Type: Package
Title: Semi-Supervised Gaussian Mixture Model with a Missing-Data Mechanism
Version: 1.1.6
Description: The algorithm of semi-supervised learning is based on finite Gaussian mixture models and includes a mechanism for handling missing data. It aims to fit a g-class Gaussian mixture model using maximum likelihood. The algorithm treats the labels of unclassified features as missing data, building on the framework introduced by Rubin (1976) <doi:10.2307/2335739> for missing data analysis. By taking into account the dependencies in the missing pattern, the algorithm provides more information for determining the optimal classifier, as specified by Bayes' rule.
Depends: R (≥ 3.1.0), mvtnorm,stats,methods
License: GPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.2.3
NeedsCompilation: no
Packaged: 2025-03-29 06:44:04 UTC; lyu
Author: Ziyang Lyu [aut, cre], Daniel Ahfock [aut], Ryan Thompson [aut], Geoffrey J. McLachlan [aut]
Maintainer: Ziyang Lyu <ziyang.lyu@unsw.edu.au>
Repository: CRAN
Date/Publication: 2025-04-17 04:20:02 UTC

Bayes' rule of allocation

Description

Bayes' rule of allocation

Usage

bayesclassifier(dat, p, g, pi = NULL, mu = NULL, sigma = NULL, paralist = NULL)

Arguments

dat

An n\times p matrix where each row represents an individual observation.

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

paralist

A list containing the required parameters (\pi, \mu, \Sigma).

Details

Classifier specified by Bayes' rule

The classifier/Bayes rule of allocation R(y_j;\theta) assigns an entity with observation y_j to class C_k (that is, R(y_j;\theta)=k) if k=\arg\max_i \tau_i(y_j;\theta),

Value

clust

Class membership for the ith entity

Examples

n <- 150
pi <- c(0.25, 0.25, 0.25, 0.25)
sigma <- array(0, dim = c(3, 3, 4))
sigma[, , 1] <- diag(1, 3)
sigma[, , 2] <- diag(2, 3)
sigma[, , 3] <- diag(3, 3)
sigma[, , 4] <- diag(4, 3)
mu <- matrix(c(0.2, 0.3, 0.4, 0.2, 0.7, 0.6, 0.1, 0.7, 1.6, 0.2, 1.7, 0.6), 3, 4)
dat <- rmix(n = n, pi = pi, mu = mu, sigma = sigma)
params <- list(pi=pi,mu = mu, sigma = sigma)
clust <- bayesclassifier(dat=dat$Y,p=3,g=4,paralist=params)

Bootstrap Analysis for gmmsslm

Description

This file provides functions to perform bootstrap analysis on the results of the gmmsslm function.

This function performs non-parametric bootstrap to assess the variability of the gmmsslm function outputs.

Usage

bootstrap_gmmsslm(
  dat,
  zm,
  pi,
  mu,
  sigma,
  paralist,
  xi,
  type,
  iter.max = 500,
  eval.max = 500,
  rel.tol = 1e-15,
  sing.tol = 1e-15,
  B = 2000
)

Arguments

dat

A matrix where each row represents an individual observation.

zm

A matrix or data frame of labels corresponding to dat.

pi

A numeric vector representing the mixing proportions.

mu

A matrix representing the location parameters.

sigma

An array representing the covariance matrix or list of covariance matrices.

paralist

A list of parameters.

xi

A numeric value representing the coefficient for a logistic function of the Shannon entropy.

type

A character value indicating the type of Gaussian mixture model.

iter.max

An integer indicating the maximum number of iterations.

eval.max

An integer indicating the maximum number of evaluations.

rel.tol

A numeric value indicating the relative tolerance.

sing.tol

A numeric value indicating the singularity tolerance.

B

An integer indicating the number of bootstrap samples.

Value

A list containing mean and sd of bootstrap samples for pi, mu, sigma, and xi.

Transform a variance matrix into a vector

Description

Transform a variance matrix into a vector i.e., Sigma=R^T*R

Usage

cov2vec(sigma)

Arguments

sigma

A p\times p variance matrix

Details

The variance matrix is decomposed by computing the Choleski factorization of a real symmetric positive-definite square matrix. Then, storing the upper triangular factor of the Choleski decomposition into a vector.

Value

par A vector representing a variance matrix

Discriminant function

Description

Discriminant function in the particular case of g=2 classes with an equal-covariance matrix

Usage

discriminant_beta(pi, mu, sigma)

Arguments

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix.

