Question

Execute the BDMO Algorithm with p = 3 on the following 1-dimensional, Euclidean data:

1, 45, 80, 24, 56, 71, 17, 40, 66, 32, 48, 96, 9, 41, 75, 11, 58, 93, 28, 39, 77

The clustering algorithms is k-means with k = 3. Only the centroid of a cluster, along with its count, is needed to represent a cluster.

Using your clusters from the above, produce the best centroids in response to a query asking for a clustering of the last 10 points.

Show all calculations and steps to prove.

Answer 1

# Custom clustering library
source("clustering_library.R")

# Load in data
x <- c( 1,  45, 80, 24, 56, 71, 17, 
        40, 66, 32, 48, 96,  9, 41, 
        75, 11, 58, 93, 28, 39, 77)

records <- data.frame(x=x)

# Cluster parameters
p <- 3
k <- 3

# Break up data into buckets
buckets <- initBuckets(records, 3, 2)

bdmo <- lapply(buckets, function(b) {
  rec <- b[['records']]
  if (nrow(rec) > k) {
    km <- kmeans(rec, k)
    return(list(centroid = km$centers,
                count = length(km$cluster)))
  } else {
    return(list(centroid = rec,
                count = nrow(rec)))
  }
    
})

for (b in bdmo) {
  print("Centroid:")
  print(t(b[['centroid']]))
  print
  print(c("Count: ", b[['count']]))
  print("---------------------------")
}