Data 609 - Module6
Amit Kapoor
10/22/2021
# Libraries
library(class)
library(cluster)Ex. 1
Use a data set such as the PlantGrowth in R to calculate three different distance metrics and discuss the results.
Solution
We will use here PlantGrowth dataset in R and dist() function that gives the distance matrix using specified distance to compute the distances between the rows of distance matrix. Here the methods considered are manhattan, euclidean and canberra.
plants_man <- dist(PlantGrowth, method = "manhattan")## Warning in dist(PlantGrowth, method = "manhattan"): NAs introduced by coercionas.matrix(plants_man)## 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 0.00plants_euc <- dist(PlantGrowth, method = "euclidean")## Warning in dist(PlantGrowth, method = "euclidean"): NAs introduced by coercionas.matrix(plants_euc)## 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 0.00000000plants_can <- dist(PlantGrowth, method = "canberra")## Warning in dist(PlantGrowth, method = "canberra"): NAs introduced by coercionas.matrix(plants_can)## 1 2 3 4 5 6
## 1 0.00000000 0.289230769 0.216042781 0.377431907 0.076124567 0.10022779
## 2 0.28923077 0.000000000 0.074349442 0.090675791 0.214285714 0.19038273
## 3 0.21604278 0.074349442 0.000000000 0.164747564 0.140495868 0.11644535
## 4 0.37743191 0.090675791 0.164747564 0.000000000 0.303487276 0.27985075
## 5 0.07612457 0.214285714 0.140495868 0.303487276 0.000000000 0.02414929
## 6 0.10022779 0.190382728 0.116445352 0.279850746 0.024149286 0.00000000
## 7 0.21413276 0.076279070 0.001932367 0.166666667 0.138572906 0.11451943
## 8 0.08275862 0.207715134 0.133882595 0.296992481 0.006644518 0.01750547
## 9 0.24421053 0.045829514 0.028544244 0.136363636 0.168870804 0.14486922
## 10 0.20837809 0.082089552 0.007751938 0.172444444 0.132780083 0.10871795
## 11 0.14253898 0.148219442 0.074074074 0.238095238 0.066595059 0.04246285
## 12 0.00000000 0.289230769 0.216042781 0.377431907 0.076124567 0.10022779
## 13 0.05594406 0.234234234 0.160583942 0.323193916 0.020202020 0.04434590
## 14 0.14948454 0.434023991 0.362599772 0.519587629 0.224969098 0.24878049
## 15 0.33864542 0.050655022 0.124886878 0.040066778 0.264223722 0.24045802
## 16 0.08500000 0.371944740 0.299667037 0.458752515 0.160864346 0.18483412
## 17 0.36470588 0.077519380 0.151650312 0.013179572 0.290598291 0.26691729
## 18 0.15894040 0.131805158 0.057596822 0.221818182 0.083067093 0.05894737
## 19 0.03533569 0.254545455 0.181052632 0.343240652 0.040816327 0.06494961
## 20 0.11738149 0.173320351 0.099290780 0.262962963 0.041349293 0.01720430
## 21 0.40839695 0.122792262 0.196692776 0.032206119 0.334875116 0.31135531
## 22 0.20452099 0.085981308 0.011650485 0.176313446 0.128898129 0.10483042
## 23 0.28218332 0.007194245 0.067164179 0.097854077 0.207171315 0.18325123
## 24 0.27507756 0.014440433 0.059925094 0.105081826 0.200000000 0.17606330
## 25 0.25157233 0.038356164 0.036018957 0.128919861 0.176291793 0.15230461
## 26 0.23678647 0.053357866 0.021012416 0.143859649 0.161389173 0.13737374
## 27 0.16501650 0.125714286 0.051485149 0.215775159 0.089171975 0.06505771
## 28 0.38372093 0.097186701 