Details

Discriminant function in the particular case of g=2 classes with an equal-covariance matrix can be expressed

d(y_i,\beta)=\beta_0+\beta_1 y_i,

where \beta_0=\log\frac{\pi_1}{\pi_2}-\frac{1}{2}\frac{\mu_1^2-\mu_2^2}{\sigma^2} and \beta_1=\frac{\mu_1-\mu_2}{\sigma^2}.

Value

beta0

An intercept of discriminant function

beta

A coefficient of discriminant function

Error rate of the Bayes rule for a g-class Gaussian mixture model

Description

Error rate of the Bayes rule for a g-class Gaussian mixture model

Usage

erate(dat, p, g, pi = NULL, mu = NULL, sigma = NULL, paralist = NULL, clust)

Arguments

dat

An n\times p matrix where each row represents an individual observation

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

paralist

A list containing the required parameters (\pi, \mu, \Sigma).

clust

An n-dimensional vector of class partition.

Details

The error rate of the Bayes rule for a g-class Gaussian mixture model is given by

err(y;\theta)=1-\sum_{i=1}^g\pi_i Pr\{R(y;\theta)=i\mid Z \in C_i\}.

Here, we write

Pr\{R(y;\theta) \in C_i\mid Z\in C_i\}=\frac{\sum_{j=1}^nI_{C_i}(z_j)Q[z_j,R(y;\theta) ]}{\sum_{j=1}^nI_{C_i}(z_j)},

where Q[u,v]=1 if u=v and Q[u,v]=0 otherwise, and I_{C_i}(z_j) is an indicator function for the ith class.

Value

errval

a value of error rate

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
xi<-c(-0.5,1)
m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi)
zm<-dat$clust
zm[m==1]<-NA
inits<-initialvalue(g=4,zm=zm,dat=dat$Y)

fit_pc<-gmmsslm(dat=dat$Y,zm=zm,pi=inits$pi,mu=inits$mu,sigma=inits$sigma,xi=xi,type='full')
parlist<-paraextract(fit_pc)
erate(dat=dat$Y,p=3,g=4,paralist=parlist,clust=dat$clust)

Error rate of the Bayes rule for two-class Gaussian homoscedastic model

Description

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model

Usage

errorrate(beta0, beta, pi, mu, sigma)

Arguments

beta0

An intercept parameter of the discriminant function coefficients.

beta

A p \times 1 vector for the slope parameter of the discriminant function.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix.

Details

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model can be expressed as

err(\beta)=\pi_1\phi\{-\frac{\beta_0+\beta_1^T\mu_1}{(\beta_1^T\Sigma\beta_1)^{\frac{1}{2}}}\}+\pi_2\phi\{\frac{\beta_0+\beta_1^T\mu_2}{(\beta_1^T\Sigma\beta_1)^{\frac{1}{2}}}\}

where \phi is a normal probability function with mean \mu_i and covariance matrix \Sigma_i.

Value

errval

A vector of error rate.

Gastrointestinal dataset

Description

The collected dataset is composed of 76 colonoscopic videos (recorded with both White Light (WL) and Narrow Band Imaging (NBI)), the histology (classification ground truth), and the endoscopist's opinion (including 4 experts and 3 beginners). There are $n=76$ observations, and each observation consists of 698 features extracted from colonoscopic videos on patients with gastrointestinal lesions.

References

http://www.depeca.uah.es/colonoscopy_dataset/

Posterior probability

Description

Get posterior probabilities of class membership

Usage

get_clusterprobs(
  dat,
  n,
  p,
  g,
  pi = NULL,
  mu = NULL,
  sigma = NULL,
  paralist = NULL
)

Arguments

dat

An n\times p matrix where each row represents an individual observation

n

Number of observations.

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

paralist

A list containing the required parameters (\pi, \mu, \Sigma).

Details

The posterior probability can be expressed as

\tau_i(y_j;\theta)=Prob\{z_{ij}=1|y_j\}=\frac{\pi_i\phi(y_j;\mu_i,\Sigma_i)}{\sum_{h=1}^g\pi_h\phi(y_j;\mu_h,\Sigma_h) },

where \phi is a normal probability function with mean \mu_i and covariance matrix \Sigma_i, and z_{ij} is is a zero-one indicator variable denoting the class of origin.

Value

clusprobs

Posterior probabilities of class membership for the ith entity

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
tau<-get_clusterprobs(dat=dat$Y,n=150,p=3,g=4,mu=mu,sigma=sigma,pi=pi)

Shannon entropy

Description

Shannon entropy

Usage

get_entropy(dat, n, p, g, pi = NULL, mu = NULL, sigma = NULL, paralist = NULL)

Arguments

dat

An n\times p matrix where each row represents an individual observation

n

Number of observations.

