.05656854
## 5 0.87681241 1.47078210 1.41421356 1.23036580 1.11722871 0.59396970 2.33345238
## 6 0.72124892 1.31521861 1.25865007 1.07480231 0.96166522 0.43840620 2.17788889
## 7 0.07071068 0.52325902 0.46669048 0.28284271 0.16970563 0.35355339 1.38592929
## 8 0.83438600 1.42835570 1.37178716 1.18793939 1.07480231 0.55154329 2.29102597
## 9 0.29698485 0.29698485 0.24041631 0.05656854 0.05656854 0.57982756 1.15965512
## 10 0.02828427 0.56568542 0.50911688 0.32526912 0.21213203 0.31112698 1.42835570
## 11 0.43840620 1.03237590 0.97580736 0.79195959 0.67882251 0.15556349 1.89504617
## 12 1.34350288 1.93747258 1.88090404 1.69705627 1.58391919 1.06066017 2.80014285
## 13 1.00409163 1.59806133 1.54149278 1.35764502 1.24450793 0.72124892 2.46073160
## 14 2.16374675 2.75771645 2.70114790 2.51730014 2.40416306 1.88090404 3.62038672
## 15 1.06066017 0.46669048 0.52325902 0.70710678 0.82024387 1.34350288 0.39597980
## 16 1.82433550 2.41830519 2.36173665 2.17788889 2.06475180 1.54149278 3.28097546
## 17 1.28693434 0.69296465 0.74953319 0.93338095 1.04651804 1.56977705 0.16970563
## 18 0.32526912 0.91923882 0.86267027 0.67882251 0.56568542 0.04242641 1.78190909
## 19 1.13137085 1.72534055 1.66877200 1.48492424 1.37178716 0.84852814 2.58801082
## 20 0.60811183 1.20208153 1.14551299 0.96166522 0.84852814 0.32526912 2.06475180
## 21 1.68291414 1.08894444 1.14551299 1.32936075 1.44249783 1.96575685 0.22627417
## 22 0.00000000 0.59396970 0.53740115 0.35355339 0.24041631 0.28284271 1.45663997
## 23 0.59396970 0.00000000 0.05656854 0.24041631 0.35355339 0.87681241 0.86267027
## 24 0.53740115 0.05656854 0.00000000 0.18384776 0.29698485 0.82024387 0.91923882
## 25 0.35355339 0.24041631 0.18384776 0.00000000 0.11313708 0.63639610 1.10308658
## 26 0.24041631 0.35355339 0.29698485 0.11313708 0.00000000 0.52325902 1.21622366
## 27 0.28284271 0.87681241 0.82024387 0.63639610 0.52325902 0.00000000 1.73948268
## 28 1.45663997 0.86267027 0.91923882 1.10308658 1.21622366 1.73948268 0.00000000
## 29 0.96166522 0.36769553 0.42426407 0.60811183 0.72124892 1.24450793 0.49497475
## 30 0.19798990 0.39597980 0.33941125 0.15556349 0.04242641 0.48083261 1.25865007
## 29 30
## 1 2.30516811 1.54149278
## 2 0.31112698 0.45254834
## 3 0.87681241 0.11313708
## 4 0.43840620 1.20208153
## 5 1.83847763 1.07480231
## 6 1.68291414 0.91923882
## 7 0.89095454 0.12727922
## 8 1.79605122 1.03237590
## 9 0.66468037 0.09899495
## 10 0.93338095 0.16970563
## 11 1.40007143 0.63639610
## 12 2.30516811 1.54149278
## 13 1.96575685 1.20208153
## 14 3.12541197 2.36173665
## 15 0.09899495 0.86267027
## 16 2.78600072 2.02232539
## 17 0.32526912 1.08894444
## 18 1.28693434 0.52325902
## 19 2.09303607 1.32936075
## 20 1.56977705 0.80610173
## 21 0.72124892 1.48492424
## 22 0.96166522 0.19798990
## 23 0.36769553 0.39597980
## 24 0.42426407 0.33941125
## 25 0.60811183 0.15556349
## 26 0.72124892 0.04242641
## 27 1.24450793 0.48083261
## 28 0.49497475 1.25865007
## 29 0.00000000 0.76367532
## 30 0.76367532 0.00000000When comparing three distances I see a similarity between euclidean and minkowski distance.
Ex.2
Use a higher dimentional dataset mtcars, try the same three distance metrics in the previous question and discuss the results.
##euclidean
cars_euclidean <- dist(mtcars, method = "euclidean")
as.matrix(cars_euclidean)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.0000000 0.6153251 54.90861 98.11252
## Mazda RX4 Wag 0.6153251 0.0000000 54.89152 98.09589
## Datsun 710 54.9086059 54.8915169 0.00000 150.99352
## Hornet 4 Drive 98.1125212 98.0958939 150.99352 0.00000
## Hornet Sportabout 210.3374396 210.3358546 265.08316 121.02976
## Valiant 65.4717710 65.4392224 117.75470 33.55087
## Duster 360 241.4076490 241.4088680 294.47902 169.42996
## Merc 240D 50.1532711 50.1146059 49.65848 121.27397
## Merc 230 25.4683117 25.3284509 33.18038 118.24331
## Merc 280 15.3641921 15.2956865 66.93635 91.42240
## Merc 280C 15.6724727 15.5837744 67.02614 91.46129
## Merc 450SE 135.4307018 135.4254826 189.19549 72.49643
## Merc 450SL 135.4014424 135.3960351 189.16317 72.43135
## Merc 450SLC 135.4794674 135.4723157 189.23454 72.57185
## Cadillac Fleetwood 326.3395903 326.3355070 381.09262 234.44039
## Lincoln Continental 318.0469808 318.0429333 372.80121 227.97261
## Chrysler Imperial 304.7203408 304.7169175 359.30149 218.15483
## Fiat 128 93.2679950 93.2530993 40.99338 184.96897
## Honda Civic 102.8307567 102.8238713 52.77046 191.55187
## Toyota Corolla 100.6040368 100.5887588 47.65350 192.67142
## Toyota Corona 42.3075233 42.2659224 12.96547 138.53047
## Dodge Challenger 163.1150750 163.1134210 217.77958 72.44039
## AMC Javelin 149.6047203 149.6014522 204.31889 61.36019
## Camaro Z28 233.2228758 233.2248748 286.00492 163.66326
## Pontiac Firebird 248.6780270 248.6762035 303.35839 156.22403
## Fiat X1-9 92.5048389 92.4940020 39.88151 184.44712
## Porsche 914-2 44.4033659 44.4073589 13.13571 139.15795
## Lotus Europa 65.7328377 65.7362635 25.09486 163.23674
## Ford Pantera L 245.4247064 245.4293785 297.29405 180.11403
## Ferrari Dino 66.7661029 66.7764167 90.24155 130.55230
## Maserati Bora 265.6454248 265.6491465 309.77182 229.34194
## Volvo 142E 39.1894029 39.1626037 20.69394 137.03633
## Hornet Sportabout Valiant Duster 360 Merc 240D Merc 230
## Mazda RX4 210.33744 65.47177 241.40765 50.15327 25.46831
## Mazda RX4 Wag 210.33585 65.43922 241.40887 50.11461 25.32845
## Datsun 710 265.08316 117.75470 294.47902 49.65848 33.18038
## Hornet 4 Drive 121.02976 33.55087 169.42996 121.27397 118.24331
## Hornet Sportabout 0.00000 152.12414 70.17673 241.50697 233.49240
## Valiant 152.12414 0.00000 194.60945 89.59111 85.00796
## Duster 360 70.17673 194.60945 0.00000 281.29625 265.88233
## Merc 240D 241.50697 89.59111 281.29625 0.00000 33.68730
## Merc 230 233.49240 85.00796 265.88233 33.68730 0.00000
## Merc 280 199.33450 60.29098 227.89985 64.77542 39.29942
## Merc 280C 199.34066 60.26557 227.88132 64.88987 39.38685
## Merc 450SE 84.38885 90.69703 106.40843 175.16201 159.81796
## Merc 450SL 84.36840 90.67697 106.43206 175.11898 159.77609
## Merc 450SLC 84.43324 90.70930 106.40103 175.21182 159.84958
## Cadillac Fleetwood 116.28042 266.62809 