0.171226831 0.006525285 0.309859155 0.28624535
## 29 0.32698094 0.038664323 0.112932605 0.052057095 0.252427184 0.22862632
## 30 0.23117709 0.059040590 0.015325670 0.149516271 0.155737705 0.13171226
## 7 8 9 10 11 12
## 1 0.214132762 0.082758621 0.244210526 0.208378088 0.14253898 0.00000000
## 2 0.076279070 0.207715134 0.045829514 0.082089552 0.14821944 0.28923077
## 3 0.001932367 0.133882595 0.028544244 0.007751938 0.07407407 0.21604278
## 4 0.166666667 0.296992481 0.136363636 0.172444444 0.23809524 0.37743191
## 5 0.138572906 0.006644518 0.168870804 0.132780083 0.06659506 0.07612457
## 6 0.114519427 0.017505470 0.144869215 0.108717949 0.04246285 0.10022779
## 7 0.000000000 0.131958763 0.030476190 0.005819593 0.07214429 0.21413276
## 8 0.131958763 0.000000000 0.162271805 0.126163392 0.05995717 0.08275862
## 9 0.030476190 0.162271805 0.000000000 0.036294174 0.10256410 0.24421053
## 10 0.005819593 0.126163392 0.036294174 0.000000000 0.06633166 0.20837809
## 11 0.072144289 0.059957173 0.102564103 0.066331658 0.00000000 0.14253898
## 12 0.214132762 0.082758621 0.244210526 0.208378088 0.14253898 0.00000000
## 13 0.158663883 0.026845638 0.188911704 0.152879581 0.08676790 0.05594406
## 14 0.360730594 0.231527094 0.390134529 0.355097365 0.29047619 0.14948454
## 15 0.126811594 0.257692308 0.096428571 0.132606721 0.19850187 0.33864542
## 16 0.297777778 0.167464115 0.327510917 0.292084727 0.22685185 0.08500000
## 17 0.153571429 0.284090909 0.123239437 0.159355416 0.22509225 0.36470588
## 18 0.055666004 0.076433121 0.086105675 0.049850449 0.01649485 0.15894040
## 19 0.179135933 0.047457627 0.209326425 0.173361522 0.10733844 0.03533569
## 20 0.097363083 0.034707158 0.127744511 0.091556460 0.02526316 0.11738149
## 21 0.198606272 0.328413284 0.168384880 0.204366812 0.26978417 0.40839695
## 22 0.009718173 0.122279793 0.040191388 0.003898635 0.06243706 0.20452099
## 23 0.069094304 0.200595829 0.038638454 0.074906367 0.14106280 0.28218332
## 24 0.061855670 0.193419741 0.031394275 0.067669173 0.13385063 0.27507756
## 25 0.037950664 0.169696970 0.007476636 0.043767840 0.11001965 0.25157233
## 26 0.022944551 0.154786151 0.007532957 0.028763183 0.09504950 0.23678647
## 27 0.049554014 0.082539683 0.080000000 0.043737575 0.02261048 0.16501650
## 28 0.173144876 0.303370787 0.142857143 0.178919398 0.24452555 0.38372093
## 29 0.114858706 0.245885770 0.084456424 0.120658135 0.18661640 0.32698094
## 30 0.017257910 0.149131767 0.013220019 0.023076923 0.08937438 0.23117709
## 13 14 15 16 17 18
## 1 0.05594406 0.14948454 0.33864542 0.08500000 0.36470588 0.158940397
## 2 0.23423423 0.43402399 0.05065502 0.37194474 0.07751938 0.131805158
## 3 0.16058394 0.36259977 0.12488688 0.29966704 0.15165031 0.057596822
## 4 0.32319392 0.51958763 0.04006678 0.45875252 0.01317957 0.221818182
## 5 0.02020202 0.22496910 0.26422372 0.16086435 0.29059829 0.083067093
## 6 0.04434590 0.24878049 0.24045802 0.18483412 0.26691729 0.058947368
## 7 0.15866388 0.36073059 0.12681159 0.29777778 0.15357143 0.055666004
## 8 0.02684564 0.23152709 0.25769231 0.16746411 0.28409091 0.076433121
## 9 0.18891170 0.39013453 0.09642857 0.32751092 