activity 7
justine bryle macaso
2022-05-22
#Loading the Data
Data <- read.csv("C:/Users/Swift/Downloads/Data.txt",header = T)
str(Data)## 'data.frame': 22 obs. of 9 variables:
## $ Company : chr "Arizona " "Boston " "Central " "Commonwealth" ...
## $ Fixed_charge: num 1.06 0.89 1.43 1.02 1.49 1.32 1.22 1.1 1.34 1.12 ...
## $ RoR : num 9.2 10.3 15.4 11.2 8.8 13.5 12.2 9.2 13 12.4 ...
## $ Cost : int 151 202 113 168 192 111 175 245 168 197 ...
## $ Load : num 54.4 57.9 53 56 51.2 60 67.6 57 60.4 53 ...
## $ D.Demand : num 1.6 2.2 3.4 0.3 1 -2.2 2.2 3.3 7.2 2.7 ...
## $ Sales : int 9077 5088 9212 6423 3300 11127 7642 13082 8406 6455 ...
## $ Nuclear : num 0 25.3 0 34.3 15.6 22.5 0 0 0 39.2 ...
## $ Fuel_Cost : num 0.628 1.555 1.058 0.7 2.044 ...head(Data)## Company Fixed_charge RoR Cost Load D.Demand Sales Nuclear Fuel_Cost
## 1 Arizona 1.06 9.2 151 54.4 1.6 9077 0.0 0.628
## 2 Boston 0.89 10.3 202 57.9 2.2 5088 25.3 1.555
## 3 Central 1.43 15.4 113 53.0 3.4 9212 0.0 1.058
## 4 Commonwealth 1.02 11.2 168 56.0 0.3 6423 34.3 0.700
## 5 Con Ed NY 1.49 8.8 192 51.2 1.0 3300 15.6 2.044
## 6 Florida 1.32 13.5 111 60.0 -2.2 11127 22.5 1.241pairs(Data[2:9])
#Scatterplot
plot(Data$Fuel_Cost~ Data$Sales, data = Data)
with(Data,text(Data$Fuel_Cost ~ Data$Sales, labels=Data$Company,pos=4))
#Normalize
z <- Data[,-c(1,1)]
means <- apply(z,2,mean)
sds <- apply(z,2,sd)
nor <- scale(z,center=means,scale=sds)
means## Fixed_charge RoR Cost Load D.Demand Sales
## 1.114091 10.736364 168.181818 56.977273 3.240909 8914.045455
## Nuclear Fuel_Cost
## 12.000000 1.102727sds## Fixed_charge RoR Cost Load D.Demand Sales
## 0.1845112 2.2440494 41.1913495 4.4611478 3.1182503 3549.9840305
## Nuclear Fuel_Cost
## 16.7919198 0.5560981nor## Fixed_charge RoR Cost Load D.Demand Sales
## [1,] -0.29315791 -0.68463896 -0.417122002 -0.57771516 -0.52622751 0.04590290
## [2,] -1.21451134 -0.19445367 0.821002037 0.20683629 -0.33381191 -1.07776413
## [3,] 1.71214073 2.07822360 -1.339645796 -0.89153574 0.05101929 0.08393124
## [4,] -0.50994695 0.20660702 -0.004413989 -0.21906307 -0.94312798 -0.70170610
## [5,] 2.03732429 -0.86288816 0.578232617 -1.29501935 -0.71864311 -1.58142837
## [6,] 1.11597086 1.23153991 -1.388199680 0.67756716 -1.74485965 0.62337028
## [7,] 0.57399826 0.65223002 0.165524604 2.38116460 -0.33381191 -0.35832428
## [8,] -0.07636887 -0.68463896 1.864910540 0.00509449 0.01895002 1.17407698
## [9,] 1.22436538 1.00872841 -0.004413989 0.76723019 1.26965142 -0.14311204
## [10,] 0.03202565 0.74135462 0.699617327 -0.89153574 -0.17346558 -0.69269198
## [11,] -1.97327298 -1.44219805 0.116970720 -1.22777208 1.04516655 2.40196983
## [12,] 0.08622291 0.07292013 0.238355430 1.12588228 0.14722709 -0.77748109
## [13,] 0.19461744 0.87504152 0.748171211 -0.73462545 1.01309729 -0.48874740
## [14,] -0.13056613 0.56310542 -1.752353809 -1.60883993 -0.59036605 0.21379097
## [15,] -0.83513051 -1.39763576 -0.101521757 1.17071379 -1.07140505 -0.68902999
## [16,] 0.24881470 -0.37270287 2.034849134 -0.21906307 1.91103676 1.99351729
## [17,] -1.91907572 -1.93238335 -0.781276132 1.10346652 1.84689822 -0.90142531
## [18,] -0.34735517 0.83047922 -0.441398944 -0.06215278 -0.17346558 0.34534086
## [19,] 0.24881470 0.42941852 -1.558138274 -0.66737818 -1.71279038 1.29379583
## [20,] 0.46560374 0.47398082 -0.489952828 0.65515141 0.08308855 -0.45832473
## [21,] -0.40155243 -0.95201276 0.869555920 0.90172472 0.08308855 -0.63776215
## [22,] -0.23896065 -0.64007666 0.141247662 -0.60013092 0.85275095 0.33210137
## Nuclear Fuel_Cost
## [1,] -0.7146294 -0.85367545
## [2,] 0.7920476 0.81329670
## [3,] -0.7146294 -0.08043055
## [4,] 1.3280197 -0.72420189
## [5,] 0.2143888 1.69263800
## [6,] 0.6253007 0.24864810
## [7,] -0.7146294 0.98772637
## [8,] -0.7146294 -1.42731528
## [9,] -0.7146294 -0.43288637
## [10,] 1.6198267 -0.86266667
## [11,] -0.7146294 -0.60192130
## [12,] -0.7146294 1.42829614
## [13,] 2.2749037 -1.03529809
## [14,] -0.7146294 -0.92560521
## [15,] -0.6610322 0.53456889
## [16,] -0.7146294 -0.86806140
## [17,] -0.2203441 1.46965575
## [18,] -0.7146294 0.00948165
## [19,] -0.7146294 -0.83928950
## [20,] 1.7329764 -0.72060540
## [21,] -0.7146294 1.82211157
## [22,] 0.8694658 0.36553395
## attr(,"scaled:center")
## Fixed_charge RoR Cost Load D.Demand Sales
## 1.114091 10.736364 168.181818 56.977273 3.240909 8914.045455
## Nuclear Fuel_Cost
## 12.000000 1.102727
## attr(,"scaled:scale")
## Fixed_charge RoR Cost Load D.Demand Sales
## 0.1845112 2.2440494 41.1913495 4.4611478 3.1182503 3549.9840305
## Nuclear Fuel_Cost
## 16.7919198 0.5560981#Calculate distance matrix
distance = dist(nor)
distance## 1 2 3 4 5 6 7 8
## 2 3.096154
## 3 3.679230 4.916465
## 4 2.462149 2.164213 4.107079
## 5 4.123129 3.852850 4.468735 4.127368
## 6 3.606269 4.218804 2.992760 3.201836 4.600183
## 7 3.901898 3.448346 4.217769 3.969367 4.596261 3.352919
## 8 2.737407 3.892524 4.990876 3.692949 5.155516 4.913953 4.364509
## 9 3.253851 3.957125 2.752623 3.753627 4.489900 3.730814 2.796298 3.594824
## 10 3.099116 2.705330 3.934935 1.491427 4.045276 3.829058 4.506512 3.673884
## 11 3.491163 4.792640 5.902882 4.864730 6.460986 6.004557 5.995814 3.462587
## 12 3.223138 2.432568 4.031434 3.498769 3.603863 3.738824 1.660047 4.059770
## 13 3.959637 3.434878 4.385973 2.577003 4.758059 4.554909 5.010221 4.140607
## 14 2.113490 4.323825 2.742000 3.230069 4.818803 3.469268 4.914949 4.335241
## 15 2.593481 2.501195 5.156977 3.190250 4.255251 4.065764 2.930142 3.849872
## 16 4.033051 4.837051 5.264442 4.967244 5.816715 5.842268 5.042444 2.201457
## 17 4.396680 3.623588 6.356548 4.893679 5.628591 6.099456 4.577294 5.426511
## 18 1.877248 2.904409 2.723954 2.651532 4.338150 2.853942 2.949006 3.237409
## 19 2.410434 4.634878 3.179392 3.464171 5.133791 2.581208 4.515428 4.107966
## 20 3.174488 2.997481 3.733274 1.816465 4.385852 2.912401 3.541931 4.094283
## 21 3.453407 2.318451 5.088018 3.884260 3.644137 4.628341 2.675404 3.977130
## 22 2.509287 2.421916 4.109321 2.578463 3.771757 4.026935 4.000096 3.239374
## 9 10 11 12 13 14 15 16
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10 3.572023
