Question

In R load the tidyverse package

Consider the `USArrests` dataset, which contains statistics, in arrests per 100,000 residents for assault, murder, and rape in each of the 50 US states in 1973. Also given is the percent of the population living in urban areas.

(a) Perform k-means clustering using all numerical variables in this dataset, scaling the variables before running the clustering algorithm

(b) Try two different values of $k$ and comment on your results.

(c) Visualize the results of the clustering using the variables `Murder` and `UrbanPop`

Answer 1

data("USArrests")
mydata <- USArrests
mydata <- na.omit(mydata)
mydata <- scale(mydata)
head(mydata, n=10)

set.seed(124)
ss <- sample(1:50,10)
df <- USArrests[ss, ]
df <- na.omit(df)
head(df,n=6)
df.scaled <- scale(df)
head(round(df.scaled, 2))
desc_stats <- data.frame(
  Min = apply(USArrests, 2, min),
  Max = apply(USArrests, 2, max),
  Med = apply(USArrests, 2, median),
  SD = apply(USArrests, 2, sd),
  Mean = apply(USArrests, 2, mean))
desc_stats <- round(desc_stats,1)
head(desc_stats)
library(stats)
eucl <- dist(df.scaled, method = "euclidean" )
round(as.matrix(eucl)[1:6,1:6],1)
cor <- cor(t(df.scaled), method = "pearson")
dist_cor <- as.dist(1 - cor)
round(as.matrix(dist_cor)[1:6,1:6],1)

#daisy() to compute dissimilarity matrices between observations 
library(cluster)
library(factoextra)
daisy(df.scaled, metric = c("euclidean", "manhattan", "gower"), stand = FALSE)
data("flower")
head(flower)
str(flower)
daisy_dist <- as.matrix(daisy(flower))
head(round(daisy_dist[1:6,1:6]),2)
library(corrplot)
corrplot(as.matrix(eucl), is.corr = FALSE, method = "color")
corrplot(as.matrix(eucl), is.corr = FALSE, method = "color", order = "hclust", type = "upper")
plot(hclust(eucl, method = "ward.D2"))

heatmap(as.matrix(eucl), symm = TRUE, distfun = function(x) as.dist(x))