Description

library(cluster) library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
library(dendextend)
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## Attaching package: ’dendextend’
## The following object is masked from ’package:stats’:
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## cutree
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
c<-read.csv(“C:/Users/suraj/Downloads/Cereals.csv”) c<- na.omit(c) head(c)
## name mfr type calories protein fat sodium fiber carbo
## 1 100%_Bran N C 70 4 1 130 10.0 5.0
## 2 100%_Natural_Bran Q C 120 3 5 15 2.0 8.0
## 3 All-Bran K C 70 4 1 260 9.0 7.0
## 4 All-Bran_with_Extra_Fiber K C 50 4 0 140 14.0 8.0
## 6 Apple_Cinnamon_Cheerios G C 110 2 2 180 1.5 10.5
## 7 Apple_Jacks K C 110 2 0 125 1.0 11.0
## sugars potass vitamins shelf
## 1 6 280 25 3 weight cups rating 1 0.33 68.40297
## 2 8 135 0 3 1 1.00 33.98368
## 3 5 320 25 3 1 0.33 59.42551
## 4 0 330 25 3 1 0.50 93.70491
## 6 10 70 25 1 1 0.75 29.50954
## 7 14
#Normalizing the 30
dataset 25 2 1 1.00 33.17409
c<- c[,4:16] c <- scale(c,center = head(c) TRUE,scale = TRUE)
## calories protein fat sodium fiber carbo sugars
## 1 -1.8659155 1.3817478 0.0000000 -0.3910227 3.22866747 -2.5001396 -0.2542051
## 2 0.6537514 0.4522084 3.9728810 -1.7804186 -0.07249167 -1.7292632 0.2046041
## 3 -1.8659155 1.3817478 0.0000000 1.1795987 2.81602258 -1.9862220 -0.4836096
## 4 -2.8737823 1.3817478 -0.9932203 -0.2702057 4.87924705 -1.7292632 -1.6306324
## 6 0.1498180 -0.4773310 0.9932203 0.2130625 -0.27881412 -1.0868662 0.6634132
## 7 0.1498180 -0.4773310 -0.9932203 -0.4514312 -0.48513656 -0.9583868 1.5810314
## potass vitamins shelf weight cups rating
## 1 2.5605229 -0.1818422 0.9419715 -0.2008324 -2.0856582 1.8549038
## 2 0.5147738 -1.3032024 0.9419715 -0.2008324 0.7567534 -0.5977113
## 3 3.1248675 -0.1818422 0.9419715 -0.2008324 -2.0856582 1.2151965
## 4 3.2659536 -0.1818422 0.9419715 -0.2008324 -1.3644493 3.6578436
## 6 -0.4022862 -0.1818422 -1.4616799 -0.2008324 -0.3038480 -0.9165248
## 7 -0.9666308 -0.1818422 -0.2598542 -0.2008324 0.7567534 -0.6553998
#Task-1.Apply hierarchical clustering to the data using Euclidean distance to the normalized measurements. #Use Agnes to compare the clustering from single linkage, complete #linkage, average linkage, and Ward. Choose the best method.
Euclidean_Dist <- dist(c, method = “euclidean”) # Hierarchical clustering using Complete Linkage cl1 <- hclust(Euclidean_Dist, method = “complete” )
# Plot the obtained dendrogram plot(cl1, cex = 0.6, hang = -1)
Cluster Dendrogram

Euclidean_Dist hclust (*, “complete”)
round(cl1$height, 3)
## [1] 0.143 0.196 0.575 0.698 0.828 0.904 1.003 1.004 1.201 1.203
## [11] 1.254 1.378 1.408 1.421 1.454 1.463 1.474 1.517 1.608 1.611
## [21] 1.616 1.625 1.650 1.687 1.692 1.720 1.730 1.795 1.839 1.897
## [31] 1.919 1.982 2.015 2.046 2.203 2.224 2.339 2.381 2.394 2.522
## [41] 2.563 2.574 2.579 2.668 2.682 2.734 2.776 2.787 3.229 3.236
## [51] 3.385 3.451 3.510 3.535 3.717 3.866 3.957 4.005 4.031 4.168
## [61] 4.456 4.779 4.839 5.342 5.488 5.920 6.169 6.669 6.731 7.650
## [71] 7.964 9.979 10.984
Compute with agnes and with different linkage methods
cl_single <- agnes(c, method = “single”) print(cl_single$ac)
## [1] 0.6067859
cl_complete <- agnes(c, method = “complete”) print(cl_complete$ac)
## [1] 0.8353712
cl_average <- agnes(c, method = “average”) print(cl_average$ac)
## [1] 0.7766075
cl_ward <- agnes(c, method = “ward”) print(cl_ward$ac)
## [1] 0.9046042
#The agglomerative coefficient obtained by Ward’s method is the largest.
#visualizing the dendrogram
cl_Ward <- agnes(Euclidean_Dist, method = “ward”)
pltree(cl_Ward, cex = 0.6, hang = -1, main = “Dendrogram of agnes for ward”)
Dendrogram of agnes for ward

Euclidean_Dist agnes (*, “ward”)
#Task-2.How many clusters would you choose?
#The largest difference in height can be used to determine the k value, hence K =5 is the best option.
cl_Ward <- hclust(Euclidean_Dist,method = “ward.D2”) clust_comp <- cutree(cl_Ward, k=5) table(clust_comp)
## clust_comp
## 1 2 3 4 5
## 3 20 21 21 9
plot(cl_Ward,cex=0.6)
rect.hclust(cl_Ward, k = 5, border = 2:10,)
Cluster Dendrogram

Euclidean_Dist hclust (*, “ward.D2”)
Temp <- cbind(as.data.frame(cbind(c,clust_comp))) #Visualizing the clusters in Scatter plot fviz_cluster(list(data=Euclidean_Dist, cluster = clust_comp))
Cluster plot

#Task-3.The elementary public schools would like to choose a set of cereals to include in their #daily cafeterias. Every day a different cereal is offered, but all cereals should support a #healthy diet. For this goal, you are requested to find a cluster of “healthy cereals.”
Healthy_cereal <- na.omit(read.csv(“C:/Users/suraj/Downloads/Cereals.csv”)) Healthy_cereal<- cbind(Healthy_cereal,clust_comp) mean(Healthy_cereal[Healthy_cereal$clust_comp==1,”rating”])
## [1] 73.84446
mean(Healthy_cereal[Healthy_cereal$clust_comp==2,”rating”])
## [1] 38.26161
mean(Healthy_cereal[Healthy_cereal$clust_comp==3,”rating”])
## [1] 28.84825
mean(Healthy_cereal[Healthy_cereal$clust_comp==4,”rating”])
## [1] 46.46513
mean(Healthy_cereal[Healthy_cereal$clust_comp==5,”rating”])
## [1] 63.0184
Cluster1 has the highest rating (73.84446), so we’ll choose it as a healthy cereal.