Activity 7
Develin Omayan
5/24/2022
Cluster Analysis in R
Getting Data
library(readr)
Data_1_ <- read_csv("C:/Users/LENOVO/Downloads/Data (1).txt")## Rows: 22 Columns: 9## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (1): Company
## dbl (8): Fixed_charge, RoR, Cost, Load, D Demand, Sales, Nuclear, Fuel_Cost##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.Data_1_## # A tibble: 22 x 9
## Company Fixed_charge RoR Cost Load `D Demand` Sales Nuclear Fuel_Cost
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Arizona 1.06 9.2 151 54.4 1.6 9077 0 0.628
## 2 Boston 0.89 10.3 202 57.9 2.2 5088 25.3 1.56
## 3 Central 1.43 15.4 113 53 3.4 9212 0 1.06
## 4 Commonweal~ 1.02 11.2 168 56 0.3 6423 34.3 0.7
## 5 Con Ed NY 1.49 8.8 192 51.2 1 3300 15.6 2.04
## 6 Florida 1.32 13.5 111 60 -2.2 11127 22.5 1.24
## 7 Hawaiian 1.22 12.2 175 67.6 2.2 7642 0 1.65
## 8 Idaho 1.1 9.2 245 57 3.3 13082 0 0.309
## 9 Kentucky 1.34 13 168 60.4 7.2 8406 0 0.862
## 10 Madison 1.12 12.4 197 53 2.7 6455 39.2 0.623
## # ... with 12 more rows#Scatter plot
library(ggplot2)
plot(Data_1_$Fuel_Cost~ Data_1_$Sales, data = Data_1_)
with(Data_1_,text(Data_1_$Fuel_Cost ~ Data_1_$Sales, labels=Data_1_$Company,pos=4))
#Normalize
z <- Data_1_[,-c(1,1)]
means <- apply(z,2,mean)
sds <- apply(z,2,sd)
nor <- scale(z,center=means,scale=sds)#Calculate distance matrix
distance = dist(nor)#Hierarchical agglomerative clustering
mydata.hclust = hclust(distance)
plot(mydata.hclust)
plot(mydata.hclust,labels=Data_1_$Company,main='Default from hclust')
plot(mydata.hclust,hang=-1, labels=Data_1_$Company,main='Default from hclust')
#Hierarchical agglomerative clustering using “average” linkage
mydata.hclust<-hclust(distance,method="average")
plot(mydata.hclust,hang=-1) 
#Cluster membership
member = cutree(mydata.hclust,3)
table(member)## member
## 1 2 3
## 18 1 3member## [1] 1 1 1 1 2 1 1 3 1 1 3 1 1 1 1 3 1 1 1 1 1 1#Characterizing clusters
aggregate(nor,list(member),mean)## Group.1 Fixed_charge RoR Cost Load D Demand Sales
## 1 1 -0.01313873 0.1868016 -0.2552757 0.1520422 -0.1253617 -0.2215631
## 2 2 2.03732429 -0.8628882 0.5782326 -1.2950193 -0.7186431 -1.5814284
## 3 3 -0.60027572 -0.8331800 1.3389101 -0.4805802 0.9917178 1.8565214
## Nuclear Fuel_Cost
## 1 0.1071944 0.06692555
## 2 0.2143888 1.69263800
## 3 -0.7146294 -0.96576599aggregate(Data_1_[,-c(1,1)],list(member),mean)## Group.1 Fixed_charge RoR Cost Load D Demand Sales Nuclear
## 1 1 1.111667 11.155556 157.6667 57.65556 2.850000 8127.50 13.8
## 2 2 1.490000 8.800000 192.0000 51.20000 1.000000 3300.00 15.6
## 3 3 1.003333 8.866667 223.3333 54.83333 6.333333 15504.67 0.0
## Fuel_Cost
## 1 1.1399444
## 2 2.0440000
## 3 0.5656667#Silhouette Plot
library(cluster)
plot(silhouette(cutree(mydata.hclust,3), distance))
#Scree Plot
wss <- (nrow(nor)-1)*sum(apply(nor,2,var))
for (i in 2:20) wss[i] <- sum(kmeans(nor, centers=i)$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) ## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBak2 <- 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).