library(dplyr)
library(ggplot2)
library(plotly)
library(ggdendro)
library(class)
library(caTools)
library(caret)
library(factoextra)1) variety of distance formulas
The best part of r in the built in distance function dist(). We can compute multiple versions of the distance formula without creating separate functions. Below, we will compute the Euclidean, Manhattan, and Minkowski distance formulas with dist(). In order to compare the weights of the different groups, we must transform the groups’ weights into a one matrix and transpose the matrix,as the groups will be measure.
# Retrieve the weights and create a new matrix from the transpose vectors
data<-PlantGrowth%>%select("weight")
a<-data%>%slice(0:10)
b<-data%>%slice(11:20)
c<-data%>%slice(21:30)
plants<-data.frame(a,b,c)
plants<-as.matrix(t(plants))Euclidean
The euclidean distance formula is \[\sqrt{\sum(x_i-y_i)^2}\]. This formula is only calculating the distance between the two points of each of the groups. It appears control and trt2 has the shortest distance of ~3.07.
dist(plants,method = "euclidean",diag = TRUE)## weight weight.1 weight.2
## weight 0.000000
## weight.1 3.730697 0.000000
## weight.2 3.071547 3.974179 0.000000Manhattan
Following along in the textbook, the Manhattan distance formula is \[D_m(x,y)=\sum^D_{i=1}|x_i-y_i|\]. The Manhattan calculates the distance on the grid plane, where it moves in two points instead of one. This has increase the distance between control and trt2 groups to be 7.58.
dist(plants,method="manhattan",diag = TRUE)## weight weight.1 weight.2
## weight 0.00
## weight.1 10.17 0.00
## weight.2 7.58 11.87 0.00Minkowski
The Minowski formula is calculated by \[d(x,y)=||x-y||_p=(\sum^D_i|x_i-y_i|^p)^{1/p}\]. It will measured the distance of the vectors in the normal vector space. Like the previous iterations of this distance, the control and trt2 group have the shortest distance in this vector space.
dist(plants,method="minkowski",diag = TRUE)## weight weight.1 weight.2
## weight 0.000000
## weight.1 3.730697 0.000000
## weight.2 3.071547 3.974179 0.0000002) Mtcars Distances
There is not much of a difference expect the amount of vehicles in mtcars. We just have to transpose this matrix so these groups distances are determine by the car’s stats.
For Euclidean, it appears merc 230 has the shortest distance with the most models (Mazda RX4, Mazda RX4, Wag Datsun 710, Hornet 4 Drive,Valiant, and merc 240D). There seems to be a average in the 200s in this method.
#Euclidean
dist(mtcars,method = "euclidean",diag = TRUE)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.0000000
## Mazda RX4 Wag 0.6153251 0.0000000
## Datsun 710 54.9086059 54.8915169 0.0000000
## Hornet 4 Drive 98.1125212 98.0958939 150.9935191 0.0000000
## Hornet Sportabout 210.3374396 210.3358546 265.0831615 121.0297564
## Valiant 65.4717710 65.4392224 117.7547018 33.5508692
## Duster 360 241.4076490 241.4088680 294.4790230 169.4299647
## Merc 240D 50.1532711 50.1146059 49.6584796 121.2739722
## Merc 230 25.4683117 25.3284509 33.1803843 118.2433145
## Merc 280 15.3641921 15.2956865 66.9363534 91.4224033
## Merc 280C 15.6724727 15.5837744 67.0261397 91.4612914
## Merc 450SE 135.4307018 135.4254826 189.1954941 72.4964325
## Merc 450SL 135.4014424 135.3960351 189.1631745 72.4313532
## Merc 450SLC 135.4794674 135.4723157 189.2345426 72.5718466
## Cadillac Fleetwood 326.3395903 326.3355070 381.0926242 234.4403876
## Lincoln Continental 318.0469808 318.0429333 372.8012090 227.9726091
## Chrysler Imperial 304.7203408 304.7169175 359.3014906 218.1548299
## Fiat 128 93.2679950 93.2530993 40.9933763 184.9689734
## Honda Civic 102.8307567 102.8238713 52.7704607 191.5518700
## Toyota Corolla 100.6040368 100.5887588 47.6535017 192.6714187
## Toyota Corona 42.3075233 42.2659224 12.9654743 138.5304725
## Dodge Challenger 163.1150750 163.1134210 217.7795805 72.4403915
## AMC Javelin 149.6047203 149.6014522 204.3188913 61.3601899
## Camaro Z28 233.2228758 233.2248748 