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g.

paralist

A list containing the required parameters (\pi, \mu, \Sigma). It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

Details

The concept of information entropy was introduced by shannon1948mathematical. The entropy of y_j is formally defined as

e_j( y_j; \theta)=-\sum_{i=1}^g \tau_i( y_j; \theta) \log\tau_i(y_j;\theta).

Value

clusprobs

The posterior probabilities of the i-th entity that belongs to the j-th group.

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
en<-get_entropy(dat=dat$Y,n=150,p=3,g=4,mu=mu,sigma=sigma,pi=pi)

Fitting Gaussian mixture model to a complete classified dataset or an incomplete classified dataset with/without the missing-data mechanism.

Description

Fitting Gaussian mixture model to a complete classified dataset or an incomplete classified dataset with/without the missing-data mechanism.

Usage

gmmsslm(
  dat,
  zm,
  pi = NULL,
  mu = NULL,
  sigma = NULL,
  paralist = NULL,
  xi = NULL,
  type,
  iter.max = 500,
  eval.max = 500,
  rel.tol = 1e-15,
  sing.tol = 1e-15
)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

paralist

A list containing the required parameters (\pi, \mu, \Sigma).

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

type

Three types of Gaussian mixture models, 'ign' indicates fitting the model to a partially classified sample on the basis of the likelihood that ignores the missing label mechanism, 'full' indicates fitting the model to a partially classified sample on the basis of the full likelihood, taking into account the missing-label mechanism, and 'com' indicate fitting the model to a completed classified sample.

iter.max

Maximum number of iterations allowed. Defaults to 500

eval.max

Maximum number of evaluations of the objective function allowed. Defaults to 500

rel.tol

Relative tolerance. Defaults to 1e-15

sing.tol

Singular convergence tolerance; defaults to 1e-20.

Value

A gmmsslmFit object containing the following slots:

objective

Value of objective likelihood

convergence

Value of convergence

iteration

Number of iterations

obs

Input data matrix

n

Number of observations

p

Number of variables

g

Number of Gaussian components

type

Type of Gaussian mixture model

pi

Estimated vector of the mixing proportions

mu

Estimated matrix of the location parameters

sigma

Estimated covariance matrix or list of covariance matrices

xi

Estimated coefficient vector for a logistic function of the Shannon entropy

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
xi<-c(-0.5,1)
m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi)
zm<-dat$clust
zm[m==1]<-NA
inits<-initialvalue(g=4,zm=zm,dat=dat$Y)

fit_pc<-gmmsslm(dat=dat$Y,zm=zm,paralist=inits,xi=xi,type='full')

gmmsslmFit Class

Description

gmmsslmFit objects store the results of fitting Gaussian mixture models using the gmmsslm function.

An S4 class representing the result of fitting a Gaussian mixture model using gmmsslm()

Slots

objective

A numeric value representing the objective likelihood.

ncov

A numeric value representing the number of covariance matrices.

convergence

A numeric value representing the convergence value.

iteration

An integer value representing the number of iterations.

obs

A matrix containing the input data.

m

A logical vector representing label indicators.

n

An integer value representing the number of observations.

p

An integer value representing the number of variables.

g

An integer value representing the number of Gaussian components.

type

A character value representing the type of Gaussian mixture model.

pi

A numeric vector representing the mixing proportions.

mu

A matrix representing the location parameters.

sigma

An array representing the covariance matrix or list of covariance matrices.

xi

A numeric value representing the coefficient for a logistic function of the Shannon entropy.

See Also

gmmsslm

Initial values for ECM

Description

Inittial values for claculating the estimates based on solely on the classified features.

Usage

initialvalue(dat, zm, g, ncov = 2)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

g

Number of multivariate normal classes.

ncov

Options of structure of sigma matrix; the default value is 2; ncov = 1 for a common covariance matrix; ncov = 2 for the unequal covariance/scale matrices.

Value

pi

A g-dimensional initial vector of the mixing proportions.

mu

A initial p \times g matrix of the location parameters.

sigma

A p\times p covariance matrix if ncov=1, or a list of g covariance matrices with dimension p\times p \times g if ncov=2.