119.02391 355.66275 349.28326
## Lincoln Continental 108.06243 259.63044 104.51130 348.99013 341.31543
## Chrysler Imperial 97.20491 248.77133 81.42977 338.19594 328.43352
## Fiat 128 302.03772 152.11533 333.97921 68.61059 69.31279
## Honda Civic 310.03246 158.96158 344.05183 72.00145 78.53872
## Toyota Corolla 309.55818 159.83030 341.02182 76.28065 76.77317
## Toyota Corona 252.33320 105.28764 282.05088 44.08510 21.09620
## Dodge Challenger 48.98389 103.43107 103.90239 192.86179 185.83319
## AMC Javelin 61.42742 91.04443 110.30849 180.54798 172.53126
## Camaro Z28 70.96653 187.84638 10.07612 273.83680 257.74697
## Pontiac Firebird 40.00525 188.52721 80.80573 277.46069 271.38720
## Fiat X1-9 301.56695 151.43794 333.48432 67.91640 68.55649
## Porsche 914-2 254.14526 106.05858 285.19862 39.44693 22.11810
## Lotus Europa 272.35824 130.82482 296.45723 72.89711 50.10940
## Ford Pantera L 89.59340 203.01779 21.26560 287.52388 269.97720
## Ferrari Dino 215.06739 106.56948 226.20363 113.30230 80.65510
## Maserati Bora 170.70945 242.43930 107.72250 313.86331 288.87556
## Volvo 142E 248.00634 104.18637 275.13535 53.68235 24.69135
## Merc 280 Merc 280C Merc 450SE Merc 450SL Merc 450SLC
## Mazda RX4 15.364192 15.672473 135.4307018 135.4014424 135.479467
## Mazda RX4 Wag 15.295686 15.583774 135.4254826 135.3960351 135.472316
## Datsun 710 66.936353 67.026140 189.1954941 189.1631745 189.234543
## Hornet 4 Drive 91.422403 91.461291 72.4964325 72.4313532 72.571847
## Hornet Sportabout 199.334496 199.340656 84.3888482 84.3683999 84.433242
## Valiant 60.290981 60.265566 90.6970264 90.6769728 90.709299
## Duster 360 227.899852 227.881317 106.4084264 106.4320572 106.401031
## Merc 240D 64.775423 64.889871 175.1620073 175.1189767 175.211822
## Merc 230 39.299416 39.386852 159.8179555 159.7760899 159.849584
## Merc 280 0.000000 1.523155 122.3642489 122.3443771 122.393497
## Merc 280C 1.523155 0.000000 122.3461050 122.3355492 122.358686
## Merc 450SE 122.364249 122.346105 0.0000000 0.9826495 1.372625
## Merc 450SL 122.344377 122.335549 0.9826495 0.0000000 2.138340
## Merc 450SLC 122.393497 122.358686 1.3726252 2.1383405 0.000000
## Cadillac Fleetwood 315.390486 315.355708 197.8842803 197.9154476 197.852624
## Lincoln Continental 306.676072 306.640619 187.5997191 187.6330806 187.567108
## Chrysler Imperial 292.714690 292.698933 171.6600758 171.6743028 171.655764
## Fiat 128 106.505315 106.682979 228.3247948 228.2592340 228.405183
## Honda Civic 116.728099 116.871148 238.0141824 237.9588183 238.082900
## Toyota Corolla 113.629072 113.811801 235.5183809 235.4481971 235.602410
## Toyota Corona 54.364171 54.425831 176.6020527 176.5727477 176.630536
## Dodge Challenger 152.892926 152.872244 51.8008639 51.8242520 51.801261
## AMC Javelin 139.145797 139.118198 41.2080044 41.2411618 41.192905
## Camaro Z28 219.552085 219.527643 98.7203049 98.7566899 98.703583
## Pontiac Firebird 238.172610 238.180629 124.3368538 124.3204160 124.372613
## Fiat X1-9 105.741291 105.856037 227.7627676 227.7173075 227.817655
## Porsche 914-2 57.645816 57.847386 179.5034108 179.4550855 179.572045
## Lotus Europa 74.144358 74.382430 193.3074449 193.2407697 193.396922
## Ford Pantera L 231.408131 231.402426 112.8181834 112.8296774 112.833260
## Ferrari Dino 56.836510 56.898760 131.0272205 131.0077635 131.070449
## Maserati Bora 250.587412 250.577436 157.1633256 157.1768956 157.168397
## Volvo 142E 48.805345 48.888462 170.4500681 170.4225164 170.484373
## Cadillac Fleetwood Lincoln Continental Chrysler Imperial
## Mazda RX4 326.33959 318.04698 304.72034
## Mazda RX4 Wag 326.33551 318.04293 304.71692
## Datsun 710 381.09262 372.80121 359.30149
## Hornet 4 Drive 234.44039 227.97261 218.15483
## Hornet Sportabout 116.28042 108.06243 97.20491
## Valiant 266.62809 259.63044 248.77133
## Duster 360 119.02391 104.51130 81.42977
## Merc 240D 355.66275 348.99013 338.19594
## Merc 230 349.28326 341.31543 328.43352
## Merc 280 315.39049 306.67607 292.71469
## Merc 280C 315.35571 306.64062 292.69893
## Merc 450SE 197.88428 187.59972 171.66008
## Merc 450SL 197.91545 187.63308 171.67430
## Merc 450SLC 197.85262 187.56711 171.65576
## Cadillac Fleetwood 0.00000 15.62244 40.83996
## Lincoln Continental 15.62244 0.00000 25.37142
## Chrysler Imperial 40.83996 25.37142 0.00000
## Fiat 128 417.76876 410.02070 397.22764
## Honda Civic 425.32716 417.96796 405.81522
## Toyota Corolla 425.34465 417.54300 404.63354
## Toyota Corona 368.31955 360.02675 346.57246
## Dodge Challenger 163.63149 156.28050 145.91948
## AMC Javelin 176.86109 169.09255 157.80976
## Camaro Z28 128.45872 114.09321 91.28809
## Pontiac Firebird 78.53853 72.69479 68.20307
## Fiat X1-9 417.24905 409.49984 396.75975
## Porsche 914-2 370.09568 362.01455 348.84669
## Lotus Europa 388.53500 379.47167 364.59943
## Ford Pantera L 134.81195 119.72365 95.38054
## Ferrari Dino 328.54416 317.70631 300.16407
## Maserati Bora 214.93669 199.34206 174.29369
## Volvo 142E 364.10009 355.40094 341.28967
## Fiat 128 Honda Civic Toyota Corolla Toyota Corona
## Mazda RX4 93.267995 102.83076 100.604037 42.30752
## Mazda RX4 Wag 93.253099 102.82387 100.588759 42.26592
## Datsun 710 40.993376 52.77046 47.653502 12.96547
## Hornet 4 Drive 184.968973 191.55187 192.671419 138.53047
## Hornet Sportabout 302.037721 310.03246 309.558178 252.33320
## Valiant 152.115326 158.96158 159.830299 105.28764
## Duster 360 333.979207 344.05183 341.021823 282.05088
## Merc 240D 68.610590 72.00145 76.280646 44.08510
## Merc 230 69.312791 78.53872 76.773167 21.09620
## Merc 280 106.505315 116.72810 113.629072 54.36417
## Merc 280C 106.682979 116.87115 113.811801 54.42583
## Merc 450SE 228.324795 238.01418 235.518381 176.60205
## Merc 450SL 228.259234 237.95882 235.448197 176.57275
## Merc 450SLC 228.405183 238.08290 235.602410 176.63054
## Cadillac Fleetwood 417.768758 425.32716 425.344652 368.31955
## Lincoln Continental 410.020698 417.96796 417.542999 360.02675
## Chrysler Imperial 397.227638 405.81522 404.633539 346.57246
## Fiat 128 0.000000 14.55909 7.832479 52.87983
## Honda Civic 14.559094 0.00000 14.348063 63.89856
## Toyota Corolla 7.832479 14.34806 0.000000 59.84513
## Toyota Corona 52.879828 63.89856 