286.0049209 163.6632641
## Pontiac Firebird 248.6780270 248.6762035 303.3583889 156.2240346
## Fiat X1-9 92.5048389 92.4940020 39.8815148 184.4471198
## Porsche 914-2 44.4033659 44.4073589 13.1357109 139.1579524
## Lotus Europa 65.7328377 65.7362635 25.0948550 163.2367437
## Ford Pantera L 245.4247064 245.4293785 297.2940489 180.1140339
## Ferrari Dino 66.7661029 66.7764167 90.2415509 130.5523007
## Maserati Bora 265.6454248 265.6491465 309.7718171 229.3419352
## Volvo 142E 39.1894029 39.1626037 20.6939436 137.0363299
## Hornet Sportabout Valiant Duster 360 Merc 240D
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout 0.0000000
## Valiant 152.1241352 0.0000000
## Duster 360 70.1767262 194.6094525 0.0000000
## Merc 240D 241.5069657 89.5911056 281.2962502 0.0000000
## Merc 230 233.4924012 85.0079649 265.8823313 33.6873047
## Merc 280 199.3344960 60.2909811 227.8998521 64.7754228
## Merc 280C 199.3406564 60.2655656 227.8813169 64.8898713
## Merc 450SE 84.3888482 90.6970264 106.4084264 175.1620073
## Merc 450SL 84.3683999 90.6769728 106.4320572 175.1189767
## Merc 450SLC 84.4332423 90.7092989 106.4010305 175.2118218
## Cadillac Fleetwood 116.2804201 266.6280942 119.0239068 355.6627498
## Lincoln Continental 108.0624299 259.6304391 104.5112999 348.9901277
## Chrysler Imperial 97.2049146 248.7713290 81.4297699 338.1959373
## Fiat 128 302.0377212 152.1153263 333.9792070 68.6105903
## Honda Civic 310.0324645 158.9615769 344.0518316 72.0014488
## Toyota Corolla 309.5581776 159.8302995 341.0218232 76.2806458
## Toyota Corona 252.3331988 105.2876428 282.0508820 44.0850975
## Dodge Challenger 48.9838851 103.4310693 103.9023864 192.8617917
## AMC Javelin 61.4274240 91.0444349 110.3084921 180.5479760
## Camaro Z28 70.9665308 187.8463771 10.0761203 273.8367985
## Pontiac Firebird 40.0052475 188.5272116 80.8057339 277.4606884
## Fiat X1-9 301.5669483 151.4379425 333.4843231 67.9163981
## Porsche 914-2 254.1452553 106.0585767 285.1986201 39.4469276
## Lotus Europa 272.3582423 130.8248192 296.4572287 72.8971106
## Ford Pantera L 89.5934049 203.0177926 21.2655990 287.5238795
## Ferrari Dino 215.0673853 106.5694802 226.2036333 113.3023005
## Maserati Bora 170.7094473 242.4393015 107.7224977 313.8633093
## Volvo 142E 248.0063378 104.1863681 275.1353516 53.6823481
## Merc 230 Merc 280 Merc 280C Merc 450SE Merc 450SL
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230 0.0000000
## Merc 280 39.2994160 0.0000000
## Merc 280C 39.3868519 1.5231546 0.0000000
## Merc 450SE 159.8179555 122.3642489 122.3461050 0.0000000
## Merc 450SL 159.7760899 122.3443771 122.3355492 0.9826495 0.0000000
## Merc 450SLC 159.8495837 122.3934970 122.3586862 1.3726252 2.1383405
## Cadillac Fleetwood 349.2832611 315.3904859 315.3557081 197.8842803 197.9154476
## Lincoln Continental 341.3154316 306.6760719 306.6406187 187.5997191 187.6330806
## Chrysler Imperial 328.4335161 292.7146896 292.6989332 171.6600758 171.6743028
## Fiat 128 69.3127910 106.5053149 106.6829794 228.3247948 228.2592340
## Honda Civic 78.5387212 116.7280991 116.8711475 238.0141824 237.9588183
## Toyota Corolla 76.7731674 113.6290721 113.8118009 235.5183809 235.4481971
## Toyota Corona 21.0962017 54.3641713 54.4258314 176.6020527 176.5727477
## Dodge Challenger 185.8331870 152.8929263 152.8722437 51.8008639 51.8242520
## AMC Javelin 172.5312555 139.1457974 139.1181977 41.2080044 41.2411618
## Camaro Z28 257.7469734 219.5520854 219.5276434 98.7203049 98.7566899
## Pontiac Firebird 271.3871978 238.1726099 238.1806292 124.3368538 124.3204160
## Fiat X1-9 68.5564864 105.7412910 105.8560373 227.7627676 227.7173075
## Porsche 914-2 22.1180967 57.6458160 57.8473863 179.5034108 179.4550855
## Lotus Europa 50.1094030 74.1443580 74.3824296 193.3074449 193.2407697
## Ford Pantera L 269.9772035 231.4081306 231.4024263 112.8181834 112.8296774
## Ferrari Dino 80.6550953 56.8365103 56.8987601 131.0272205 131.0077635
## Maserati Bora 288.8755628 250.5874125 250.5774357 157.1633256 157.1768956
## Volvo 142E 24.6913548 48.8053450 48.8884618 170.4500681 170.4225164
## Merc 450SLC Cadillac Fleetwood Lincoln Continental
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC 0.0000000
