Below are the solutions to these exercises on density-based clustering.

#################### # # # Exercise 1 # # # #################### df <- iris[, -ncol(iris)] #################### # # # Exercise 2 # # # #################### df <- scale(df) df <- as.data.frame(df) #################### # # # Exercise 3 # # # #################### require(dbscan) kNNdistplot(df, k = 5) abline(h = 0.8, col = "red")

#################### # # # Exercise 4 # # # #################### require(dbscan) db_clusters_iris <- dbscan(df, eps=0.8, minPts=5) print(db_clusters_iris)

## DBSCAN clustering for 150 objects. ## Parameters: eps = 0.8, minPts = 5 ## The clustering contains 2 cluster(s) and 4 noise points. ## ## 0 1 2 ## 4 49 97 ## ## Available fields: cluster, eps, minPts

#################### # # # Exercise 5 # # # #################### require(factoextra) fviz_cluster(db_clusters_iris, df, ellipse = FALSE, geom = "point")

#################### # # # Exercise 6 # # # #################### df_copy <- df df_copy[['cluster']] <- db_clusters_iris[['cluster']] print(head(df_copy))

## Sepal.Length Sepal.Width Petal.Length Petal.Width cluster ## 1 -0.8976739 1.01560199 -1.335752 -1.311052 1 ## 2 -1.1392005 -0.13153881 -1.335752 -1.311052 1 ## 3 -1.3807271 0.32731751 -1.392399 -1.311052 1 ## 4 -1.5014904 0.09788935 -1.279104 -1.311052 1 ## 5 -1.0184372 1.24503015 -1.335752 -1.311052 1 ## 6 -0.5353840 1.93331463 -1.165809 -1.048667 1

#################### # # # Exercise 7 # # # #################### require(dbscan) require(factoextra) # create a vector of epsilon values epsilon_values <- c(1.8, 0.5, 0.4) # plot the distribution of distances kNNdistplot(df, k = 5) # plot lines at epsilon values for (e in epsilon_values) { abline(h = e, col = "red") }

# find clusters for each epsilon value and plot those clusters for (e in epsilon_values) { db_clusters_iris <- dbscan(df, eps=e, minPts=4) title <- paste("Plot for epsilon = ", e) g <- fviz_cluster(db_clusters_iris, df, ellipse = TRUE, geom = "point", main = title) print(g) }

#################### # # # Exercise 8 # # # #################### require(dbscan) require(factoextra) # load and prepare the data customers <- read.csv("Wholesale customers data.csv") customers <- customers[, c("Fresh","Milk")] customers <- scale(customers) customers <- as.data.frame(customers) # plot the distribution of distances to the fifth nearest neighbors kNNdistplot(customers, k = 5) abline(h = 0.4, col = "red")

# find clusters db_clusters_customers <- dbscan(customers, eps=0.4, minPts=5) print(db_clusters_customers)

## DBSCAN clustering for 440 objects. ## Parameters: eps = 0.4, minPts = 5 ## The clustering contains 1 cluster(s) and 22 noise points. ## ## 0 1 ## 22 418 ## ## Available fields: cluster, eps, minPts

# plot clusters fviz_cluster(db_clusters_customers, customers, ellipse = FALSE, geom = "point")

#################### # # # Exercise 9 # # # #################### require(factoextra) # remove values beyond 2.5 standard deviations customers_core <- customers[customers[['Fresh']] > -2.5 & customers[['Fresh']] < 2.5, ] customers_core <- customers_core[customers_core[['Milk']] > -2.5 & customers_core[['Milk']] < 2.5, ] # find clusters and plot them km_clusters_customers <- kmeans(customers_core, centers = 4, nstart = 10) fviz_cluster(km_clusters_customers, customers_core, ellipse = FALSE, geom = "point")

#################### # # # Exercise 10 # # # #################### require(dbscan) require(cluster) require(factoextra) ## DBSCAN results # retrieve a vector of cluster assignments db_clusters_vector <- db_clusters_customers[['cluster']] # calculate distances between data points db_distances <- dist(customers) # get a silhouette information object db_silhouette <- silhouette(db_clusters_vector, db_distances) # plot the silhouette fviz_silhouette(db_silhouette)

## cluster size ave.sil.width ## 0 0 22 -0.02 ## 1 1 418 0.72

## k-means results # retrieve a vector of cluster assignments km_clusters_vector <- km_clusters_customers[['cluster']] # calculate distances between data points km_distances <- dist(customers_core) # get a silhouette information object km_silhouette <- silhouette(km_clusters_vector, km_distances) # plot the silhouette fviz_silhouette(km_silhouette)

## cluster size ave.sil.width ## 1 1 47 0.28 ## 2 2 190 0.46 ## 3 3 69 0.37 ## 4 4 113 0.41

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Vik says

Excelellent exercise.

Vik says

Excelellent exercise. It obviously is done with a wit and heart, looking forward to further exercises from this author.