59.845128 0.00000
## Dodge Challenger 254.236789 261.84988 261.834531 205.03479
## AMC Javelin 241.120362 248.96365 248.691707 191.55805
## Camaro Z28 325.663624 335.88832 332.658970 273.63169
## Pontiac Firebird 339.585766 347.06554 347.166764 290.62407
## Fiat X1-9 5.147342 14.78071 10.392286 51.84117
## Porsche 914-2 49.064437 59.45888 56.324303 8.65359
## Lotus Europa 49.911251 64.04952 53.884656 31.25369
## Ford Pantera L 337.163924 347.83377 343.992096 285.12879
## Ferrari Dino 128.395005 141.70445 133.470762 82.23557
## Maserati Bora 349.533883 362.16208 355.260162 299.18652
## Volvo 142E 61.330125 73.37660 67.718942 12.25053
## Dodge Challenger AMC Javelin Camaro Z28 Pontiac Firebird
## Mazda RX4 163.11508 149.60472 233.22288 248.67803
## Mazda RX4 Wag 163.11342 149.60145 233.22487 248.67620
## Datsun 710 217.77958 204.31889 286.00492 303.35839
## Hornet 4 Drive 72.44039 61.36019 163.66326 156.22403
## Hornet Sportabout 48.98389 61.42742 70.96653 40.00525
## Valiant 103.43107 91.04443 187.84638 188.52721
## Duster 360 103.90239 110.30849 10.07612 80.80573
## Merc 240D 192.86179 180.54798 273.83680 277.46069
## Merc 230 185.83319 172.53126 257.74697 271.38720
## Merc 280 152.89293 139.14580 219.55209 238.17261
## Merc 280C 152.87224 139.11820 219.52764 238.18063
## Merc 450SE 51.80086 41.20800 98.72030 124.33685
## Merc 450SL 51.82425 41.24116 98.75669 124.32042
## Merc 450SLC 51.80126 41.19291 98.70358 124.37261
## Cadillac Fleetwood 163.63149 176.86109 128.45872 78.53853
## Lincoln Continental 156.28050 169.09255 114.09321 72.69479
## Chrysler Imperial 145.91948 157.80976 91.28809 68.20307
## Fiat 128 254.23679 241.12036 325.66362 339.58577
## Honda Civic 261.84988 248.96365 335.88832 347.06554
## Toyota Corolla 261.83453 248.69171 332.65897 347.16676
## Toyota Corona 205.03479 191.55805 273.63169 290.62407
## Dodge Challenger 0.00000 14.01550 100.30461 85.80752
## AMC Javelin 14.01550 0.00000 105.60626 99.28361
## Camaro Z28 100.30461 105.60626 0.00000 86.26658
## Pontiac Firebird 85.80752 99.28361 86.26658 0.00000
## Fiat X1-9 253.66240 240.52668 325.14909 339.13962
## Porsche 914-2 206.64526 193.30806 276.89244 292.16465
## Lotus Europa 226.50048 212.75688 287.61790 311.38623
## Ford Pantera L 118.75168 123.38320 19.35890 101.73897
## Ferrari Dino 174.92804 161.10603 216.74899 255.05705
## Maserati Bora 185.90593 185.15534 102.59462 188.32400
## Volvo 142E 201.36825 187.69784 266.52777 286.74978
## Fiat X1-9 Porsche 914-2 Lotus Europa Ford Pantera L
## Mazda RX4 92.504839 44.40337 65.73284 245.42471
## Mazda RX4 Wag 92.494002 44.40736 65.73626 245.42938
## Datsun 710 39.881515 13.13571 25.09486 297.29405
## Hornet 4 Drive 184.447120 139.15795 163.23674 180.11403
## Hornet Sportabout 301.566948 254.14526 272.35824 89.59340
## Valiant 151.437942 106.05858 130.82482 203.01779
## Duster 360 333.484323 285.19862 296.45723 21.26560
## Merc 240D 67.916398 39.44693 72.89711 287.52388
## Merc 230 68.556486 22.11810 50.10940 269.97720
## Merc 280 105.741291 57.64582 74.14436 231.40813
## Merc 280C 105.856037 57.84739 74.38243 231.40243
## Merc 450SE 227.762768 179.50341 193.30744 112.81818
## Merc 450SL 227.717307 179.45509 193.24077 112.82968
## Merc 450SLC 227.817655 179.57204 193.39692 112.83326
## Cadillac Fleetwood 417.249048 370.09568 388.53500 134.81195
## Lincoln Continental 409.499836 362.01455 379.47167 119.72365
## Chrysler Imperial 396.759752 348.84669 364.59943 95.38054
## Fiat 128 5.147342 49.06444 49.91125 337.16392
## Honda Civic 14.780707 59.45888 64.04952 347.83377
## Toyota Corolla 10.392286 56.32430 53.88466 343.99210
## Toyota Corona 51.841175 8.65359 31.25369 285.12879
## Dodge Challenger 253.662405 206.64526 226.50048 118.75168
## AMC Javelin 240.526682 193.30806 212.75688 123.38320
## Camaro Z28 325.149091 276.89244 287.61790 19.35890
## Pontiac Firebird 339.139618 292.16465 311.38623 101.73897
## Fiat X1-9 0.000000 48.37752 49.84069 336.70188
## Porsche 914-2 48.377521 0.00000 33.76787 288.58530
## Lotus Europa 49.840688 33.76787 0.00000 297.53769
## Ford Pantera L 336.701878 288.58530 297.53769 0.00000
## Ferrari Dino 127.821081 87.91060 80.45535 224.45875
## Maserati Bora 349.119958 303.92225 303.27965 86.93833
## Volvo 142E 60.412043 18.75559 27.81045 277.48033
## Ferrari Dino Maserati Bora Volvo 142E
## Mazda RX4 66.76610 265.64542 39.18940
## Mazda RX4 Wag 66.77642 265.64915 39.16260
## Datsun 710 90.24155 309.77182 20.69394
## Hornet 4 Drive 130.55230 229.34194 137.03633
## Hornet Sportabout 215.06739 170.70945 248.00634
## Valiant 106.56948 242.43930 104.18637
## Duster 360 226.20363 107.72250 275.13535
## Merc 240D 113.30230 313.86331 53.68235
## Merc 230 80.65510 288.87556 24.69135
## Merc 280 56.83651 250.58741 48.80534
## Merc 280C 56.89876 250.57744 48.88846
## Merc 450SE 131.02722 157.16333 170.45007
## Merc 450SL 131.00776 157.17690 170.42252
## Merc 450SLC 131.07045 157.16840 170.48437
## Cadillac Fleetwood 328.54416 214.93669 364.10009
## Lincoln Continental 317.70631 199.34206 355.40094
## Chrysler Imperial 300.16407 174.29369 341.28967
## Fiat 128 128.39501 349.53388 61.33012
## Honda Civic 141.70445 362.16208 73.37660
## Toyota Corolla 133.47076 355.26016 67.71894
## Toyota Corona 82.23557 299.18652 12.25053
## Dodge Challenger 174.92804 185.90593 201.36825
## AMC Javelin 161.10603 185.15534 187.69784
## Camaro Z28 216.74899 102.59462 266.52777
## Pontiac Firebird 255.05705 188.32400 286.74978
## Fiat X1-9 127.82108 349.11996 60.41204
## Porsche 914-2 87.91060 303.92225 18.75559
## Lotus Europa 80.45535 303.27965 27.81045
## Ford Pantera L 224.45875 86.93833 277.48033
## Ferrari Dino 0.00000 223.53422 70.47510
## Maserati Bora 223.53422 0.00000 289.11574
## Volvo 142E 70.47510 289.11574 0.00000## Manhattan
cars_manhattan <- dist(mtcars, method = "manhattan")
as.matrix(cars_manhattan)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.000 0.815 79.300 108.795
