| Title: | Fit 'CemCO' Algorithm |
| Version: | 0.2 |
| Author: | Carlos Relvas [aut], Andre Fujita [aut, cre] |
| Maintainer: | Andre Fujita <andrefujita@usp.br> |
| Description: | 'CemCO' algorithm, a model-based (Gaussian) clustering algorithm that removes/minimizes the effects of undesirable covariates during the clustering process both in cluster centroids and in cluster covariance structures (Relvas C. & Fujita A., (2020) <doi:10.48550/arXiv.2004.02333>). |
| Depends: | R (≥ 3.1.0) |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| Imports: | doParallel, nnet, rootSolve, foreach, MASS, mclust, mvtnorm |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-04-24 18:43:05 UTC; carlosrelvas |
| Repository: | CRAN |
| Date/Publication: | 2023-04-25 08:00:02 UTC |
Fit CemCO algorithm using multiple threads of the machine
Description
Model-based clustering based on parameterized finite Gaussian mixture models with covariates effects on the distribution means. Models are estimated by an EM algorithm running in multiple threads of the machine
Usage
CemCO(data, y, G, max_iter=100, n_start=20, cores=4)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
G |
An integer specifying the numbers of mixture components (clusters) |
max_iter |
maximum number of iterations of the EM optimization (default value equals to 100) |
n_start |
how many random sets should be chosen? (default value equals to 20) |
cores |
number of cores for EM optimization (default value equals to 4) |
Details
This function optimizes the log likelihood of the CemCO algorithm using a implementation of the EM algorithm. If categorial features need to be used, please create dummies or use another encode method.
Value
The function output is a list
fitted parameters |
The estimated parameters of the CemCO algorithm, including clusters centroids, covariance matrix, covariate effects of each cluster and a priori probability of each cluster. |
log likelihood |
The optimal log likelihood estimated by the model |
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(60), rnorm(60))
Y = cbind(rnorm(60), rnorm(60))
K = 2
fit <- CemCO(X, Y, K, max_iter=10, n_start=1, cores=1)
params <- fit[[1]] ## fitted parameters
ll <- fit[[2]] ## log likelihood
Fit CemCO algorithm with covariates effects on cluster centroids and covariance matrices.
Description
Model-based clustering based on parameterized finite Gaussian mixture models with covariates effects on the distribution means and the distribution covariance matrices. Models are estimated by an EM algorithm.
Usage
CemCOVar(data, y, G, y_cov, max_iter=100, n_start=20, cores=4)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
G |
An integer specifying the numbers of mixture components (clusters) |
y_cov |
numeric matrix of data to use as covariates for the covariance effect. Non-numerical values should be converted to integer or float (e.g. dummies) |
max_iter |
maximum number of iterations of the EM optimization (default value equals to 100) |
n_start |
how many random sets should be chosen? (default value equals to 20) |
cores |
number of cores for EM optimization (default value equals to 4) |
Details
This function optimizes the log likelihood of the CemCO algorithm with covariates effects on cluster centroids and covariance matrices using a implementation of the EM algorithm. The covariates associated with the distributions means and with the distributions covariance matrices do not need to be the same.
Value
The function output is a list
fitted parameters |
The estimated parameters of the CemCO algorithm, including clusters centroids, covariance matrix, covariate effects of each cluster and a priori probability of each cluster. |
log likelihood |
The optimal log likelihood estimated by the model |
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(20), rnorm(20))
Y = cbind(rnorm(20), rnorm(20))
K = 2
fit <- CemCOVar(X, Y, K, Y[,1], max_iter=5, n_start=1, cores=1)
params <- fit[[1]] ## fitted parameters
ll <- fit[[2]] ## log likelihood
Calculate the E step of the CemCO algorithm with covariates effects on distributions means.
Description
Implements the expectation step of EM algorithm for parameterized Gaussian mixture models with covariates effects on the distribution means. It is also used to calculate the a posteriori probability of each observation belong to each cluster.
Usage
EStep(data, Y, phi, G)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
Y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
phi |
list of fitted parameters in the same format as the output of the CemCO function |
G |
An integer specifying the numbers of mixture components (clusters) |
Details
Calculate the a posteriori probability of each observation belong to each cluster given the data and the current parameters estimation.