0.12323944 0.086105675
## 10 0.15287958 0.35509737 0.13260672 0.29208473 0.15935542 0.049850449
## 11 0.08676790 0.29047619 0.19850187 0.22685185 0.22509225 0.016494845
## 12 0.05594406 0.14948454 0.33864542 0.08500000 0.36470588 0.158940397
## 13 0.00000000 0.20500000 0.28404669 0.14077670 0.31034483 0.103225806
## 14 0.20500000 0.00000000 0.48202960 0.06469003 0.50727651 0.306603774
## 15 0.28404669 0.48202960 0.00000000 0.42061856 0.02689076 0.182156134
## 16 0.14077670 0.06469003 0.42061856 0.00000000 0.44624746 0.243119266
## 17 0.31034483 0.50727651 0.02689076 0.44624746 0.00000000 0.208791209
## 18 0.10322581 0.30660377 0.18215613 0.24311927 0.20879121 0.000000000
## 19 0.02061856 0.18457649 0.30421982 0.12024540 0.33043478 0.123778502
## 20 0.06153846 0.26570048 0.22348485 0.20187793 0.25000000 0.041753653
## 21 0.35447761 0.54949495 0.07224959 0.48915187 0.04538088 0.253571429
## 22 0.14900315 0.35132032 0.13648772 0.28826816 0.16322870 0.045954046
## 23 0.22713568 0.42716320 0.05784400 0.36499466 0.08470182 0.124640460
## 24 0.21997982 0.42024202 0.06508355 0.35798499 0.09193408 0.117420597
## 25 0.19631902 0.39732143 0.08896797 0.33478261 0.11578947 0.093567251
## 26 0.18144330 0.38288288 0.10394265 0.32017544 0.13074205 0.078585462
## 27 0.10932476 0.31257344 0.17608897 0.24914286 0.20273973 0.006116208
## 28 0.32954545 0.52566735 0.04658902 0.46492986 0.01970443 0.228260870
## 29 0.27228208 0.47071353 0.01199657 0.40913811 0.03888419 0.170252572
## 30 0.17580145 0.37740113 0.10961366 0.31463146 0.13640390 0.072906404
## 19 20 21 22 23 24
## 1 0.03533569 0.11738149 0.40839695 0.204520990 0.282183316 0.275077559
## 2 0.25454545 0.17332035 0.12279226 0.085981308 0.007194245 0.014440433
## 3 0.18105263 0.09929078 0.19669278 0.011650485 0.067164179 0.059925094
## 4 0.34324065 0.26296296 0.03220612 0.176313446 0.097854077 0.105081826
## 5 0.04081633 0.04134929 0.33487512 0.128898129 0.207171315 0.200000000
## 6 0.06494961 0.01720430 0.31135531 0.104830421 0.183251232 0.176063304
## 7 0.17913593 0.09736308 0.19860627 0.009718173 0.069094304 0.061855670
## 8 0.04745763 0.03470716 0.32841328 0.122279793 0.200595829 0.193419741
## 9 0.20932642 0.12774451 0.16838488 0.040191388 0.038638454 0.031394275
## 10 0.17336152 0.09155646 0.20436681 0.003898635 0.074906367 0.067669173
## 11 0.10733844 0.02526316 0.26978417 0.062437059 0.141062802 0.133850630
## 12 0.03533569 0.11738149 0.40839695 0.204520990 0.282183316 0.275077559
## 13 0.02061856 0.06153846 0.35447761 0.149003148 0.227135678 0.219979818
## 14 0.18457649 0.26570048 0.54949495 0.351320321 0.427163198 0.420242024
## 15 0.30421982 0.22348485 0.07224959 0.136487716 0.057843996 0.065083553
## 16 0.12024540 0.20187793 0.48915187 0.288268156 0.364994664 0.357984995
## 17 0.33043478 0.25000000 0.04538088 0.163228700 0.084701815 0.091934085
## 18 0.12377850 0.04175365 0.25357143 0.045954046 0.124640460 0.117420597
## 19 0.00000000 0.08213097 0.37441204 0.169491525 0.247464503 0.240325866
## 20 0.08213097 0.00000000 0.29454545 0.087665647 0.166177908 0.158979392
## 21 0.37441204 0.29454545 0.00000000 0.208223972 0.129957806 0.137171888
