| Type: | Package |
| Title: | Quantile-Based Clustering Algorithms |
| Version: | 1.0.1 |
| Date: | 2022-05-26 |
| Author: | Christian Hennig, Cinzia Viroli and Laura Anderlucci |
| Maintainer: | Laura Anderlucci <laura.anderlucci@unibo.it> |
| Description: | Various quantile-based clustering algorithms: algorithm CU (Common theta and Unscaled variables), algorithm CS (Common theta and Scaled variables through lambda_j), algorithm VU (Variable-wise theta_j and Unscaled variables) and algorithm VW (Variable-wise theta_j and Scaled variables through lambda_j). Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering." Electronic Journal of Statistics. 13 (2) 4849 - 4883 <doi:10.1214/19-EJS1640>. |
| License: | GPL-2 | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.0 |
| Imports: | stats |
| NeedsCompilation: | no |
| Packaged: | 2022-05-26 15:43:45 UTC; laura |
| Repository: | CRAN |
| Date/Publication: | 2022-05-26 16:40:02 UTC |
CS quantile-based clustering algorithm
Description
This function allows to run the CS (Common theta and Scaled variables through lambda_j) version of the quantile-based clustering algorithm.
Usage
alg.CS(data, k = 2, eps = 1e-08, it.max = 100, B = 30, lambda = rep(1, p))
Arguments
data |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |
k |
The number of clusters. The default is k=2. |
eps |
The relative convergence tolerances for objective function. The default is set to 1e-8. |
it.max |
A number that gives integer limits on the number of the CS algorithm iterations. By default, it is set to 100. |
B |
The number of times the initialization step is repeated; the default is 30. |
lambda |
The initial value for lambda_j, the variable scaling parameters. By default, lambdas are set to be equal to 1. |
Details
Algorithm CS: Common theta and Scaled variables via lambda_j. A common value of theta is taken but variables are scaled through lambda_j.
Value
A list containing the following elements:
cl |
A vector whose [i]th entry is classification of observation i in the test data. |
qq |
A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h. |
theta |
The estimated common theta. |
Vseq |
The values of the objective function V at each step of the algorithm. |
V |
The final value of the objective function V. |
lambda |
A vector containing the scaling factor for each variable. |
References
Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>
Examples
out <- alg.CS(iris[,-5],k=3)
out$theta
out$qq
out$lambda
table(out$cl)
CU quantile-based clustering algorithm
Description
This function allows to run the CU (Common theta and Unscaled variables) version of the quantile-based clustering algorithm.
Usage
alg.CU(data, k = 2, eps = 1e-08, it.max = 100, B = 30)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |
k |
The number of clusters. The default is k=2. |
eps |
The relative convergence tolerances for objective function. The default is set to 1e-8. |
it.max |
A number that gives integer limits on the number of the CU algorithm iterations. By default, it is set to 100. |
B |
The number of times the initialization step is repeated; the default is 30. |
Details
Algorithm CU: Common theta and Unscaled variables. A common value of theta for all the variables is assumed. This strategy directly generalizes the conventional k-means to other moments of the distribution to better accommodate skewness in the data.
Value
A list containing the following elements:
method |
The chosen parameterization, CU, Common theta and Unscaled variables |
k |
The number of clusters. |
cl |
A vector whose [i]th entry is classification of observation i in the test data. |
qq |
A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h. |
theta |
A vector whose [j]th entry is the percentile theta for variable j. |
Vseq |
The values of the objective function V at each step of the algorithm. |
V |
The final value of the objective function V. |
lambda |
A vector containing the scaling factor for each variable. |
References
Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>
Examples
out <- alg.CU(iris[,-5],k=3)
out$theta
out$qq
table(out$cl)
VS quantile-based clustering algorithm
Description
This function allows to run the VS (Variable-wise theta_j and Scaled variables through lambda_j) version of the quantile-based clustering algorithm.
Usage
alg.VS(data, k = 2, eps = 1e-08, it.max = 100, B = 30, lambda = rep(1, p))
Arguments
data |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |
k |
The number of clusters. The default is k=2. |
eps |
The relative convergence tolerances for objective function. The default is set to 1e-8. |
it.max |
A number that gives integer limits on the number of the VS algorithm iterations. By default, it is set to 100. |
B |
The number of times the initialization step is repeated; the default is 30. |
lambda |
The initial value for lambda_j, the variable scaling parameters. By default, lambdas are set to be equal to 1. |
Details
Algorithm VS: Variable-wise theta_j and Scaled variables via lambda_j. A different theta for every single variable is estimated to better accomodate different degree of skeweness in the data and variables are scaled through lambda_j.