## 11 5.175240 5.081469
## 12 2.735861 3.942171 5.208504
## 13 3.658647 1.407032 5.309741 4.496249
## 14 3.816443 3.610272 4.315584 4.335484 4.385649
## 15 4.113606 4.264133 4.735659 2.328833 5.103646 4.239522
## 16 3.627307 4.531420 3.429962 4.617791 4.406173 5.169314 5.175157
## 17 4.901037 5.484537 4.751387 3.497555 5.606577 5.558002 3.399659 5.559320
## 18 2.428533 3.070750 3.945595 2.451935 3.780942 2.301050 2.998784 3.973815
## 19 4.109049 4.130120 4.522319 4.414578 5.010864 1.876051 4.030721 5.232256
## 20 2.948021 2.054393 5.352136 3.430937 2.226493 3.744430 3.782111 4.823711
## 21 3.742680 4.361961 4.883977 1.384124 4.937119 4.926966 2.097150 4.568885
## 22 3.208932 2.559945 3.436927 2.995066 2.739910 3.512207 3.352644 3.457129
## 17 18 19 20 21
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18 4.426129
## 19 6.089597 2.473696
## 20 4.866540 2.922392 3.903723
## 21 3.095002 3.185250 4.972551 4.145222
## 22 3.628061 2.548060 3.967618 2.618050 3.012264#Hierarchical agglomerative clustering
Data.hclust = hclust(distance)
plot(Data.hclust)
plot(Data.hclust,labels=Data$Company,main='Default from hclust')
plot(Data.hclust,hang=-1, labels=Data$Company,main='Default from hclust')
#Hierarchical agglomerative clustering using “average” linkage
Data.hclust<-hclust(distance,method="average")
plot(Data.hclust,hang=-1) 
#Cluster membership
member = cutree(Data.hclust,3)
table(member)## member
## 1 2 3
## 18 1 3member## [1] 1 1 1 1 2 1 1 3 1 1 3 1 1 1 1 3 1 1 1 1 1 1#Characterizing clusters
aggregate(nor,list(member),mean)## Group.1 Fixed_charge RoR Cost Load D.Demand Sales
## 1 1 -0.01313873 0.1868016 -0.2552757 0.1520422 -0.1253617 -0.2215631
## 2 2 2.03732429 -0.8628882 0.5782326 -1.2950193 -0.7186431 -1.5814284
## 3 3 -0.60027572 -0.8331800 1.3389101 -0.4805802 0.9917178 1.8565214
## Nuclear Fuel_Cost
## 1 0.1071944 0.06692555
## 2 0.2143888 1.69263800
## 3 -0.7146294 -0.96576599aggregate(Data[,-c(1,1)],list(member),mean)## Group.1 Fixed_charge RoR Cost Load D.Demand Sales Nuclear
## 1 1 1.111667 11.155556 157.6667 57.65556 2.850000 8127.50 13.8
## 2 2 1.490000 8.800000 192.0000 51.20000 1.000000 3300.00 15.6
## 3 3 1.003333 8.866667 223.3333 54.83333 6.333333 15504.67 0.0
## Fuel_Cost
## 1 1.1399444
## 2 2.0440000
## 3 0.5656667#Silhouette Plot
library(cluster)
plot(silhouette(cutree(Data.hclust,3), distance))
#Scree Plot
wss <- (nrow(nor)-1)*sum(apply(nor,2,var))
for (i in 2:20) wss[i] <- sum(kmeans(nor, centers=i)$withinss)
plot(1:20, wss, type="b", xlab="Number of Clusters", ylab="Within groups sum of squares")
#K-means clustering
set.seed(123)
kc<-kmeans(nor,3)
kc## K-means clustering with 3 clusters of sizes 7, 5, 10
