Package 'cstab'

Title: Selection of Number of Clusters via Normalized Clustering Instability
Description: Selection of the number of clusters in cluster analysis using stability methods.
Authors: Jonas M. B. Haslbeck [aut, cre], Dirk U. Wulff [aut]
Maintainer: Jonas M. B. Haslbeck <[email protected]>
License: GPL (>= 2)
Version: 0.2-4
Built: 2024-11-07 03:25:35 UTC
Source: https://github.com/jmbh/cstab

Help Index

Selection of number of clusters via distance-based measures

Description

Selection of number of clusters via gap statistic, jump statistic, and slope statistic

Usage

cDistance(
  data,
  kseq,
  method = "kmeans",
  linkage = "complete",
  kmIter = 10,
  gapIter = 10
)

Arguments

data

a n x p data matrix of type numeric.
kseq

a vector with considered numbers clusters k > 1
method

character string indicating the clustering algorithm. 'kmeans' for the k-means algorithm, 'hierarchical' for hierarchical clustering.
linkage

character specifying the linkage criterion, in case type='hierarchical'. The available options are "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid" or "median". See hclust.
kmIter

integer specifying the the number of restarts of the k-means algorithm in order to avoid local minima.
gapIter

integer specifying the number of simulated datasets to compute the gap statistic (see Tibshirani et al., 2001).

Value

a list with the optimal numbers of cluster determined by the gap statistic (Tibshirani et al., 2001), the jump Statistic (Sugar & James, 2011) and the slope statistic (Fujita et al., 2014). Along the function returns the gap, jump and slope for each k in kseq.

Author(s)

Dirk U. Wulff <[email protected]> Jonas M. B. Haslbeck <[email protected]>

References

Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423.

Sugar, C. A., & James, G. M. (2011). Finding the number of clusters in a dataset. Journal of the American Statistical Association, 98(463), 750-763,

Fujita, A., Takahashi, D. Y., & Patriota, A. G. (2014). A non-parametric method to estimate the number of clusters. Computational Statistics & Data Analysis, 73, 27-39.

Examples

## Not run: 
  # Generate Data from Gaussian Mixture
  s <- .1
  n <- 50
  data <- rbind(cbind(rnorm(n, 0, s), rnorm(n, 0, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 0, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 0, s)))
  plot(data)

 # Selection of Number of Clusters using Distance-based Measures
 cDistance(data, kseq=2:10)
 
## End(Not run)

Cluster example

Description

An example, 2-dimensional dataset containing the 100 points for each of five bivariate normal distributions arranged equidistant along the outline of a circle.

Usage

cluster_example

Format

An object of class matrix (inherits from array) with 500 rows and 2 columns.

Details

To inspect execute plot(cluster_example).

Selection of number of clusters via clustering instability

Description

Selection of number of clusters via model-based or model-free, normalized or unnormalized clustering instability.

Usage

cStability(
  data,
  kseq = 2:20,
  nB = 10,
  norm = TRUE,
  predict = TRUE,
  method = "kmeans",
  linkage = "complete",
  kmIter = 5,
  pbar = TRUE
)

Arguments

data

a n x p data matrix of type numeric.
kseq

a vector with considered numbers clusters k > 1
nB

an integer specifying the number of bootstrap comparisons.
norm

logical specifying whether the instability path should be normalized. If TRUE, the instability path is normalized, accounting for a trivial decrease in instability due to a increasing k (see Haslbeck & Wulff, 2016).
predict

boolean specifying whether the model-based or the model-free variant should be used (see Haslbeck & Wulff, 2016).
method

character string specifying the clustering algorithm. 'kmeans' for the k-means algorithm, 'hierarchical' for hierarchical clustering.
linkage

character specifying the linkage criterion, in case type='hierarchical'. The available options are "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid" or "median". See hclust.
kmIter

integer specifying the the number of restarts of the k-means algorithm in order to avoid local minima.
pbar

logical

Value

a list that contains the optimal k selected by the unnormalized and normalized instability method. It also includes a vector containing the averaged instability path (over bootstrap samples), k-wise confidence intervals around these paths and a matrix containing the instability path of each bootstrap sample for both the normalized and the unnormalized method.

Author(s)

Dirk U. Wulff <[email protected]> Jonas M. B. Haslbeck <[email protected]>

References

Ben-Hur, A., Elisseeff, A., & Guyon, I. (2001). A stability based method for discovering structure in clustered data. Pacific symposium on biocomputing, 7, 6-17.

Tibshirani, R., & Walther, G. (2005). Cluster validation by prediction strength. Journal of Computational and Graphical Statistics, 14(3), 511-528.

Examples

## Not run: 
  # Generate Data from Gaussian Mixture
  s <- .1
  n <- 50
  data <- rbind(cbind(rnorm(n, 0, s), rnorm(n, 0, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 0, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 0, s)))
  plot(data)

  # Selection of Number of Clusters using Instability-based Measures
  stab_obj <- cStability(data, kseq=2:10)
  print(stab_obj)
  
## End(Not run)

!Deprecated! Selection of number of clusters via clustering instability

Description

!Deprecated! Selection of number of clusters via model-based or model-free, normalized or unnormalized clustering instability.