## 22 0.16949153 0.08766565 0.20822397 0.000000000 0.078799250 0.071563089
## 23 0.24746450 0.16617791 0.12995781 0.078799250 0.000000000 0.007246377
## 24 0.24032587 0.15897939 0.13717189 0.071563089 0.007246377 0.000000000
## 25 0.21671827 0.13518887 0.16095890 0.047664442 0.031164070 0.023919043
## 26 0.20187305 0.12024048 0.17586207 0.032660903 0.046168052 0.038924930
## 27 0.12987013 0.04786681 0.24755120 0.039840637 0.118546845 0.111324376
## 28 0.34957020 0.26937269 0.02568218 0.182786158 0.104362703 0.111587983
## 29 0.29249012 0.21163012 0.08422791 0.124542125 0.045855379 0.053097345
## 30 0.19624217 0.11457286 0.18150389 0.026974952 0.051851852 0.044609665
## 25 26 27 28 29 30
## 1 0.251572327 0.236786469 0.165016502 0.383720930 0.32698094 0.231177094
## 2 0.038356164 0.053357866 0.125714286 0.097186701 0.03866432 0.059040590
## 3 0.036018957 0.021012416 0.051485149 0.171226831 0.11293260 0.015325670
## 4 0.128919861 0.143859649 0.215775159 0.006525285 0.05205709 0.149516271
## 5 0.176291793 0.161389173 0.089171975 0.309859155 0.25242718 0.155737705
## 6 0.152304609 0.137373737 0.065057712 0.286245353 0.22862632 0.131712259
## 7 0.037950664 0.022944551 0.049554014 0.173144876 0.11485871 0.017257910
## 8 0.169696970 0.154786151 0.082539683 0.303370787 0.24588577 0.149131767
## 9 0.007476636 0.007532957 0.080000000 0.142857143 0.08445642 0.013220019
## 10 0.043767840 0.028763183 0.043737575 0.178919398 0.12065814 0.023076923
## 11 0.110019646 0.095049505 0.022610483 0.244525547 0.18661640 0.089374379
## 12 0.251572327 0.236786469 0.165016502 0.383720930 0.32698094 0.231177094
## 13 0.196319018 0.181443299 0.109324759 0.329545455 0.27228208 0.175801448
## 14 0.397321429 0.382882883 0.312573443 0.525667351 0.47071353 0.377401130
## 15 0.088967972 0.103942652 0.176088971 0.046589018 0.01199657 0.109613657
## 16 0.334782609 0.320175439 0.249142857 0.464929860 0.40913811 0.314631463
## 17 0.115789474 0.130742049 0.202739726 0.019704433 0.03888419 0.136403897
## 18 0.093567251 0.078585462 0.006116208 0.228260870 0.17025257 0.072906404
## 19 0.216718266 0.201873049 0.129870130 0.349570201 0.29249012 0.196242171
## 20 0.135188867 0.120240481 0.047866805 0.269372694 0.21163012 0.114572864
## 21 0.160958904 0.175862069 0.247551202 0.025682183 0.08422791 0.181503889
## 22 0.047664442 0.032660903 0.039840637 0.182786158 0.12454212 0.026974952
## 23 0.031164070 0.046168052 0.118546845 0.104362703 0.04585538 0.051851852
## 24 0.023919043 0.038924930 0.111324376 0.111587983 0.05309735 0.044609665
## 25 0.000000000 0.015009381 0.087463557 0.135416667 0.07699194 0.020696143
## 26 0.015009381 0.000000000 0.072477963 0.150349650 0.09197475 0.005687204
## 27 0.087463557 0.072477963 0.000000000 0.222222222 0.16417910 0.066797642
## 28 0.135416667 0.150349650 0.222222222 0.000000000 0.05857741 0.156003506
## 29 0.076991943 0.091974752 0.164179104 0.058577406 0.00000000 0.097649186
## 30 0.020696143 0.005687204 0.066797642 0.156003506 0.09764919 0.000000000Ex. 2
Now use a higher-dimensional data set mtcars, try the same three distance metrics in the previous question and discuss the results.