## Mazda RX4 Wag 0.815 0.000 78.995 107.980
## Datsun 710 79.300 78.995 0.000 174.895
## Hornet 4 Drive 108.795 107.980 174.895 0.000
## Hornet Sportabout 275.430 274.615 349.510 176.415
## Valiant 84.640 83.825 141.540 42.645
## Duster 360 347.960 348.265 427.160 254.185
## Merc 240D 75.020 74.205 75.720 167.495
## Merc 230 48.990 48.175 41.990 141.965
## Merc 280 27.080 26.265 100.700 111.805
## Merc 280C 29.080 28.265 102.080 112.605
## Merc 450SE 198.620 197.805 273.940 100.705
## Merc 450SL 197.580 196.765 272.500 99.265
## Merc 450SLC 200.130 199.315 274.250 101.015
## Cadillac Fleetwood 426.720 425.905 502.880 329.645
## Lincoln Continental 424.664 423.849 501.144 327.909
## Chrysler Imperial 414.655 413.840 491.935 319.000
## Fiat 128 146.310 146.005 67.110 240.345
## Honda Civic 160.795 160.490 83.775 258.670
## Toyota Corolla 157.345 157.040 78.145 251.380
## Toyota Corona 65.305 65.000 21.095 154.940
## Dodge Challenger 211.950 211.435 286.330 113.095
## AMC Javelin 198.205 197.390 271.725 98.630
## Camaro Z28 339.140 339.445 418.340 246.405
## Pontiac Firebird 315.435 314.620 389.455 216.220
## Fiat X1-9 140.605 140.300 61.405 235.720
## Porsche 914-2 69.950 70.285 23.170 173.465
## Lotus Europa 84.977 84.912 45.097 185.832
## Ford Pantera L 356.030 356.335 435.330 267.725
## Ferrari Dino 85.690 86.205 134.890 193.625
## Maserati Bora 382.170 382.475 461.370 293.055
## Volvo 142E 47.910 47.285 32.130 145.305
## Hornet Sportabout Valiant Duster 360 Merc 240D Merc 230
## Mazda RX4 275.430 84.640 347.960 75.020 48.990
## Mazda RX4 Wag 274.615 83.825 348.265 74.205 48.175
## Datsun 710 349.510 141.540 427.160 75.720 41.990
## Hornet 4 Drive 176.415 42.645 254.185 167.495 141.965
## Hornet Sportabout 0.000 213.210 77.770 341.770 316.240
## Valiant 213.210 0.000 289.740 133.020 107.050
## Duster 360 77.770 289.740 0.000 419.420 393.890
## Merc 240D 341.770 133.020 419.420 0.000 43.670
## Merc 230 316.240 107.050 393.890 43.670 0.000
## Merc 280 252.950 83.600 326.600 93.280 67.290
## Merc 280C 253.950 82.200 325.800 94.080 68.090
## Merc 450SE 93.590 136.240 154.500 266.200 240.670
## Merc 450SL 92.550 134.800 155.260 264.760 239.230
## Merc 450SLC 95.100 136.550 153.610 266.510 240.980
## Cadillac Fleetwood 155.290 364.900 160.000 495.140 469.610
## Lincoln Continental 153.234 363.304 137.944 493.404 467.874
## Chrysler Imperial 143.385 354.555 98.775 484.195 458.665
## Fiat 128 416.620 206.930 494.270 83.910 107.240
## Honda Civic 431.105 225.315 508.755 92.295 123.625
## Toyota Corolla 427.655 217.105 505.305 92.085 117.415
## Toyota Corona 331.215 120.445 408.865 67.245 29.795
## Dodge Challenger 70.820 148.010 141.730 278.590 253.060
## AMC Javelin 84.785 134.235 155.555 263.985 238.455
## Camaro Z28 89.990 281.960 12.220 410.680 385.070
## Pontiac Firebird 41.005 253.975 118.515 381.715 356.185
## Fiat X1-9 410.915 202.365 488.565 79.345 102.675
## Porsche 914-2 340.900 140.110 417.910 65.090 38.420
## Lotus Europa 349.267 162.477 426.677 115.457 81.087
## Ford Pantera L 109.760 303.770 35.250 429.950 403.920
## Ferrari Dino 227.660 166.870 298.950 133.390 104.380
## Maserati Bora 234.640 328.610 158.270 455.630 430.100
## Volvo 142E 317.900 119.950 395.550 78.930 41.060
## Merc 280 Merc 280C Merc 450SE Merc 450SL Merc 450SLC
## Mazda RX4 27.080 29.080 198.620 197.580 200.130
## Mazda RX4 Wag 26.265 28.265 197.805 196.765 199.315
## Datsun 710 100.700 102.080 273.940 272.500 274.250
## Hornet 4 Drive 111.805 112.605 100.705 99.265 101.015
## Hornet Sportabout 252.950 253.950 93.590 92.550 95.100
## Valiant 83.600 82.200 136.240 134.800 136.550
## Duster 360 326.600 325.800 154.500 155.260 153.610
## Merc 240D 93.280 94.080 266.200 264.760 266.510
## Merc 230 67.290 68.090 240.670 239.230 240.980
## Merc 280 0.000 2.000 175.380 173.940 175.690
## Merc 280C 2.000 0.000 174.580 173.140 174.890
## Merc 450SE 175.380 174.580 0.000 1.440 2.090
## Merc 450SL 173.940 173.140 1.440 0.000 2.550
## Merc 450SLC 175.690 174.890 2.090 2.550 0.000
## Cadillac Fleetwood 402.320 401.520 230.100 231.140 228.630
## Lincoln Continental 400.584 399.784 228.044 229.084 226.894
## Chrysler Imperial 391.375 390.575 218.355 219.755 218.005
## Fiat 128 167.670 168.470 341.050 339.610 341.360
## Honda Civic 182.155 183.715 355.535 354.095 355.845
## Toyota Corolla 178.705 179.505 352.085 350.645 352.395
## Toyota Corona 84.705 85.505 255.645 254.205 255.955
## Dodge Challenger 189.770 188.970 75.490 76.250 75.200
## AMC Javelin 175.175 174.375 61.215 61.975 60.325
## Camaro Z28 317.780 316.980 146.180 147.160 145.410
## Pontiac Firebird 292.895 294.895 133.585 132.775 135.225
## Fiat X1-9 161.965 162.765 335.345 333.905 335.655
## Porsche 914-2 96.510 98.510 266.090 265.050 267.600
## Lotus Europa 103.177 105.177 274.457 273.417 275.967
## Ford Pantera L 337.170 336.370 168.750 169.510 169.060
## Ferrari Dino 83.870 85.870 150.850 149.810 152.360
## Maserati Bora 362.810 362.010 193.370 194.130 192.480
## Volvo 142E 68.950 70.350 242.330 240.890 242.640
## Cadillac Fleetwood Lincoln Continental Chrysler Imperial
## Mazda RX4 426.720 424.664 414.655
## Mazda RX4 Wag 425.905 423.849 413.840
## Datsun 710 502.880 501.144 491.935
## Hornet 4 Drive 329.645 327.909 319.000
## Hornet Sportabout 155.290 153.234 143.385
## Valiant 364.900 363.304 354.555
## Duster 360 160.000 137.944 98.775
## Merc 240D 495.140 493.404 484.195
## Merc 230 469.610 467.874 458.665
## Merc 280 402.320 400.584 391.375
## Merc 280C 401.520 399.784 390.575
## Merc 450SE 230.100 228.044 218.355
## Merc 450SL 231.140 229.084 219.755
## Merc 450SLC 228.630 226.894 218.005
## Cadillac Fleetwood 0.000 22.404 62.255
## Lincoln Continental 22.404 0.000 40.009
## Chrysler Imperial 62.255 40.009 0.000
## Fiat 128 569.990 568.254 559.045
## Honda Civic 584.475 582.739 573.530
## Toyota Corolla 581.025 579.289 570.080
## Toyota Corona 484.585 482.849 473.640
## Dodge Challenger 219.110 217.194 207.645
## AMC Javelin 232.515 230.459 220.610
## Camaro Z28 169.680 147.624 110.415
## Pontiac Firebird 115.285 113.229 103.520
## Fiat X1-9 564.285 562.549 553.340
## Porsche 914-2 496.190 494.134 484.125
## Lotus Europa 504.557 502.501 492.492
## Ford Pantera L 195.250 173.194 133.185
## Ferrari Dino 378.950 376.894 366.885
## Maserati Bora 318.270 296.214 256.205
## Volvo 142E 471.270 469.534 460.325
## Fiat 128 Honda Civic Toyota Corolla Toyota Corona
## Mazda RX4 146.310 