Value
Returns a n x G numeric matrix where n represents the number of observations (number of rows of data) and G (the number of clusters). The value i, j represents the probability of the i-th observation belong to j-th cluster.
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(60), rnorm(60))
Y = cbind(rnorm(60), rnorm(60))
K = 2
fit <- CemCO(X, Y, K, max_iter=10, n_start=1, cores=1)
prob <- EStep(X, Y, fit[[1]], K)
Calculate the E step of the CemCO algorithm with covariates effects on distributions means and distributions covariance matrices.
Description
Implements the expectation step of EM algorithm for parameterized Gaussian mixture models with covariates effects on the distribution means and the distribution covariance matrices. It is also used to calculate the posteriori probability of each observation belong to each cluster.
Usage
EStepVar(data, Y, phi, G, y_cov)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
Y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
phi |
list of fitted parameters in the same format as the output of the CemCO function |
G |
An integer specifying the numbers of mixture components (clusters) |
y_cov |
numeric matrix of data to use as covariates for the covariance effect. Non-numerical values should be converted to integer or float (e.g. dummies). |
Details
Calculate the a posteriori probability of each observation belong to each cluster given the data and the current parameters estimation.
Value
Returns a n x G numeric matrix where n represents the number of observations (number of rows of data) and G (the number of clusters). The value i, j represents the probability of the i-th observation belong to j-th cluster.
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(10), rnorm(10))
Y = cbind(rnorm(10), rnorm(10))
K = 2
fit <- CemCOVar(X, Y, K, Y[,1], max_iter=2, n_start=1, cores=1)
prob <- EStepVar(X, Y, fit[[1]], K, Y[,1])
Log likelihood of the CemCO algorithm with covariates effects on distributions means.
Description
Returns the log-likelihood of the CemCO algorithm with covariates effects on distributions means.
Usage
LogLike(data, Y, phi, G)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
Y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
phi |
list of fitted parameters in the same format as the output of the CemCO function |
G |
An integer specifying the numbers of mixture components (clusters) |
Details
Calculate the log likelihood of the mixture guassian with covariates effects on distributions means. This function is used in the optimization process of the EM algorithm used to estimate the CemCO parameters.
Value
Return the value of the log likelihood.
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(60), rnorm(60))
Y = cbind(rnorm(60), rnorm(60))
K = 2
fit <- CemCO(X, Y, K, max_iter=10, n_start=1, cores=1)
ll <- LogLike(X, Y, fit[[1]], K)
Log likelihood of the CemCO algorithm with covariates effects on distributions means and distributions covariance matrices.
Description
Returns the log-likelihood of the CemCO algorithm with covariates effects on distributions means and distributions covariance matrices.
Usage
LogLikeVar(data, Y, phi, G, y_cov)
Arguments
data |
A numeric vector, matrix, or data frame of observations. Non-numerical values should be converted to integer or float (e.g. dummies). If matrix or data frame, rows and columns correspond to observations (n) and variables (P). |
Y |
numeric matrix of data to use as covariates. Non-numerical values should be converted to integer or float (e.g. dummies). |
phi |
list of fitted parameters in the same format as the output of the CemCO function. |
G |
An integer specifying the numbers of mixture components (clusters). |
y_cov |
numeric matrix of data to use as covariates for the covariance effect. Non-numerical values should be converted to integer or float (e.g. dummies). |
Details
Calculate the log likelihood of the mixture guassian distribution given by the CemCO algorithm with covariates effects on distributions means and distributions covariance matrices. This function is used in the optimization process of the EM algorithm used to estimate the CemCO parameters.
Value
Return the value of the log likelihood.
Author(s)
Relvas, C. & Fujita, A.
References
Stage I non-small cell lung cancer stratification by using a model-based clustering algorithm with covariates, Relvas et al.
Examples
set.seed(42)
X = cbind(rnorm(10), rnorm(10))
Y = cbind(rnorm(10), rnorm(10))
K = 2
fit <- CemCOVar(X, Y, K, Y[,1], max_iter=2 , n_start=1, cores=1)
ll <- LogLikeVar(X, Y, fit[[1]], K, Y[,1])