Solution
Now we will have mtcars dataset.
head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1We will take transpose of mtcars dataset and apply the same 3 distance methods.
head(t(mtcars))## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive Hornet Sportabout
## mpg 21.00 21.000 22.80 21.400 18.70
## cyl 6.00 6.000 4.00 6.000 8.00
## disp 160.00 160.000 108.00 258.000 360.00
## hp 110.00 110.000 93.00 110.000 175.00
## drat 3.90 3.900 3.85 3.080 3.15
## wt 2.62 2.875 2.32 3.215 3.44
## Valiant Duster 360 Merc 240D Merc 230 Merc 280 Merc 280C Merc 450SE
## mpg 18.10 14.30 24.40 22.80 19.20 17.80 16.40
## cyl 6.00 8.00 4.00 4.00 6.00 6.00 8.00
## disp 225.00 360.00 146.70 140.80 167.60 167.60 275.80
## hp 105.00 245.00 62.00 95.00 123.00 123.00 180.00
## drat 2.76 3.21 3.69 3.92 3.92 3.92 3.07
## wt 3.46 3.57 3.19 3.15 3.44 3.44 4.07
## Merc 450SL Merc 450SLC Cadillac Fleetwood Lincoln Continental
## mpg 17.30 15.20 10.40 10.400
## cyl 8.00 8.00 8.00 8.000
## disp 275.80 275.80 472.00 460.000
## hp 180.00 180.00 205.00 215.000
## drat 3.07 3.07 2.93 3.000
## wt 3.73 3.78 5.25 5.424
## Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla Toyota Corona
## mpg 14.700 32.40 30.400 33.900 21.500
## cyl 8.000 4.00 4.000 4.000 4.000
## disp 440.000 78.70 75.700 71.100 120.100
## hp 230.000 66.00 52.000 65.000 97.000
## drat 3.230 4.08 4.930 4.220 3.700
## wt 5.345 2.20 1.615 1.835 2.465
## Dodge Challenger AMC Javelin Camaro Z28 Pontiac Firebird Fiat X1-9
## mpg 15.50 15.200 13.30 19.200 27.300
## cyl 8.00 8.000 8.00 8.000 4.000
## disp 318.00 304.000 350.00 400.000 79.000
## hp 150.00 150.000 245.00 175.000 66.000
## drat 2.76 3.150 3.73 3.080 4.080
## wt 3.52 3.435 3.84 3.845 1.935
## Porsche 914-2 Lotus Europa Ford Pantera L Ferrari Dino Maserati Bora
## mpg 26.00 30.400 15.80 19.70 15.00
## cyl 4.00 4.000 8.00 6.00 8.00
## disp 120.30 95.100 351.00 145.00 301.00
## hp 91.00 113.000 264.00 175.00 335.00
## drat 4.43 3.770 4.22 3.62 3.54
## wt 2.14 1.513 3.17 2.77 3.57
## Volvo 142E
## mpg 21.40
## cyl 4.00
## disp 121.00
## hp 109.00
## drat 4.11
## wt 2.78mtcars_man <- dist(t(mtcars), method = "manhattan")
as.matrix(mtcars_man)## mpg cyl disp hp drat wt qsec vs
## mpg 0.000 444.900 6740.200 4051.100 527.810 539.948 136.260 628.900
## cyl 444.900 0.000 7185.100 4496.000 86.610 95.048 373.160 184.000
## disp 6740.200 7185.100 0.000 2852.900 7268.010 7280.148 6811.940 7369.100
## hp 4051.100 4496.000 2852.900 0.000 4578.910 4591.048 4122.840 4680.000
## drat 527.810 86.610 7268.010 4578.910 0.000 37.466 456.070 101.090
## wt 539.948 95.048 7280.148 4591.048 37.466 0.000 468.208 88.952
## qsec 136.260 373.160 6811.940 4122.840 456.070 468.208 0.000 557.160
## vs 628.900 184.000 7369.100 4680.000 101.090 88.952 557.160 0.000
## am 629.900 185.000 7370.100 4681.000 102.090 89.952 558.160 13.000
## gear 524.900 84.000 7265.100 4576.000 10.830 42.896 453.160 104.000