160.795 157.345 65.305
## Mazda RX4 Wag 146.005 160.490 157.040 65.000
## Datsun 710 67.110 83.775 78.145 21.095
## Hornet 4 Drive 240.345 258.670 251.380 154.940
## Hornet Sportabout 416.620 431.105 427.655 331.215
## Valiant 206.930 225.315 217.105 120.445
## Duster 360 494.270 508.755 505.305 408.865
## Merc 240D 83.910 92.295 92.085 67.245
## Merc 230 107.240 123.625 117.415 29.795
## Merc 280 167.670 182.155 178.705 84.705
## Merc 280C 168.470 183.715 179.505 85.505
## Merc 450SE 341.050 355.535 352.085 255.645
## Merc 450SL 339.610 354.095 350.645 254.205
## Merc 450SLC 341.360 355.845 352.395 255.955
## Cadillac Fleetwood 569.990 584.475 581.025 484.585
## Lincoln Continental 568.254 582.739 579.289 482.849
## Chrysler Imperial 559.045 573.530 570.080 473.640
## Fiat 128 0.000 22.385 11.035 86.485
## Honda Civic 22.385 0.000 24.410 104.870
## Toyota Corolla 11.035 24.410 0.000 96.660
## Toyota Corona 86.485 104.870 96.660 0.000
## Dodge Challenger 353.440 367.925 364.475 268.035
## AMC Javelin 338.835 353.320 349.870 253.430
## Camaro Z28 485.450 499.935 496.485 400.105
## Pontiac Firebird 456.565 471.050 467.600 371.160
## Fiat X1-9 6.235 22.950 16.740 81.920
## Porsche 914-2 79.180 92.845 89.815 20.065
## Lotus Europa 70.967 84.282 81.272 58.032
## Ford Pantera L 501.980 516.185 512.735 421.335
## Ferrari Dino 202.000 216.485 213.035 120.595
## Maserati Bora 528.480 542.965 539.515 447.075
## Volvo 142E 98.780 113.365 109.755 18.135
## Dodge Challenger AMC Javelin Camaro Z28 Pontiac Firebird
## Mazda RX4 211.950 198.205 339.140 315.435
## Mazda RX4 Wag 211.435 197.390 339.445 314.620
## Datsun 710 286.330 271.725 418.340 389.455
## Hornet 4 Drive 113.095 98.630 246.405 216.220
## Hornet Sportabout 70.820 84.785 89.990 41.005
## Valiant 148.010 134.235 281.960 253.975
## Duster 360 141.730 155.555 12.220 118.515
## Merc 240D 278.590 263.985 410.680 381.715
## Merc 230 253.060 238.455 385.070 356.185
## Merc 280 189.770 175.175 317.780 292.895
## Merc 280C 188.970 174.375 316.980 294.895
## Merc 450SE 75.490 61.215 146.180 133.585
## Merc 450SL 76.250 61.975 147.160 132.775
## Merc 450SLC 75.200 60.325 145.410 135.225
## Cadillac Fleetwood 219.110 232.515 169.680 115.285
## Lincoln Continental 217.194 230.459 147.624 113.229
## Chrysler Imperial 207.645 220.610 110.415 103.520
## Fiat 128 353.440 338.835 485.450 456.565
## Honda Civic 367.925 353.320 499.935 471.050
## Toyota Corolla 364.475 349.870 496.485 467.600
## Toyota Corona 268.035 253.430 400.105 371.160
## Dodge Challenger 0.000 15.205 133.950 111.525
## AMC Javelin 15.205 0.000 147.775 125.730
## Camaro Z28 133.950 147.775 0.000 130.195
## Pontiac Firebird 111.525 125.730 130.195 0.000
## Fiat X1-9 347.735 333.130 479.745 450.860
## Porsche 914-2 277.420 263.675 409.090 380.905
## Lotus Europa 285.847 272.042 417.857 389.272
## Ford Pantera L 156.480 170.735 27.570 150.765
## Ferrari Dino 214.180 200.435 289.670 267.665
## Maserati Bora 214.600 200.425 148.970 275.385
## Volvo 142E 254.720 240.115 386.730 357.845
## Fiat X1-9 Porsche 914-2 Lotus Europa Ford Pantera L
## Mazda RX4 140.605 69.950 84.977 356.030
## Mazda RX4 Wag 140.300 70.285 84.912 356.335
## Datsun 710 61.405 23.170 45.097 435.330
## Hornet 4 Drive 235.720 173.465 185.832 267.725
## Hornet Sportabout 410.915 340.900 349.267 109.760
## Valiant 202.365 140.110 162.477 303.770
## Duster 360 488.565 417.910 426.677 35.250
## Merc 240D 79.345 65.090 115.457 429.950
## Merc 230 102.675 38.420 81.087 403.920
## Merc 280 161.965 96.510 103.177 337.170
## Merc 280C 162.765 98.510 105.177 336.370
## Merc 450SE 335.345 266.090 274.457 168.750
## Merc 450SL 333.905 265.050 273.417 169.510
## Merc 450SLC 335.655 267.600 275.967 169.060
## Cadillac Fleetwood 564.285 496.190 504.557 195.250
## Lincoln Continental 562.549 494.134 502.501 173.194
## Chrysler Imperial 553.340 484.125 492.492 133.185
## Fiat 128 6.235 79.180 70.967 501.980
## Honda Civic 22.950 92.845 84.282 516.185
## Toyota Corolla 16.740 89.815 81.272 512.735
## Toyota Corona 81.920 20.065 58.032 421.335
## Dodge Challenger 347.735 277.420 285.847 156.480
## AMC Javelin 333.130 263.675 272.042 170.735
## Camaro Z28 479.745 409.090 417.857 27.570
## Pontiac Firebird 450.860 380.905 389.272 150.765
## Fiat X1-9 0.000 73.355 70.932 496.275
## Porsche 914-2 73.355 0.000 54.087 423.340
## Lotus Europa 70.932 54.087 0.000 433.007
## Ford Pantera L 496.275 423.340 433.007 0.000
## Ferrari Dino 196.295 123.640 132.407 304.900
## Maserati Bora 522.775 450.120 458.887 126.980
## Volvo 142E 93.075 28.160 43.207 403.200
## Ferrari Dino Maserati Bora Volvo 142E
## Mazda RX4 85.690 382.170 47.910
## Mazda RX4 Wag 86.205 382.475 47.285
## Datsun 710 134.890 461.370 32.130
## Hornet 4 Drive 193.625 293.055 145.305
## Hornet Sportabout 227.660 234.640 317.900
## Valiant 166.870 328.610 119.950
## Duster 360 298.950 158.270 395.550
## Merc 240D 133.390 455.630 78.930
## Merc 230 104.380 430.100 41.060
## Merc 280 83.870 362.810 68.950
## Merc 280C 85.870 362.010 70.350
## Merc 450SE 150.850 193.370 242.330
## Merc 450SL 149.810 194.130 240.890
## Merc 450SLC 152.360 192.480 242.640
## Cadillac Fleetwood 378.950 318.270 471.270
## Lincoln Continental 376.894 296.214 469.534
## Chrysler Imperial 366.885 256.205 460.325
## Fiat 128 202.000 528.480 98.780
## Honda Civic 216.485 542.965 113.365
## Toyota Corolla 213.035 539.515 109.755
## Toyota Corona 120.595 447.075 18.135
## Dodge Challenger 214.180 214.600 254.720
## AMC Javelin 200.435 200.425 240.115
## Camaro Z28 289.670 148.970 386.730
## Pontiac Firebird 267.665 275.385 357.845
## Fiat X1-9 196.295 522.775 93.075
## Porsche 914-2 123.640 450.120 28.160
## Lotus Europa 132.407 458.887 43.207
## Ford Pantera L 304.900 126.980 403.200
## Ferrari Dino 0.000 326.480 103.300
## Maserati Bora 326.480 0.000 429.760
## Volvo 142E 103.300 429.760 0.000## minkowski
cars_minkowski <- dist(mtcars, method = "minkowski")
as.matrix(cars_minkowski)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.0000000 0.6153251 54.90861 98.11252