## Cadillac Fleetwood 197.8526242 0.0000000
## Lincoln Continental 187.5671081 15.6224446 0.0000000
## Chrysler Imperial 171.6557637 40.8399636 25.3714237
## Fiat 128 228.4051825 417.7687579 410.0206984
## Honda Civic 238.0828999 425.3271621 417.9679574
## Toyota Corolla 235.6024098 425.3446517 417.5429986
## Toyota Corona 176.6305359 368.3195488 360.0267515
## Dodge Challenger 51.8012606 163.6314881 156.2805020
## AMC Javelin 41.1929050 176.8610896 169.0925457
## Camaro Z28 98.7035830 128.4587210 114.0932078
## Pontiac Firebird 124.3726128 78.5385347 72.6947903
## Fiat X1-9 227.8176554 417.2490481 409.4998363
## Porsche 914-2 179.5720446 370.0956775 362.0145494
## Lotus Europa 193.3969216 388.5350012 379.4716659
## Ford Pantera L 112.8332602 134.8119464 119.7236456
## Ferrari Dino 131.0704490 328.5441628 317.7063117
## Maserati Bora 157.1683970 214.9366858 199.3420611
## Volvo 142E 170.4843735 364.1000930 355.4009443
## Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial 0.0000000
## Fiat 128 397.2276375 0.0000000
## Honda Civic 405.8152201 14.5590942 0.0000000
## Toyota Corolla 404.6335386 7.8324789 14.3480626 0.0000000
## Toyota Corona 346.5724649 52.8798281 63.8985563 59.8451285
## Dodge Challenger 145.9194779 254.2367888 261.8498815 261.8345312
## AMC Javelin 157.8097554 241.1203621 248.9636504 248.6917065
## Camaro Z28 91.2880886 325.6636235 335.8883188 332.6589699
## Pontiac Firebird 68.2030747 339.5857659 347.0655360 347.1667643
## Fiat X1-9 396.7597522 5.1473415 14.7807070 10.3922856
## Porsche 914-2 348.8466861 49.0644372 59.4588768 56.3243031
## Lotus Europa 364.5994326 49.9112509 64.0495153 53.8846563
## Ford Pantera L 95.3805385 337.1639236 347.8337714 343.9920962
## Ferrari Dino 300.1640703 128.3950054 141.7044478 133.4707617
## Maserati Bora 174.2936864 349.5338830 362.1620777 355.2601619
## Volvo 142E 341.2896659 61.3301247 73.3766041 67.7189421
## Toyota Corona Dodge Challenger AMC Javelin Camaro Z28
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona 0.0000000
## Dodge Challenger 205.0347927 0.0000000
## AMC Javelin 191.5580526 14.0154995 0.0000000
## Camaro Z28 273.6316895 100.3046106 105.6062618 0.0000000
## Pontiac Firebird 290.6240706 85.8075196 99.2836114 86.2665759
## Fiat X1-9 51.8411748 253.6624046 240.5266823 325.1490914
## Porsche 914-2 8.6535903 206.6452569 193.3080584 276.8924414
## Lotus Europa 31.2536926 226.5004836 212.7568765 287.6179004
## Ford Pantera L 285.1287911 118.7516779 123.3832044 19.3589023
## Ferrari Dino 82.2355734 174.9280395 161.1060307 216.7489910
## Maserati Bora 299.1865216 185.9059273 185.1553411 102.5946154
## Volvo 142E 12.2505275 201.3682522 187.6978440 266.5277736
## Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird 0.0000000
## Fiat X1-9 339.1396182 0.0000000
## Porsche 914-2 292.1646488 48.3775209 0.0000000
## Lotus Europa 311.3862342 49.8406880 33.7678653 0.0000000
## Ford Pantera L 101.7389686 336.7018783 288.5852993 297.5376920
## Ferrari Dino 255.0570519 127.8210813 87.9105966 80.4553451
## Maserati Bora 188.3240020 349.1199576 303.9222549 303.2796468
## Volvo 142E 286.7497823 60.4120429 18.7555858 27.8104457
## Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
## Mazda RX4
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird
## Fiat X1-9
## Porsche 914-2
## Lotus Europa
## Ford Pantera L 0.0000000
## Ferrari Dino 224.4587490 0.0000000
## Maserati Bora 86.9383253 223.5342175 0.0000000
## Volvo 142E 277.4803312 70.4751034 289.1157363 0.0000000Our golden model; merc 300, has its distance reduced further along its models above. However, the overall distance average increases. This means the models secondary point is further away in distance, which makes the secondary points useless than a short cut.
#Manhattan