Usage

cStability_mEst(
  data,
  kseq = 2:20,
  nB = 10,
  norm = TRUE,
  predict = TRUE,
  method = "kmeans",
  linkage = "complete",
  kmIter = 5,
  pbar = TRUE
)

Arguments

data

a n x p data matrix of type numeric.
kseq

a vector with considered numbers clusters k > 1
nB

an integer specifying the number of bootstrap comparisons.
norm

logical specifying whether the instability path should be normalized. If TRUE, the instability path is normalized, accounting for a trivial decrease in instability due to a increasing k (see Haslbeck & Wulff, 2016).
predict

boolean specifying whether the model-based or the model-free variant should be used (see Haslbeck & Wulff, 2016).
method

character string specifying the clustering algorithm. 'kmeans' for the k-means algorithm, 'hierarchical' for hierarchical clustering.
linkage

character specifying the linkage criterion, in case type='hierarchical'. The available options are "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid" or "median". See hclust.
kmIter

integer specifying the the number of restarts of the k-means algorithm in order to avoid local minima.
pbar

logical

Value

a list that contains the optimal k selected by the unnormalized and normalized instability method. It also includes a vector containing the averaged instability path (over bootstrap samples) and a matrix containing the instability path of each bootstrap sample for both the normalized and the unnormalized method.

Author(s)

Dirk U. Wulff <[email protected]> Jonas M. B. Haslbeck <[email protected]>

References

Ben-Hur, A., Elisseeff, A., & Guyon, I. (2001). A stability based method for discovering structure in clustered data. Pacific symposium on biocomputing, 7, 6-17.

Tibshirani, R., & Walther, G. (2005). Cluster validation by prediction strength. Journal of Computational and Graphical Statistics, 14(3), 511-528.

Examples

## Not run: 
  # Generate Data from Gaussian Mixture
  s <- .1
  n <- 50
  data <- rbind(cbind(rnorm(n, 0, s), rnorm(n, 0, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 0, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 0, s)))
  plot(data)

  # Selection of Number of Clusters using Instability-based Measures
  stab_obj <- cStability(data, kseq=2:10)
  print(stab_obj)
  
## End(Not run)

!Deprecated! Selection of number of clusters via clustering instability

Description

!Deprecated! Selection of number of clusters via model-based or model-free, normalized or unnormalized clustering instability.

Usage

cStability_orig(
  data,
  kseq = 2:20,
  nB = 10,
  norm = TRUE,
  predict = TRUE,
  method = "kmeans",
  linkage = "complete",
  kmIter = 5,
  pbar = TRUE
)

Arguments

data

a n x p data matrix of type numeric.
kseq

a vector with considered numbers clusters k > 1
nB

an integer specifying the number of bootstrap comparisons.
norm

logical specifying whether the instability path should be normalized. If TRUE, the instability path is normalized, accounting for a trivial decrease in instability due to a increasing k (see Haslbeck & Wulff, 2016).
predict

boolean specifying whether the model-based or the model-free variant should be used (see Haslbeck & Wulff, 2016).
method

character string specifying the clustering algorithm. 'kmeans' for the k-means algorithm, 'hierarchical' for hierarchical clustering.
linkage

character specifying the linkage criterion, in case type='hierarchical'. The available options are "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid" or "median". See hclust.
kmIter

integer specifying the the number of restarts of the k-means algorithm in order to avoid local minima.
pbar

logical

Value

a list that contains the optimal k selected by the unnormalized and normalized instability method. It also includes a vector containing the averaged instability path (over bootstrap samples) and a matrix containing the instability path of each bootstrap sample for both the normalized and the unnormalized method.

Author(s)

Dirk U. Wulff <[email protected]> Jonas M. B. Haslbeck <[email protected]>

References

Ben-Hur, A., Elisseeff, A., & Guyon, I. (2001). A stability based method for discovering structure in clustered data. Pacific symposium on biocomputing, 7, 6-17.

Tibshirani, R., & Walther, G. (2005). Cluster validation by prediction strength. Journal of Computational and Graphical Statistics, 14(3), 511-528.

Examples

## Not run: 
  # Generate Data from Gaussian Mixture
  s <- .1
  n <- 50
  data <- rbind(cbind(rnorm(n, 0, s), rnorm(n, 0, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 0, s), rnorm(n, 1, s)),
                cbind(rnorm(n, 1, s), rnorm(n, 0, s)))
  plot(data)

  # Selection of Number of Clusters using Instability-based Measures
  stab_obj <- cStability(data, kseq=2:10)
  print(stab_obj)
  
## End(Not run)

Create lookup table

Description

Create lookup table for faculties

Usage

lookup(n = 10000L, root = 200)

Arguments

n

integer specifying the number of
root

numeric specifying the root used to avoid machine limit.

Plot method for cstab objects

Description

plot.cstab plots instability path.

Usage

## S3 method for class 'cstab'
plot(x, ...)

Arguments

x

a cstab object (output of functions cStability).
...

additional arguments passed to print.

Author(s)

Jonas M. B. Haslbeck <[email protected]> Dirk U. Wulff <[email protected]>

Print method for cstab objects

Description

print.cstab prints key variables of cstab objects.

Usage

## S3 method for class 'cstab'
print(x, ...)

Arguments

x

a cstab object (output of functions cStability).
...

additional arguments passed to print.

Author(s)

Jonas M. B. Haslbeck <[email protected]> Dirk U. Wulff <[email protected]>