## carb 552.900 108.000 7293.100 4604.000 47.290 40.106 481.160 76.000
## am gear carb
## mpg 629.900 524.900 552.900
## cyl 185.000 84.000 108.000
## disp 7370.100 7265.100 7293.100
## hp 4681.000 4576.000 4604.000
## drat 102.090 10.830 47.290
## wt 89.952 42.896 40.106
## qsec 558.160 453.160 481.160
## vs 13.000 104.000 76.000
## am 0.000 105.000 77.000
## gear 105.000 0.000 46.000
## carb 77.000 46.000 0.000mtcars_euc <- dist(t(mtcars), method = "euclidian")
as.matrix(mtcars_euc)## mpg cyl disp hp drat wt
## mpg 0.00000 89.32586 1391.4955 824.3755 98.511658 102.877138
## cyl 89.32586 0.00000 1441.2518 878.1765 19.078540 18.058047
## disp 1391.49546 1441.25177 0.0000 656.6404 1459.404217 1458.014195
## hp 824.37547 878.17652 656.6404 0.0000 895.520090 895.374454
## drat 98.51166 19.07854 1459.4042 895.5201 0.000000 8.139647
## wt 102.87714 18.05805 1458.0142 895.3745 8.139647 0.000000
## qsec 33.26109 68.31076 1390.0784 826.0673 81.255418 83.655198
## vs 115.62314 34.78505 1475.1043 911.9945 18.130932 17.371962
## am 115.84951 34.71311 1475.0962 911.5882 18.179403 17.641289
## gear 98.08420 18.86796 1459.0335 894.7100 2.981728 8.929562
## carb 105.32099 21.21320 1460.6606 896.1362 10.689747 8.596341
## qsec vs am gear carb
## mpg 33.26109 115.623138 115.849514 98.084199 105.320986
## cyl 68.31076 34.785054 34.713110 18.867962 21.213203
## disp 1390.07839 1475.104291 1475.096156 1459.033540 1460.660559
## hp 826.06729 911.994518 911.588175 894.710009 896.136150
## drat 81.25542 18.130932 18.179403 2.981728 10.689747
## wt 83.65520 17.371962 17.641289 8.929562 8.596341
## qsec 0.00000 98.823784 99.272958 80.935531 86.787904
## vs 98.82378 0.000000 3.605551 18.920888 17.262677
## am 99.27296 3.605551 0.000000 18.734994 16.462078
## gear 80.93553 18.920888 18.734994 0.000000 10.099505
## carb 86.78790 17.262677 16.462078 10.099505 0.000000mtcars_can <- dist(t(mtcars), method = "canberra")
as.matrix(mtcars_can)## mpg cyl disp hp drat wt qsec
## mpg 0.000000 15.985928 24.728626 22.460192 21.870636 22.286293 3.379737
## cyl 15.985928 0.000000 30.047021 29.175986 8.103136 10.061722 15.597100
## disp 24.728626 30.047021 0.000000 6.700758 30.578813 30.968494 25.892404
## hp 22.460192 29.175986 6.700758 0.000000 30.051098 30.475757 23.669036
## drat 21.870636 8.103136 30.578813 30.051098 0.000000 5.591582 21.233229
## wt 22.286293 10.061722 30.968494 30.475757 5.591582 0.000000 22.241270
## qsec 3.379737 15.597100 25.892404 23.669036 21.233229 22.241270 0.000000
## vs 30.860381 26.857143 31.756080 31.673126 26.175546 23.935629 30.617539
## am 30.914876 27.498413 31.773202 31.732619 26.827919 24.142597 30.570900
## gear 21.684967 7.838739 30.553348 30.036581 1.384173 6.216516 21.006830
## carb 23.437221 12.992208 31.105555 30.761211 8.151473 7.171846 23.351412
## vs am gear carb
## mpg 30.86038 30.91488 21.684967 23.437221
## cyl 26.85714 27.49841 7.838739 12.992208
## disp 31.75608 31.77320 30.553348 31.105555
## hp 31.67313 31.73262 30.036581 30.761211
## drat 26.17555 26.82792 1.384173 8.151473
## wt 23.93563 24.14260 6.216516 7.171846
## qsec 30.61754 30.57090 21.006830 23.351412
## vs 0.00000 20.80000 26.166667 20.866667
## am 20.80000 0.00000 27.133333 23.625397
## gear 26.16667 27.13333 0.000000 8.037551
## carb 20.86667 23.62540 8.037551 0.000000Ex. 