## Mazda RX4 Wag 0.6153251 0.0000000 54.89152 98.09589
## Datsun 710 54.9086059 54.8915169 0.00000 150.99352
## Hornet 4 Drive 98.1125212 98.0958939 150.99352 0.00000
## Hornet Sportabout 210.3374396 210.3358546 265.08316 121.02976
## Valiant 65.4717710 65.4392224 117.75470 33.55087
## Duster 360 241.4076490 241.4088680 294.47902 169.42996
## Merc 240D 50.1532711 50.1146059 49.65848 121.27397
## Merc 230 25.4683117 25.3284509 33.18038 118.24331
## Merc 280 15.3641921 15.2956865 66.93635 91.42240
## Merc 280C 15.6724727 15.5837744 67.02614 91.46129
## Merc 450SE 135.4307018 135.4254826 189.19549 72.49643
## Merc 450SL 135.4014424 135.3960351 189.16317 72.43135
## Merc 450SLC 135.4794674 135.4723157 189.23454 72.57185
## Cadillac Fleetwood 326.3395903 326.3355070 381.09262 234.44039
## Lincoln Continental 318.0469808 318.0429333 372.80121 227.97261
## Chrysler Imperial 304.7203408 304.7169175 359.30149 218.15483
## Fiat 128 93.2679950 93.2530993 40.99338 184.96897
## Honda Civic 102.8307567 102.8238713 52.77046 191.55187
## Toyota Corolla 100.6040368 100.5887588 47.65350 192.67142
## Toyota Corona 42.3075233 42.2659224 12.96547 138.53047
## Dodge Challenger 163.1150750 163.1134210 217.77958 72.44039
## AMC Javelin 149.6047203 149.6014522 204.31889 61.36019
## Camaro Z28 233.2228758 233.2248748 286.00492 163.66326
## Pontiac Firebird 248.6780270 248.6762035 303.35839 156.22403
## Fiat X1-9 92.5048389 92.4940020 39.88151 184.44712
## Porsche 914-2 44.4033659 44.4073589 13.13571 139.15795
## Lotus Europa 65.7328377 65.7362635 25.09486 163.23674
## Ford Pantera L 245.4247064 245.4293785 297.29405 180.11403
## Ferrari Dino 66.7661029 66.7764167 90.24155 130.55230
## Maserati Bora 265.6454248 265.6491465 309.77182 229.34194
## Volvo 142E 39.1894029 39.1626037 20.69394 137.03633
## Hornet Sportabout Valiant Duster 360 Merc 240D Merc 230
## Mazda RX4 210.33744 65.47177 241.40765 50.15327 25.46831
## Mazda RX4 Wag 210.33585 65.43922 241.40887 50.11461 25.32845
## Datsun 710 265.08316 117.75470 294.47902 49.65848 33.18038
## Hornet 4 Drive 121.02976 33.55087 169.42996 121.27397 118.24331
## Hornet Sportabout 0.00000 152.12414 70.17673 241.50697 233.49240
## Valiant 152.12414 0.00000 194.60945 89.59111 85.00796
## Duster 360 70.17673 194.60945 0.00000 281.29625 265.88233
## Merc 240D 241.50697 89.59111 281.29625 0.00000 33.68730
## Merc 230 233.49240 85.00796 265.88233 33.68730 0.00000
## Merc 280 199.33450 60.29098 227.89985 64.77542 39.29942
## Merc 280C 199.34066 60.26557 227.88132 64.88987 39.38685
## Merc 450SE 84.38885 90.69703 106.40843 175.16201 159.81796
## Merc 450SL 84.36840 90.67697 106.43206 175.11898 159.77609
## Merc 450SLC 84.43324 90.70930 106.40103 175.21182 159.84958
## Cadillac Fleetwood 116.28042 266.62809 119.02391 355.66275 349.28326
## Lincoln Continental 108.06243 259.63044 104.51130 348.99013 341.31543
## Chrysler Imperial 97.20491 248.77133 81.42977 338.19594 328.43352
## Fiat 128 302.03772 152.11533 333.97921 68.61059 69.31279
## Honda Civic 310.03246 158.96158 344.05183 72.00145 78.53872
## Toyota Corolla 309.55818 159.83030 341.02182 76.28065 76.77317
## Toyota Corona 252.33320 105.28764 282.05088 44.08510 21.09620
## Dodge Challenger 48.98389 103.43107 103.90239 192.86179 185.83319
## AMC Javelin 61.42742 91.04443 110.30849 180.54798 172.53126
## Camaro Z28 70.96653 187.84638 10.07612 273.83680 257.74697
## Pontiac Firebird 40.00525 188.52721 80.80573 277.46069 271.38720
## Fiat X1-9 301.56695 151.43794 333.48432 67.91640 68.55649
## Porsche 914-2 254.14526 106.05858 285.19862 39.44693 22.11810
## Lotus Europa 272.35824 130.82482 296.45723 72.89711 50.10940
## Ford Pantera L 89.59340 203.01779 21.26560 287.52388 269.97720
## Ferrari Dino 215.06739 106.56948 226.20363 113.30230 80.65510
## Maserati Bora 170.70945 242.43930 107.72250 313.86331 288.87556
## Volvo 142E 248.00634 104.18637 275.13535 53.68235 24.69135
## Merc 280 Merc 280C Merc 450SE Merc 450SL Merc 450SLC
## Mazda RX4 15.364192 15.672473 135.4307018 135.4014424 135.479467
## Mazda RX4 Wag 15.295686 15.583774 135.4254826 135.3960351 135.472316
## Datsun 710 66.936353 67.026140 189.1954941 189.1631745 189.234543
## Hornet 4 Drive 91.422403 91.461291 72.4964325 72.4313532 72.571847
## Hornet Sportabout 199.334496 199.340656 84.3888482 84.3683999 84.433242
## Valiant 60.290981 60.265566 90.6970264 90.6769728 90.709299
## Duster 360 227.899852 227.881317 106.4084264 106.4320572 106.401031
## Merc 240D 64.775423 64.889871 175.1620073 175.1189767 175.211822
## Merc 230 39.299416 39.386852 159.8179555 159.7760899 159.849584
## Merc 280 0.000000 1.523155 122.3642489 122.3443771 122.393497
## Merc 280C 1.523155 0.000000 122.3461050 122.3355492 122.358686
## Merc 450SE 122.364249 122.346105 0.0000000 0.9826495 1.372625
## Merc 450SL 122.344377 122.335549 0.9826495 0.0000000 2.138340
## Merc 450SLC 122.393497 122.358686 1.3726252 2.1383405 0.000000
## Cadillac Fleetwood 315.390486 315.355708 197.8842803 197.9154476 197.852624
## Lincoln Continental 306.676072 306.640619 187.5997191 187.6330806 187.567108
## Chrysler Imperial 292.714690 292.698933 171.6600758 171.6743028 171.655764
## Fiat 128 106.505315 106.682979 228.3247948 228.2592340 228.405183
## Honda Civic 116.728099 116.871148 238.0141824 237.9588183 238.082900
## Toyota Corolla 113.629072 113.811801 235.5183809 235.4481971 235.602410
## Toyota Corona 54.364171 54.425831 176.6020527 176.5727477 176.630536
## Dodge Challenger 152.892926 152.872244 51.8008639 51.8242520 51.801261
## AMC Javelin 139.145797 139.118198 41.2080044 41.2411618 41.192905
## Camaro Z28 219.552085 219.527643 98.7203049 98.7566899 98.703583
## Pontiac Firebird 238.172610 238.180629 124.3368538 124.3204160 124.372613
## Fiat X1-9 105.741291 105.856037 227.7627676 227.7173075 227.817655
## Porsche 914-2 57.645816 57.847386 179.5034108 179.4550855 179.572045
## Lotus Europa 74.144358 74.382430 193.3074449 193.2407697 193.396922
## Ford Pantera L 231.408131 231.402426 112.8181834 112.8296774 112.833260
## Ferrari Dino 56.836510 56.898760 131.0272205 131.0077635 131.070449
## Maserati Bora 250.587412 250.577436 157.1633256 157.1768956 157.168397
## Volvo 142E 48.805345 48.888462 170.4500681 170.4225164 170.484373
## Cadillac Fleetwood Lincoln Continental Chrysler Imperial
## Mazda RX4 