dist(mtcars,method="manhattan",diag = TRUE)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.000
## Mazda RX4 Wag 0.815 0.000
## Datsun 710 79.300 78.995 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout 0.000
## Valiant 213.210 0.000
## Duster 360 77.770 289.740 0.000
## Merc 240D 341.770 133.020 419.420 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280 0.000
## Merc 280C 2.000 0.000
## Merc 450SE 175.380 174.580 0.000
## Merc 450SL 173.940 173.140 1.440 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood 0.000
## Lincoln Continental 22.404 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128 0.000
## Honda Civic 22.385 0.000
## Toyota Corolla 11.035 24.410 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger 0.000
## AMC Javelin 15.205 0.000
## Camaro Z28 133.950 147.775 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird
## Fiat X1-9 0.000
## Porsche 914-2 73.355 0.000
## Lotus Europa 70.932 54.087 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird
## Fiat X1-9
## Porsche 914-2
## Lotus Europa
## Ford Pantera L
## Ferrari Dino 0.000
## Maserati Bora 326.480 0.000
## Volvo 142E 103.300 429.760 0.000Minkowski also sees better distances compared to euclidean for the merc 300. Overall, it seems a the averages looks similar to eucildean compared the manttahan. However, I will need more visualizations to confirm.
#Minkowski
dist(mtcars,method="manhattan",diag = TRUE)## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## Mazda RX4 0.000
## Mazda RX4 Wag 0.815 0.000
## Datsun 710 79.300 78.995 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout 0.000
## Valiant 213.210 0.000
## Duster 360 77.770 289.740 0.000
## Merc 240D 341.770 133.020 419.420 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280 0.000
## Merc 280C 2.000 0.000
## Merc 450SE 175.380 174.580 0.000
## Merc 450SL 173.940 173.140 1.440 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood 0.000
## Lincoln Continental 22.404 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128 0.000
## Honda Civic 22.385 0.000
## Toyota Corolla 11.035 24.410 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger 0.000
## AMC Javelin 15.205 0.000
## Camaro Z28 133.950 147.775 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird
## Fiat X1-9 0.000
## Porsche 914-2 73.355 0.000
## Lotus Europa 70.932 54.087 0.000
## 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
## Mazda RX4 Wag
## Datsun 710
## Hornet 4 Drive
## Hornet Sportabout
## Valiant
## Duster 360
## Merc 240D
## Merc 230
## Merc 280
## Merc 280C
## Merc 450SE
## Merc 450SL
## Merc 450SLC
## Cadillac Fleetwood
## Lincoln Continental
## Chrysler Imperial
## Fiat 128
## Honda Civic
## Toyota Corolla
## Toyota Corona
## Dodge Challenger
## AMC Javelin
## Camaro Z28
## Pontiac Firebird
## Fiat X1-9
## Porsche 914-2
## Lotus Europa
## Ford Pantera L
## Ferrari Dino 0.000
## Maserati Bora 326.480 0.000
## Volvo 142E 103.300 429.760 0.0003) Hierarchy Clustering
Visually, these two types of hierarchical cluster graph looks identical. We can confirm if these are truly identical with the clustering within the models using rect.hclust(). It cannot be used with ggplot; it only be used with base plot. Looking at the rectangular clustering, we can confirm the minkowski and euclidean
#Euclidean
hc1<-hclust(dist(mtcars,method = "euclidean"),"complete")
g<-ggdendrogram(hc1,size=3,theme_dendro = TRUE)+labs(title="Distance with the Euclidean Method")
g
#Minkowski
hc2<-hclust(dist(mtcars,method = "minkowski"),"complete")
g<-ggdendrogram(hc2,size=3,theme_dendro = TRUE)+labs(title="Distance with the Minkowski Method")
g
#base version
plot(hc1)
rect.hclust(hc1,k=3,border=2:5)
plot(hc2)
rect.hclust(hc2,k=3,border=2:5)
4) KNN Clustering with iris
We can split up the data set to 120 training items and 40 testing items with sample.split(). The model will the two random data sets, we want the system to make educated quess on the plant specices. We can test the prediction accuracy with the confusion matrix.
