Selection of K in K-Means Clustering

Description

Selection of k in k-means clustering based on Pham et al. paper “Selection of k in k-means clustering”

Details

This package implements the method for selecting the number of clusters for the algorithm K-means introduced in the publication of Pham, Dimov and Nguyen of 2004.

Author(s)

Daniel Rodriguez daniel.rodriguez.perez@gmail.com

References

D T Pham, S S Dimov, and C D Nguyen, "Selection of k in k-means clustering", Mechanical Engineering Science, 2004, pp. 103-119.

Get the f(K) vector

Description

Get the f(K) vector.

Usage

get_f_k(obj)

Arguments

Value

the vector of f(K) function.

Author(s)

Daniel Rodriguez

See Also

num_clusters, num_clusters_all

Examples

# Create a data set with two clusters
dat <- matrix(c(rnorm(100, 2, .1), rnorm(100, 3, .1),
                rnorm(100, -2, .1), rnorm(100, -3, .1)), 200, 2)

# Get the f(k) vector
sol <- kselection(dat)
f_k <- get_f_k(sol)

Get the k_threshold

Description

Get the maximum value of f(K) from which can not be considered the existence of more than one cluster.

Usage

get_k_threshold(obj)

Arguments

Value

the k_threshold value.

Author(s)

Daniel Rodriguez

See Also

set_k_threshold

Selection of K in K-means Clustering

Description

Selection of k in k-means clustering based on Pham et al. paper.

Usage

kselection(
  x,
  fun_cluster = stats::kmeans,
  max_centers = 15,
  k_threshold = 0.85,
  progressBar = FALSE,
  trace = FALSE,
  parallel = FALSE,
  ...
)

Arguments

Details

This function implements the method proposed by Pham, Dimov and Nguyen for selecting the number of clusters for the K-means algorithm. In this method a function f(K) is used to evaluate the quality of the resulting clustering and help decide on the optimal value of K for each data set. The f(K) function is defined as

f(K) = \left\{ \begin{array}{rl} 1 & \mbox{if $K = 1$} \\ \frac{S_K}{\alpha_K S_{K-1}} & \mbox{if $S_{K-1} \ne 0$, $\forall K >1$} \\ 1 & \mbox{if $S_{K-1} = 0$, $\forall K >1$} \end{array} \right.

where S_K is the sum of the distortion of all cluster and \alpha_K is a weight factor which is defined as

\alpha_K = \left\{ \begin{array}{rl} 1 - \frac{3}{4 N_d} & \mbox{if $K = 1$ and $N_d > 1$} \\ \alpha_{K-1} + \frac{1 - \alpha_{K-1}}{6} & \mbox{if $K > 2$ and $N_d > 1$} \end{array} \right.

where N_d is the number of dimensions of the data set.

In this definition f(K) is the ratio of the real distortion to the estimated distortion and decreases when there are areas of concentration in the data distribution.

The values of K that yield f(K) < 0.85 can be recommended for clustering. If there is not a value of K which f(K) < 0.85, it cannot be considered the existence of clusters in the data set.

Value

an object with the f(K) results.

Author(s)

Daniel Rodriguez

References

D T Pham, S S Dimov, and C D Nguyen, "Selection of k in k-means clustering", Mechanical Engineering Science, 2004, pp. 103-119.

See Also

num_clusters, get_f_k

Examples

# Create a data set with two clusters
dat <- matrix(c(rnorm(100, 2, .1), rnorm(100, 3, .1),
                rnorm(100, -2, .1), rnorm(100, -3, .1)), 200, 2)

# Execute the method
sol <- kselection(dat)

# Get the results
k   <- num_clusters(sol) # optimal number of clustes
f_k <- get_f_k(sol)      # the f(K) vector

# Plot the results
plot(sol)

## Not run: 
# Parallel
require(doMC)
registerDoMC(cores = 4)

system.time(kselection(dat, max_centers = 50 , nstart = 25))
system.time(kselection(dat, max_centers = 50 , nstart = 25, parallel = TRUE))

## End(Not run)

Get the number of clusters.

Description

The optimal number of clusters proposed by the method.

Usage

num_clusters(obj)

Arguments

Value

the number of clusters proposed.

Author(s)

Daniel Rodriguez

See Also

num_clusters_all, get_f_k

Examples

# Create a data set with two clusters
dat <- matrix(c(rnorm(100, 2, .1), rnorm(100, 3, .1),
                rnorm(100, -2, .1), rnorm(100, -3, .1)), 200, 2)

# Get the optimal number of clustes
sol <- kselection(dat)
k   <- num_clusters(sol)

Get all recommended numbers of clusters

Description

The number of cluster which could be recommender according the method threshold.

Usage

num_clusters_all(obj)

Arguments

Value

an array of number of clusters that could be recommended.

Author(s)

Daniel Rodriguez

See Also

num_clusters, get_f_k

Examples

# Create a data set with two clusters
dat <- matrix(c(rnorm(100, 2, .1), rnorm(100, 3, .1),
                rnorm(100, -2, .1), rnorm(100, -3, .1)), 200, 2)

# Get the optimal number of clustes
sol <- kselection(dat)
k   <- num_clusters(sol)

Set the k_threshold

Description

Set the maximum value of f(K) from which can not be considered the existence of more than one cluster.

Usage

set_k_threshold(obj, k_threshold)

Arguments

Value

the output of kselection function with new k_threshold.

Author(s)

Daniel Rodriguez

See Also

get_k_threshold