Value
A list containing the following elements:
method |
The chosen parameterization, VS, Variable-wise theta_j and Scaled variables |
k |
The number of clusters. |
cl |
A vector whose [i]th entry is classification of observation i in the test data. |
qq |
A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h. |
theta |
A vector whose [j]th entry is the percentile theta for variable j. |
Vseq |
The values of the objective function V at each step of the algorithm. |
V |
The final value of the objective function V. |
lambda |
A vector containing the scaling factor for each variable. |
References
Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>
Examples
out <- alg.VS(iris[,-5],k=3)
out$theta
out$qq
out$lambda
table(out$cl)
VU quantile-based clustering algorithm
Description
This function allows to run the VU (Variable-wise theta_j and Unscaled variables) version of the quantile-based clustering algorithm.
Usage
alg.VU(data, k = 2, eps = 1e-08, it.max = 100, B = 30)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |
k |
The number of clusters. The default is k=2. |
eps |
The relative convergence tolerances for objective function. The default is set to 1e-8. |
it.max |
A number that gives integer limits on the number of the VU algorithm iterations. By default, it is set to 100. |
B |
The number of times the initialization step is repeated; the default is 30. |
Details
Algorithm VU: Variable-wise theta_j and Unscaled variables. A different theta for every single variable is estimated to better accomodate different degree of skeweness in the data.
Value
A list containing the following elements:
method |
The chosen parameterization, VU, Variable-wise theta_j and Unscaled variables |
k |
The number of clusters. |
cl |
A vector whose [i]th entry is classification of observation i in the test data. |
qq |
A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h. |
theta |
A vector whose [j]th entry is the percentile theta for variable j. |
Vseq |
The values of the objective function V at each step of the algorithm. |
V |
The final value of the objective function V. |
lambda |
A vector containing the scaling factor for each variable. |
References
Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>
Examples
out <- alg.VU(iris[,-5],k=3)
out$theta
out$qq
table(out$cl)
Quantile-based clustering algorithm
Description
This function allows to run the $k$-quantile clustering algorithm, allowing for different constraints: common theta and unscaled variables (CU), common theta and scaled variables (CS), variable-wise theta and unscaled variables (VU) and the variable-wise theta and scaled variables (VS).
Usage
kquantiles(
data,
k = 2,
method = "VS",
eps = 1e-08,
it.max = 100,
B = 30,
lambda = NULL
)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |
k |
The number of clusters. The default is k=2. |
method |
The chosen constrained method. The options are: CU (Common theta and Unscaled variables), CS (Common theta and Scaled variables), VU (Variable-wise theta and Unscaled variables), VS (Variable-wise theta and Scaled variables).The default is the unconstrained method, VS. |
eps |
The relative convergence tolerances for objective function. The default is set to 1e-8. |
it.max |
A number that gives integer limits on the number of the algorithm iterations. By default, it is set to 100. |
B |
The number of times the initialization step is repeated; the default is 30. |
lambda |
The initial value for lambda_j, the variable scaling parameters, for models CS and VS. By default, lambdas are set to be equal to 1. |
Details
Algorithm CU: Common theta and Unscaled variables. A common value of theta for all the variables is assumed. Algorithm CS: Common theta and Scaled variables via lambda_j. A common value of theta is taken but variables are scaled through lambda_j. Algorithm VU: Variable-wise theta_j and Unscaled variables. A different theta for every single variable is estimated to better accomodate different degree of skeweness in the data. Algorithm VS: Variable-wise theta_j and Scaled variables via lambda_j. A different theta for every single variable is estimated to better accomodate different degree of skeweness in the data and variables are scaled through lambda_j.
Value
A list containing the following elements:
method |
The chosen parameterization. |
k |
The number of clusters. |
cl |
A vector whose [i]th entry is classification of observation i in the test data. |
qq |
A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h. |
theta |
A vector whose [j]th entry is the percentile theta for variable j. |
Vseq |
The values of the objective function V at each step of the algorithm. |
V |
The final value of the objective function V. |
lambda |
A vector containing the scaling factor for each variable. |
References
Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>
Examples
out <- kquantiles(iris[,-5],k=3,method="VS")
out$theta
out$qq
table(out$cl)