Assessment of the stability of individual objects, clusters and a whole clustering solution based on repeated runs of a clustering algorithm.

Description

The ClusterStability package uses a probabilistic framework and some well-known clustering criteria (e.g. Calinski-Harabasz, Silhouette, Dunn and Davies-Bouldin) to compute the stability scores (ST) of each individual object (i.e., element) in the clustering solution provided by the K-means and K-medoids partitioning algorithms.

Details

Function ClusterStability computes the individual and global stability scores (ST) for a partitioning solution using either K-means or K-medoids (the approximate solution is provided).

Function ClusterStability_exact is similar to the ClusterStability function but uses the Stirling numbers of the second kind to compute the exact stability scores (but is limited to a small number of objects).

Function Kcombination computes the k-combination of a set of numbers for a given k.

Function Reorder returns the re-ordered partitioning of a series of clusters.

Function Stirling2nd computes the Stirling numbers of the second kind.

Author(s)

Etienne Lord, François-Joseph Lapointe and Vladimir Makarenkov

See Also

ClusterStability, ClusterStability_exact, Kcombination, Reorder, Stirling2nd

Calculates the approximate stability score (ST) of individual objects in a clustering solution (the approximate version allowing one to avoid possible variable overflow errors).

Description

This function will return the individual stability score ST and the global score STglobal using either the K-means or K-medoids algorithm and four different clustering indices: Calinski-Harabasz, Silhouette, Dunn or Davies-Bouldin.

Usage

ClusterStability(dat, k, replicate, type) 

Arguments

Value

Returns the individual (ST) and global (ST_global) stability scores for the four clustering indices: Calinski-Harabasz (ch), Silhouette (sil), Dunn (dunn) or Davies-Bouldin (db).

Examples

   ## Calculates the stability scores of individual objects of the Iris dataset
   ## using K-means, 100 replicates (random starts) and k=3
   ClusterStability(dat=iris[1:4],k=3,replicate=100,type='kmeans');

Calculates the exact stability score (ST) for individual objects in a clustering solution.

Description

This function will return the exact individual stability score ST and the exact global score STglobal using either the K-means or K-medoids algorithm and four different clustering indices: Calinski-Harabasz, Silhouette, Dunn or Davies-Bouldin. Variable overflow errors are possible for large numbers of objects.

Usage

ClusterStability_exact(dat, k, replicate, type) 

Arguments

Value

Returns the exact individual (ST) and global (ST_global) stability scores for the four clustering indices: Calinski-Harabasz (ch), Silhouette (sil), Dunn (dunn) or Davies-Bouldin (db).

Examples

   ## Calculate the stability scores of individual objects of the Iris dataset
   ## using K-means, 100 replicates (random starts) and k=3
   ClusterStability_exact(dat=iris[1:4],k=3,replicate=100,type='kmeans');

Kcombination returns the list of all possible combinations of a set of numbers of a given length k.

Description

This function, given a vector of numbers, will return all the possible combinations of a given length k.

Usage

Kcombination(data, k, selector)

Arguments

Value

Return a list of all possible combinations for the given vector of numbers.

Examples

   ## Returns the k-combination of the list of numbers: 1,2,3 of length=2.
   ## i.e. (1,2), (1,3), (2,3) 
	Kcombination(c(1,2,3),k=2)
   ## Returns only the k-combination containing the number 1.
   ## i.e. (1,2), (1,3)	
	Kcombination(c(1,2,3),k=2,selector=1)

This function returns the ordering of a partitioning solution in ascending order.

Description

This function returns the ordered partition of a set of numbers in ascending order and reorderd to start at one. This is an auxiliary function.

Usage

Reorder(data)

Arguments

Value

A vector of ordered partition numbers for this data.

Examples

  Reorder(c(1,3,4,4,3,1))
  # Expected : 1 2 3 3 2 1

Stirling2nd function computes the Stirling numbers of the second kind.

Description

This function returns the estimated Stirling numbers of the second kind i.e., the number of ways of partitioning a set of n objects into k nonempty groups.

Usage

Stirling2nd(n,k)

Arguments

Value

The Stirling number of the 2nd kind for n elements and k groups or NaN (if the Stirling number for those n and k is greater than 1e300).

Examples

  Stirling2nd(n=3,k=2)
  # Expected value=3
  Stirling2nd(n=300,k=20)
  # Expected value=NaN  

Undocumented functions

Description

The following functions are for internal computation only: calculate_global_PSG, calculate_indices, calculate_singleton, is_partition_group, p_n_k, p_tilde_n_k, calculate_individual_PSG_approximative, calculate_individual_PSG_exact, calculate_individual_PSG.

This function returns the Calinski Harabasz score.

Description

This function returns the Calinski Harabasz score of a partition (also known as the Variance Ratio Criterion).

Usage

calinski_harabasz_score(X, labels)

Arguments

Value

The Calinski Harabasz score for this data.

References

T. Calinski and J. Harabasz. A dendrite method for cluster analysis. Communications in Statistics, 3, no. 1:1–27, 1974

Examples

  calinski_harabasz_score(iris[1:10,1:4], c(3,2,2,2,3,1,2,3,2,2))
  # Expected : 11.34223

This function returns the Davies Bouldin score.

Description

This function returns the Davies Bouldin score of a partition.

Usage

davies_bouldin_score(X, labels)

Arguments

Value

The Davies Bouldin score for this data.

References

D. L. Davies and D. W. Bouldin. A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1, no. 2:224-227, 1979

Examples

  davies_bouldin_score(iris[1:10,1:4], c(3,2,2,2,3,1,2,3,2,2))
  # Expected : 0.5103277

This function returns the Dunn_score.

Description

This function returns the Dunn score (also known as the e Dunn index) of a partition .

Usage

dunn_score(X, labels)

Arguments

Value

The Dunn index score for this data.

References

J. Dunn. Well separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4:95–104, 1974.

Examples

  dunn_score(iris[1:10,1:4], c(3,2,2,2,3,1,2,3,2,2))
  # Expected : 0.5956834