326.33959 318.04698 304.72034
## Mazda RX4 Wag 326.33551 318.04293 304.71692
## Datsun 710 381.09262 372.80121 359.30149
## Hornet 4 Drive 234.44039 227.97261 218.15483
## Hornet Sportabout 116.28042 108.06243 97.20491
## Valiant 266.62809 259.63044 248.77133
## Duster 360 119.02391 104.51130 81.42977
## Merc 240D 355.66275 348.99013 338.19594
## Merc 230 349.28326 341.31543 328.43352
## Merc 280 315.39049 306.67607 292.71469
## Merc 280C 315.35571 306.64062 292.69893
## Merc 450SE 197.88428 187.59972 171.66008
## Merc 450SL 197.91545 187.63308 171.67430
## Merc 450SLC 197.85262 187.56711 171.65576
## Cadillac Fleetwood 0.00000 15.62244 40.83996
## Lincoln Continental 15.62244 0.00000 25.37142
## Chrysler Imperial 40.83996 25.37142 0.00000
## Fiat 128 417.76876 410.02070 397.22764
## Honda Civic 425.32716 417.96796 405.81522
## Toyota Corolla 425.34465 417.54300 404.63354
## Toyota Corona 368.31955 360.02675 346.57246
## Dodge Challenger 163.63149 156.28050 145.91948
## AMC Javelin 176.86109 169.09255 157.80976
## Camaro Z28 128.45872 114.09321 91.28809
## Pontiac Firebird 78.53853 72.69479 68.20307
## Fiat X1-9 417.24905 409.49984 396.75975
## Porsche 914-2 370.09568 362.01455 348.84669
## Lotus Europa 388.53500 379.47167 364.59943
## Ford Pantera L 134.81195 119.72365 95.38054
## Ferrari Dino 328.54416 317.70631 300.16407
## Maserati Bora 214.93669 199.34206 174.29369
## Volvo 142E 364.10009 355.40094 341.28967
## Fiat 128 Honda Civic Toyota Corolla Toyota Corona
## Mazda RX4 93.267995 102.83076 100.604037 42.30752
## Mazda RX4 Wag 93.253099 102.82387 100.588759 42.26592
## Datsun 710 40.993376 52.77046 47.653502 12.96547
## Hornet 4 Drive 184.968973 191.55187 192.671419 138.53047
## Hornet Sportabout 302.037721 310.03246 309.558178 252.33320
## Valiant 152.115326 158.96158 159.830299 105.28764
## Duster 360 333.979207 344.05183 341.021823 282.05088
## Merc 240D 68.610590 72.00145 76.280646 44.08510
## Merc 230 69.312791 78.53872 76.773167 21.09620
## Merc 280 106.505315 116.72810 113.629072 54.36417
## Merc 280C 106.682979 116.87115 113.811801 54.42583
## Merc 450SE 228.324795 238.01418 235.518381 176.60205
## Merc 450SL 228.259234 237.95882 235.448197 176.57275
## Merc 450SLC 228.405183 238.08290 235.602410 176.63054
## Cadillac Fleetwood 417.768758 425.32716 425.344652 368.31955
## Lincoln Continental 410.020698 417.96796 417.542999 360.02675
## Chrysler Imperial 397.227638 405.81522 404.633539 346.57246
## Fiat 128 0.000000 14.55909 7.832479 52.87983
## Honda Civic 14.559094 0.00000 14.348063 63.89856
## Toyota Corolla 7.832479 14.34806 0.000000 59.84513
## Toyota Corona 52.879828 63.89856 59.845128 0.00000
## Dodge Challenger 254.236789 261.84988 261.834531 205.03479
## AMC Javelin 241.120362 248.96365 248.691707 191.55805
## Camaro Z28 325.663624 335.88832 332.658970 273.63169
## Pontiac Firebird 339.585766 347.06554 347.166764 290.62407
## Fiat X1-9 5.147342 14.78071 10.392286 51.84117
## Porsche 914-2 49.064437 59.45888 56.324303 8.65359
## Lotus Europa 49.911251 64.04952 53.884656 31.25369
## Ford Pantera L 337.163924 347.83377 343.992096 285.12879
## Ferrari Dino 128.395005 141.70445 133.470762 82.23557
## Maserati Bora 349.533883 362.16208 355.260162 299.18652
## Volvo 142E 61.330125 73.37660 67.718942 12.25053
## Dodge Challenger AMC Javelin Camaro Z28 Pontiac Firebird
## Mazda RX4 163.11508 149.60472 233.22288 248.67803
## Mazda RX4 Wag 163.11342 149.60145 233.22487 248.67620
## Datsun 710 217.77958 204.31889 286.00492 303.35839
## Hornet 4 Drive 72.44039 61.36019 163.66326 156.22403
## Hornet Sportabout 48.98389 61.42742 70.96653 40.00525
## Valiant 103.43107 91.04443 187.84638 188.52721
## Duster 360 103.90239 110.30849 10.07612 80.80573
## Merc 240D 192.86179 180.54798 273.83680 277.46069
## Merc 230 185.83319 172.53126 257.74697 271.38720
## Merc 280 152.89293 139.14580 219.55209 238.17261
## Merc 280C 152.87224 139.11820 219.52764 238.18063
## Merc 450SE 51.80086 41.20800 98.72030 124.33685
## Merc 450SL 51.82425 41.24116 98.75669 124.32042
## Merc 450SLC 51.80126 41.19291 98.70358 124.37261
## Cadillac Fleetwood 163.63149 176.86109 128.45872 78.53853
## Lincoln Continental 156.28050 169.09255 114.09321 72.69479
## Chrysler Imperial 145.91948 157.80976 91.28809 68.20307
## Fiat 128 254.23679 241.12036 325.66362 339.58577
## Honda Civic 261.84988 248.96365 335.88832 347.06554
## Toyota Corolla 261.83453 248.69171 332.65897 347.16676
## Toyota Corona 205.03479 191.55805 273.63169 290.62407
## Dodge Challenger 0.00000 14.01550 100.30461 85.80752
## AMC Javelin 14.01550 0.00000 105.60626 99.28361
## Camaro Z28 100.30461 105.60626 0.00000 86.26658
## Pontiac Firebird 85.80752 99.28361 86.26658 0.00000
## Fiat X1-9 253.66240 240.52668 325.14909 339.13962
## Porsche 914-2 206.64526 193.30806 276.89244 292.16465
## Lotus Europa 226.50048 212.75688 287.61790 311.38623
## Ford Pantera L 118.75168 123.38320 19.35890 101.73897
## Ferrari Dino 174.92804 161.10603 216.74899 255.05705
## Maserati Bora 185.90593 185.15534 102.59462 188.32400
## Volvo 142E 201.36825 187.69784 266.52777 286.74978
## Fiat X1-9 Porsche 914-2 Lotus Europa Ford Pantera L
## Mazda RX4 92.504839 44.40337 65.73284 245.42471
## Mazda RX4 Wag 92.494002 44.40736 65.73626 245.42938
## Datsun 710 39.881515 13.13571 25.09486 297.29405
## Hornet 4 Drive 184.447120 139.15795 163.23674 180.11403
## Hornet Sportabout 301.566948 254.14526 272.35824 89.59340
## Valiant 151.437942 106.05858 130.82482 203.01779
## Duster 360 333.484323 285.19862 296.45723 21.26560
## Merc 240D 67.916398 39.44693 72.89711 287.52388
## Merc 230 68.556486 22.11810 50.10940 269.97720
## Merc 280 105.741291 57.64582 74.14436 231.40813
## Merc 280C 105.856037 57.84739 74.38243 231.40243
## Merc 450SE 227.762768 179.50341 193.30744 112.81818
## Merc 450SL 227.717307 179.45509 193.24077 112.82968
## Merc 450SLC 227.817655 179.57204 193.39692 112.83326
## Cadillac Fleetwood 417.249048 370.09568 388.53500 134.81195
## Lincoln Continental 409.499836 362.01455 379.47167 119.72365
## Chrysler Imperial 396.759752 348.84669 364.59943 95.38054
## Fiat 128 5.147342 49.06444 49.91125 337.16392
## Honda Civic 14.780707 59.45888 