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
xi<-c(-0.5,1)
m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi)
zm<-dat$clust
zm[m==1]<-NA
initlist<-initialvalue(g=4,zm=zm,dat=dat$Y,ncov=2)

Transfer a list into a vector

Description

Transfer a list into a vector

Usage

list2par(p, g, pi, mu, sigma, xi = NULL, type = c("ign", "full", "com"))

Arguments

p

Dimension of observation vecor.

g

Number of multivariate normal classes.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

type

Three types to fit to the model, 'ign' indicates fitting the model on the basis of the likelihood that ignores the missing label mechanism, 'full' indicates that the model to be fitted on the basis of the full likelihood, taking into account the missing-label mechanism, and 'com' indicate that the model to be fitted to a completed classified sample.

Value

par

a vector including all list information

Full log-likelihood function

Description

Full log-likelihood function with both terms of ignoring and missing

Usage

loglk_full(dat, zm, pi, mu, sigma, xi)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Details

The full log-likelihood function can be expressed as

\log L_{PC}^{({full})}(\boldsymbol{\Psi})=\log L_{PC}^{({ig})}(\theta)+\log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi}),

where\log L_{PC}^{({ig})}(\theta)is the log likelihood function formed ignoring the missing in the label of the unclassified features, and \log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi}) is the log likelihood function formed on the basis of the missing-label indicator.

Value

lk

Log-likelihood value

Log likelihood for partially classified data with ingoring the missing mechanism

Description

Log likelihood for partially classified data with ingoring the missing mechanism

Usage

loglk_ig(dat, zm, pi, mu, sigma)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

Details

The log-likelihood function for partially classified data with ingoring the missing mechanism can be expressed as

\log L_{PC}^{({ig})}(\theta)=\sum_{j=1}^n \left[ (1-m_j)\sum_{i=1}^g z_{ij}\left\lbrace \log\pi_i+\log f_i(y_j;\omega_i)\right\rbrace +m_j\log \left\lbrace \sum_{i=1}^g\pi_i f_i(y_j;\omega_i)\right\rbrace \right],

where m_j is a missing label indicator, z_{ij} is a zero-one indicator variable defining the known group of origin of each, and f_i(y_j;\omega_i) is a probability density function with parameters \omega_i.

Value

lk

Log-likelihood value.

Log likelihood function formed on the basis of the missing-label indicator

Description

Log likelihood for partially classified data based on the missing mechanism with the Shanon entropy

Usage

loglk_miss(dat, zm, pi, mu, sigma, xi)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

xi

A 2-dimensional vector containing the initial values of the coefficients in the logistic function of the Shannon entropy.

Details

The log-likelihood function formed on the basis of the missing-label indicator can be expressed by

\log L_{PC}^{({miss})}(\theta,\boldsymbol{\xi})=\sum_{j=1}^n\big[ (1-m_j)\log\left\lbrace 1-q(y_j;\theta,\boldsymbol{\xi})\right\rbrace +m_j\log q(y_j;\theta,\boldsymbol{\xi})\big],

where q(y_j;\theta,\boldsymbol{\xi}) is a logistic function of the Shannon entropy e_j(y_j;\theta), and m_j is a missing label indicator.

Value

lk

loglikelihood value

log summation of exponential function

Description

log summation of exponential variable vector.

Usage

logsumexp(x)

Arguments

x

A variable vector.

Value

val

log summation of exponential variable vector.

Label matrix

Description

Convert class indicator into a label maxtrix.

Usage

makelabelmatrix(clust)

Arguments

clust

An n-dimensional vector of class partition.

Value

Z

A matrix of class indicator.

Examples

cluster<-c(1,1,2,2,3,3)
label_maxtrix<-makelabelmatrix(cluster)

Negative objective function for gmmssl

Description

Negative objective function for gmmssl

Usage

neg_objective_function(
  dat,
  zm,
  g,
  par,
  ncov = 2,
  type = c("ign", "full", "com")
)

Arguments

dat

An n\times p matrix where each row represents an individual observation

zm

An n-dimensional vector of group partition including the missing-label, denoted as NA.

g

Number of multivariate Gaussian groups.

par

An informative vector including mu, pi,sigma and xi.

ncov

Options of structure of sigma matrix; the default value is 2; ncov = 1 for a common covariance matrix; ncov = 2 for the unequal covariance/scale matrices.

type

Three types to fit to the model, 'ign' indicates fitting the model on the basis of the likelihood that ignores the missing label mechanism, 'full' indicates that the model to be fitted on the basis of the full likelihood, taking into account the missing-label mechanism, and 'com' indicate that the model to be fitted to a completed classified sample.

Value

val

Value of negatvie objective function.

Normalize log-probability

Description

Normalize log-probability.

Usage

normalise_logprob(x)

Arguments

x

A variable vector.

Value

val

A normalize log probability of variable vector.