set.seed(3)
#Scale dataset
data<-iris
data[,1:4]<-scale(data[,1:4])
#We need 120 items in the train set, 80/20 ratio will work for the items below
split<-sample.split(data,SplitRatio = 0.8)
train_set<-subset(data,split=="TRUE")
test_set<-subset(data,split=="FALSE")
#Fit to the KNN Model
knn_model<-knn(train=train_set[1:4],test=test_set[1:4],cl=train_set$Species,k=1)
#We can use caret's confusion matrix to test the model's accuracy
cfm<-confusionMatrix(test_set$Species,knn_model)
cfm## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 10 0 0
## versicolor 0 10 0
## virginica 0 1 9
##
## Overall Statistics
##
## Accuracy : 0.9667
## 95% CI : (0.8278, 0.9992)
## No Information Rate : 0.3667
## P-Value [Acc > NIR] : 4.476e-12
##
## Kappa : 0.95
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 0.9091 1.0000
## Specificity 1.0000 1.0000 0.9524
## Pos Pred Value 1.0000 1.0000 0.9000
## Neg Pred Value 1.0000 0.9500 1.0000
## Prevalence 0.3333 0.3667 0.3000
## Detection Rate 0.3333 0.3333 0.3000
## Detection Prevalence 0.3333 0.3333 0.3333
## Balanced Accuracy 1.0000 0.9545 0.97625) Kmeans with Iris data
we can use kmeans() to find the clustering in this data set. I’m not so fmailar with k-means so I used a doc to help create the cluster plot.
For the estimated cluster accuracy, it depends on the cluster group size.I saw a lot of overlap in the cluster groups after specifying four centers. Less than three centers, there were a lot of points not in any of the cluster centers. I think 3-4 centers will be the closet fit without overlapping centers.
set.seed(3)
#Compute the kmeans of iris
km<-kmeans(data[,1:4],centers=4)
km## K-means clustering with 4 clusters of sizes 28, 47, 22, 53
##
## Cluster means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1 -0.74671975 1.42529513 -1.2932659 -1.2173431
## 2 1.13217737 0.08812645 0.9928284 1.0141287
## 3 -1.34779164 0.11874645 -1.3100027 -1.2931622
## 4 -0.05005221 -0.88042696 0.3465767 0.2805873
##
## Clustering vector:
## [1] 1 3 3 3 1 1 3 1 3 3 1 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 3 3 1 1 1 3 3 1
## [38] 1 3 1 1 3 3 1 1 3 1 3 1 3 2 2 2 4 4 4 2 4 4 4 4 4 4 4 4 2 4 4 4 4 2 4 4 4
## [75] 4 2 2 2 4 4 4 4 4 4 4 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 2 2 2 2 4 2 2 2 2
## [112] 2 2 4 4 2 2 2 2 4 2 4 2 4 2 2 4 2 2 2 2 2 2 4 4 2 2 2 4 2 2 2 4 2 2 2 4 2
## [149] 2 4
##
## Within cluster sum of squares by cluster:
## [1] 13.761588 47.450194 8.032603 44.087545
## (between_SS / total_SS = 81.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#visualize the cluster groups
fviz_cluster(km,data = data[,1:4],geom = c("point"),ellipse.type = "euclid")