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.
Solution
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000euc_clus <- hclust(dist(mtcars, method = "euclidian"))
plot(euc_clus)
ct1 <- cutree(euc_clus, k = 3)
table(ct1)## ct1
## 1 2 3
## 16 7 9man_clus <- hclust(dist(mtcars, method = "manhattan"))
plot(man_clus)
ct2 <- cutree(man_clus, k = 3)
table(ct2)## ct2
## 1 2 3
## 18 10 4We see above both the methods give higher elements to first cluster but second and third clusters are more evenly distributed in euclidian.
Ex. 4
Load the well-known Fisher’s iris flower data set that consists of 150 samples for 3 species (50 samples each species). The four measures or features are the lengths and widths of sepals and petals. Use the kNN clustering to analyze this iris data set by selecting 120 samples for training and 30 samples for testing.
Solution
# iris dataset
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 setosaset.seed(609)
# to split
split <- sample(nrow(iris), nrow(iris)*0.80)
# feature variables
train <- iris[split, -5] #120 rows
test <- iris[-split, -5] #30 rows
# target variable
train_trgt <- iris[split, 5] #120 rows
test_trgt <- iris[-split, 5] #30 rows
# knn
knn <- knn(train, test, cl=train_trgt, k=5)
# contingency table
knn_tbl <- table(knn, test_trgt)
# knn accuracy
acc_knn <- sum(diag(knn_tbl)) / sum(knn_tbl)
acc_knn## [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.
Solution
set.seed(609)
iris_kmeans <- kmeans(iris[,-5], centers = 3)
iris_kmeans## K-means clustering with 3 clusters of sizes 33, 21, 96
##
## Cluster means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1 5.175758 3.624242 1.472727 0.2727273
## 2 4.738095 2.904762 1.790476 0.3523810
## 3 6.314583 2.895833 4.973958 1.7031250
##
## Clustering vector:
## [1] 1 2 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1 2 1 1
## [38] 1 2 1 1 2 2 1 1 2 1 2 1 1 3 3 3 3 3 3 3 2 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3
## [75] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3
## [112] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [149] 3 3
##
## Within cluster sum of squares by cluster:
## [1] 6.432121 17.669524 118.651875
## (between_SS / total_SS = 79.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# contingency table
iris_clus <- iris_kmeans$cluster
table(iris_clus)## iris_clus
## 1 2 3
## 33 21 96clusplot(iris[,-5], iris_clus)
# kmeans accuracy
tbl_kmeans <- table(iris$Species, iris_clus)
acc_kmeans <- sum(diag(tbl_kmeans)) / sum(tbl_kmeans)
acc_kmeans## [1] 0.58