Transfer a vector into a list

Description

Transfer a vector into a list

Usage

par2list(par, g, p, ncov = 2, type = c("ign", "full", "com"))

Arguments

par

A vector with list information.

g

Number of multivariate normal classes.

p

Dimension of observation vecor.

ncov

Options of structure of sigma matrix; the default value is 2; ncov = 1 for a common covariance matrix that sigma is a p\times p matrix. ncov = 2 for the unequal covariance/scale matrices that sigma represents a list of g matrices with dimension p\times p \times g.

type

Three types to fit to the model, 'ign' indicates fitting the model on the basis of the likelihood that ignores the missing label mechanism, 'full' indicates that the model to be fitted on the basis of the full likelihood, taking into account the missing-label mechanism, and 'com' indicate that the model to be fitted to a completed classified sample.

Value

parlist

Return a list including mu, pi, sigma and xi.

Extract parameter list from gmmsslmFit objects

Description

This function extracts the parameters from a gmmsslmFit object, including p, g, pi, mu, and sigma.

Usage

paraextract(object)

Arguments

object

A gmmsslmFit object.

Plot Missingness Mechanism and Boxplot

Description

This function plots the smoothed values of '-log(entropy)' against the missingness mechanism and a boxplot of entropy for labeled vs. unlabeled observations.

Usage

plot_missingness(
  dat,
  g,
  parlist,
  zm,
  bandwidth = 5,
  range.x = c(0, 5),
  ylim = NULL,
  kernel = "normal"
)

Arguments

dat

An n\times p matrix where each row represents an individual observation

g

Number of multivariate normal classes.

parlist

A list containing the required parameters (\pi, \mu, \Sigma).

zm

An n-dimensional vector containing the class labels including the missing-label denoted as NA.

bandwidth

Bandwidth for kernel smoothing. Default is 5.

range.x

Range for x values. Default is c(0, 5).

ylim

The y-axis limits in the form of c(ylim[1], ylim[2]). Default is NULL.

kernel

Kernel type for smoothing. Default is 'normal'.

Value

A plot.

Predict unclassified label

Description

This function predicts unclassified label from a gmmsslmFit object.

Usage

predict(object)

Arguments

object

A gmmsslmFit object.

Transfer a probability vector into a vector

Description

Transfer a probability vector into an informative vector

Usage

pro2vec(pro)

Arguments

pro

An propability vector

Value

y An informative vector

Generation of a missing-data indicator

Description

Generate the missing label indicator

Usage

rlabel(dat, pi, mu, sigma, xi)

Arguments

dat

An n\times p matrix where each row represents an individual observation.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

xi

A 2-dimensional coefficient vector for a logistic function of the Shannon entropy.

Value

m

A n-dimensional vector of missing label indicator. The element of outputs m represents its label indicator is missing if m equals 1, otherwise its label indicator is available if m equals to 0.

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)
xi<-c(-0.5,1)
m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi)

Normal mixture model generator.

Description

Generate random observations from the normal mixture distributions.

Usage

rmix(n, pi, mu, sigma)

Arguments

n

Number of observations.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix,or a list of g covariance matrices with dimension p\times p \times g. It is assumed to fit the model with a common covariance matrix if sigma is a p\times p covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices.

Value

Y

An n\times p numeric matrix with samples drawn in rows.

Z

An n\times g numeric matrix; each row represents zero-one indicator variables defining the known class of origin of each.

clust

An n-dimensional vector of class partition.

Examples

n<-150
pi<-c(0.25,0.25,0.25,0.25)
sigma<-array(0,dim=c(3,3,4))
sigma[,,1]<-diag(1,3)
sigma[,,2]<-diag(2,3)
sigma[,,3]<-diag(3,3)
sigma[,,4]<-diag(4,3)
mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4)
dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma)

Summary method for gmmsslmFit objects

Description

This function extracts summary information from a gmmsslmFit object, including objective value, ncov, convergence, iteration, and type.

Usage

summary(object)

Arguments

object

A gmmsslmFit object.

Transform a vector into a matrix

Description

Transform a vector into a matrix i.e., Sigma=R^T*R

Usage

vec2cov(par)

Arguments

par

A vector representing a variance matrix

Details

The variance matrix is decomposed by computing the Choleski factorization of a real symmetric positive-definite square matrix. Then, storing the upper triangular factor of the Choleski decomposition into a vector.

Value

sigma A variance matrix

Transfer an informative vector to a probability vector

Description

Transfer an informative vector to a probability vector

Usage

vec2pro(vec)

Arguments

vec

An informative vector

Value

pro A probability vector