##
## Cluster means:
## Fixed_charge RoR Cost Load D.Demand Sales
## 1 -0.23896065 -0.65917479 0.2556961 0.7992527 -0.05435116 -0.8604593
## 2 0.51980100 1.02655333 -1.2959473 -0.5104679 -0.83409247 0.5120458
## 3 -0.09262805 -0.05185431 0.4689864 -0.3042429 0.45509205 0.3462986
## Nuclear Fuel_Cost
## 1 -0.2884040 1.2497562
## 2 -0.4466434 -0.3174391
## 3 0.4252045 -0.7161098
##
## Clustering vector:
## [1] 3 1 2 3 1 2 1 3 3 3 3 1 3 2 1 3 1 2 2 3 1 3
##
## Within cluster sum of squares by cluster:
## [1] 34.16481 15.15613 57.53424
## (between_SS / total_SS = 36.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"ot<-nor
datadistshortset<-dist(ot,method = "euclidean")
hc1 <- hclust(datadistshortset, method = "complete" )
pamvshortset <- pam(datadistshortset,4, diss = FALSE)
clusplot(pamvshortset, shade = FALSE,labels=2,col.clus="blue",col.p="red",span=FALSE,main="Cluster Mapping",cex=1.2)
#Cluster Analysis in R
library(factoextra) ## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(ggplot2)
k2 <- kmeans(nor, centers = 3, nstart = 25)
k2## K-means clustering with 3 clusters of sizes 3, 7, 12
##
## Cluster means:
## Fixed_charge RoR Cost Load D.Demand Sales
## 1 -0.6002757 -0.8331800 1.3389101 -0.4805802 0.99171778 1.85652137
## 2 -0.2389606 -0.6591748 0.2556961 0.7992527 -0.05435116 -0.86045933
## 3 0.2894626 0.5928136 -0.4838836 -0.3460857 -0.21622460 0.03780427
## Nuclear Fuel_Cost
## 1 -0.7146294 -0.965766
## 2 -0.2884040 1.249756
## 3 0.3468930 -0.487583
##
## Clustering vector:
## [1] 3 2 3 3 2 3 2 1 3 3 1 2 3 3 2 1 2 3 3 3 2 3
##
## Within cluster sum of squares by cluster:
## [1] 9.533522 34.164812 58.012322
## (between_SS / total_SS = 39.5 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"str(k2)## List of 9
## $ cluster : int [1:22] 3 2 3 3 2 3 2 1 3 3 ...
## $ centers : num [1:3, 1:8] -0.6 -0.239 0.289 -0.833 -0.659 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:3] "1" "2" "3"
## .. ..$ : chr [1:8] "Fixed_charge" "RoR" "Cost" "Load" ...
## $ totss : num 168
## $ withinss : num [1:3] 9.53 34.16 58.01
## $ tot.withinss: num 102
## $ betweenss : num 66.3
## $ size : int [1:3] 3 7 12
## $ iter : int 2
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"fviz_cluster(k2, data = nor)
#Optimal Clusters
fviz_nbclust(nor, kmeans, method = "wss")
#Average Silhouette Method
fviz_nbclust(nor, kmeans, method = "silhouette")
#Gap Statistic Method
gap_stat <- clusGap(nor, FUN = kmeans, nstart = 25,
K.max = 10, B = 50)
fviz_gap_stat(gap_stat)
Conclusion K-means clustering is a very simple and fast algorithm and it can efficiently deal with very large data sets.
K-means clustering needs to provide a number of clusters as an input, Hierarchical clustering is an alternative approach that does not require that we commit to a particular choice of clusters.
Hierarchical clustering has an added advantage over K-means clustering because it has an attractive tree-based representation of the observations (dendrogram).