Kmeans
mileage = (mtcars$mpg - mean(mtcars$mpg)) / sd(mtcars$mpg)
cylinder = (mtcars$cyl - mean(mtcars$cyl)) / sd(mtcars$cyl)
displacement = (mtcars$disp - mean(mtcars$disp)) / sd(mtcars$disp)
mtcars_stddv = as.data.frame(cbind(mileage, cylinder, displacement))
set.seed(2)
mtcars_kmean = kmeans(mtcars_stddv,
centers = 3)
## Performing kmean cluster for frist, second and thrid column
mtcars_kmean
## K-means clustering with 3 clusters of sizes 12, 14, 6
##
## Cluster means:
## mileage cylinder displacement
## 1 0.1384407 -0.5716003 -0.5707543
## 2 -0.8280518 1.0148821 0.9874085
## 3 1.6552394 -1.2248578 -1.1624447
##
## Clustering vector:
## [1] 1 1 1 1 2 1 2 1 1 1 1 2 2 2 2 2 2 3 3 3 1 2 2 2 2 3 3 3 2 1 2 1
##
## Within cluster sum of squares by cluster:
## [1] 6.154099 6.232612 1.336385
## (between_SS / total_SS = 85.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"
mtcars_kmean$size # Size of clusters
## [1] 12 14 6
Centers of each cluster
mtcars_mod = mtcars[,1:3]
mtcars_cluster <- kmeans(mtcars_mod, centers=3)
mtcars_cluster$centers
## mpg cyl disp
## 1 16.7625 7.500 279.1750
## 2 24.5000 4.625 122.2937
## 3 14.6000 8.000 399.1250
First cluster is cars with low mileage, high power and cylinder capacity. Very energy efficent.
Second cluster is for the mid-powered cars with better mileage.
Third cluser is fo cars with great mileage and low power. Middle ground cars.
calculating the mean disp, weight and qsec for each cluster
mtcars_mod = mtcars
mtcars_mod$clusterid = mtcars_cluster$cluster
mtcars_mod
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
## clusterid
## Mazda RX4 2
## Mazda RX4 Wag 2
## Datsun 710 2
## Hornet 4 Drive 1
## Hornet Sportabout 3
## Valiant 1
## Duster 360 3
## Merc 240D 2
## Merc 230 2
## Merc 280 2
## Merc 280C 2
## Merc 450SE 1
## Merc 450SL 1
## Merc 450SLC 1
## Cadillac Fleetwood 3
## Lincoln Continental 3
## Chrysler Imperial 3
## Fiat 128 2
## Honda Civic 2
## Toyota Corolla 2
## Toyota Corona 2
## Dodge Challenger 1
## AMC Javelin 1
## Camaro Z28 3
## Pontiac Firebird 3
## Fiat X1-9 2
## Porsche 914-2 2
## Lotus Europa 2
## Ford Pantera L 3
## Ferrari Dino 2
## Maserati Bora 1
## Volvo 142E 2
aggregate(mtcars_mod[, 3:7], list(mtcars_mod$clusterid), mean)
## Group.1 disp hp drat wt qsec
## 1 1 279.1750 173.750 3.06250 3.5975 17.67875
## 2 2 122.2938 96.875 4.00250 2.5180 18.54312
## 3 3 399.1250 219.250 3.31875 4.2355 16.63000
The mean displacement, qsec and weight for each cluster matches the values for each class of cars differentitated in the cluster.
Part 2
Modified diamonds dataset with the first 5 columns
Running kmean with cluster size 3
diamondscluster$centers
## depth table price x y z
## 1 61.81558 57.87373 5781.019 6.617928 6.614152 4.087780
## 2 61.73626 57.19052 1458.081 4.992075 4.999063 3.084140
## 3 61.64657 57.88201 13345.484 7.634476 7.636127 4.699634
The more expenisve diamonds in cluster have greater dimentions.. As expected since the size is one of the attributes that determine the prize..
Analyzing diamond price based on cut
library(ggplot2)
data(diamonds)
diamonds$clusterid = diamondscluster$cluster
table(diamonds$cut,diamonds$clusterid)
##
## 1 2 3
## Fair 583 872 155
## Good 1736 2761 409
## Very Good 3728 7122 1232
## Premium 4593 7266 1932
## Ideal 4691 14934 1926
There is no much difference in price with respect to cut. Not a great attriubte for determining price
Calculating mean
aggregate(diamonds[, 5:10], list(diamonds$clusterid), mean)
## Group.1 depth table price x y z
## 1 1 61.81558 57.87373 5781.019 6.617928 6.614152 4.087780
## 2 2 61.73626 57.19052 1458.081 4.992075 4.999063 3.084140
## 3 3 61.64657 57.88201 13345.484 7.634476 7.636127 4.699634
The means of the clusture are inline with the expected trends for the attributes.