64.04952 347.83377
## Toyota Corolla 10.392286 56.32430 53.88466 343.99210
## Toyota Corona 51.841175 8.65359 31.25369 285.12879
## Dodge Challenger 253.662405 206.64526 226.50048 118.75168
## AMC Javelin 240.526682 193.30806 212.75688 123.38320
## Camaro Z28 325.149091 276.89244 287.61790 19.35890
## Pontiac Firebird 339.139618 292.16465 311.38623 101.73897
## Fiat X1-9 0.000000 48.37752 49.84069 336.70188
## Porsche 914-2 48.377521 0.00000 33.76787 288.58530
## Lotus Europa 49.840688 33.76787 0.00000 297.53769
## Ford Pantera L 336.701878 288.58530 297.53769 0.00000
## Ferrari Dino 127.821081 87.91060 80.45535 224.45875
## Maserati Bora 349.119958 303.92225 303.27965 86.93833
## Volvo 142E 60.412043 18.75559 27.81045 277.48033
## Ferrari Dino Maserati Bora Volvo 142E
## Mazda RX4 66.76610 265.64542 39.18940
## Mazda RX4 Wag 66.77642 265.64915 39.16260
## Datsun 710 90.24155 309.77182 20.69394
## Hornet 4 Drive 130.55230 229.34194 137.03633
## Hornet Sportabout 215.06739 170.70945 248.00634
## Valiant 106.56948 242.43930 104.18637
## Duster 360 226.20363 107.72250 275.13535
## Merc 240D 113.30230 313.86331 53.68235
## Merc 230 80.65510 288.87556 24.69135
## Merc 280 56.83651 250.58741 48.80534
## Merc 280C 56.89876 250.57744 48.88846
## Merc 450SE 131.02722 157.16333 170.45007
## Merc 450SL 131.00776 157.17690 170.42252
## Merc 450SLC 131.07045 157.16840 170.48437
## Cadillac Fleetwood 328.54416 214.93669 364.10009
## Lincoln Continental 317.70631 199.34206 355.40094
## Chrysler Imperial 300.16407 174.29369 341.28967
## Fiat 128 128.39501 349.53388 61.33012
## Honda Civic 141.70445 362.16208 73.37660
## Toyota Corolla 133.47076 355.26016 67.71894
## Toyota Corona 82.23557 299.18652 12.25053
## Dodge Challenger 174.92804 185.90593 201.36825
## AMC Javelin 161.10603 185.15534 187.69784
## Camaro Z28 216.74899 102.59462 266.52777
## Pontiac Firebird 255.05705 188.32400 286.74978
## Fiat X1-9 127.82108 349.11996 60.41204
## Porsche 914-2 87.91060 303.92225 18.75559
## Lotus Europa 80.45535 303.27965 27.81045
## Ford Pantera L 224.45875 86.93833 277.48033
## Ferrari Dino 0.00000 223.53422 70.47510
## Maserati Bora 223.53422 0.00000 289.11574
## Volvo 142E 70.47510 289.11574 0.00000Just like in Ex.1 similar observation can be found in mtcars dataset as well. Euclidean and Minkowski have similar results wherer Manhattan have different reults.
Ex.3
Use the built-in data set mtcars to carry out hierarchy clustering using two different distance metrics and compare if they get the same results. Discuss the results.
## Euclidean
cluster_euclidean <- hclust(cars_euclidean)
summary(cluster_euclidean)## Length Class Mode
## merge 62 -none- numeric
## height 31 -none- numeric
## order 32 -none- numeric
## labels 32 -none- character
## method 1 -none- character
## call 2 -none- call
## dist.method 1 -none- character# dendrogram to visualize number of clusters
plot(cluster_euclidean, xlab = "observations", ylab = "proximity measure")
rect.hclust(cluster_euclidean, k = 3, border = 2:6)
# assign clusters based on number of clusters
clust_assgn1 <- cutree(cluster_euclidean, k=3)
table(clust_assgn1)## clust_assgn1
## 1 2 3
## 16 7 9## manhattan
cluster_manhattan <- hclust(cars_manhattan)
summary(cluster_manhattan)## Length Class Mode
## merge 62 -none- numeric
## height 31 -none- numeric
## order 32 -none- numeric
## labels 32 -none- character
## method 1 -none- character
## call 2 -none- call
## dist.method 1 -none- character##dendrogram to visualize number of clusters
plot(cluster_manhattan, xlab = "observations", ylab = "proximity measure")
rect.hclust(cluster_manhattan, k = 3, border = 2:6)
#assign clusters based on number of clusters
clust_assgn2 <- cutree(cluster_manhattan, k=3)
table(clust_assgn2)## clust_assgn2
## 1 2 3
## 18 10 4We can see than in both methods, euclidean and manhattan, first cluster is with higher number of elements. Also we can see that second and third clusters are more evenly distibuted in euclidean compared to manhattan.
Ex.4
Load the well-known Fisher’s iris flower data set that consists of 150 samples for three 3 species (50 samples each species). The four measures or features are the lengths and widths of sepal and petals. Use the kNN clustering to analyze this iris data set by selecting 120 samples for training and 30 samples for testing.
head(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosalibrary(class)
set.seed(123)
iris_split <- sort(sample(nrow(iris), nrow(iris) * 0.8))
train <- iris[iris_split, -5]
test <- iris[-iris_split, -5]
train_category <- iris[iris_split, 5]
test_category <- iris[-iris_split, 5]
iris_knn <- knn(train, test, cl = train_category, k = 5)
knn_table <- table(iris_knn, test_category)
knn_accuracy <- sum(diag(knn_table)) / sum(knn_table)
knn_accuracy## [1] 0.9666667Ex.5
Use the iris data set to carry out k-means clustering. Compare the results to the actual classes and estimate the clustering accuracy.
set.seed(123)
iris_kmeans <- kmeans(iris[, -5], centers = 3)
iris_kmeans## K-means clustering with 3 clusters of sizes 50, 62, 38
##
## Cluster means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1 5.006000 3.428000 1.462000 0.246000
## 2 5.901613 2.748387 4.393548 1.433871
## 3 6.850000 3.073684 5.742105 2.071053
##
## Clustering vector:
## [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 3 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 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 3 3 3 2 3 3 3 3
## [112] 3 3 2 2 3 3 3 3 2 3 2 3 2 3 3 2 2 3 3 3 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 2 3
## [149] 3 2
##
## Within cluster sum of squares by cluster:
## [1] 15.15100 39.82097 23.87947
## (between_SS / total_SS = 88.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"iris_clusters <- iris_kmeans$cluster
table(iris_clusters)## iris_clusters
## 1 2 3
## 50 62 38library(cluster)clusplot(iris[, -5], iris_clusters)
iris$cluster.kmeans <- iris_clusters
cluster_table <- table(iris$Species, iris$cluster.kmeans)
cluster_table##
## 1 2 3
## setosa 50 0 0
## versicolor 0 48 2
## virginica 0 14 36kmeans_accuracy <- sum(diag(cluster_table)) / sum(cluster_table)
kmeans_accuracy## [1] 0.8933333