neg_objective_function

Negative objective function for gmmssl

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.

Ziyang Lyu

gmmsslm

Semi-Supervised Gaussian Mixture Model with a Missing-Data
Mechanism

Ziyang Lyu 

Daniel Ahfock 

Ryan Thompson 

Geoffrey J. McLachlan 

neg_objective_function function

<dl><dt>dat</dt>
<dd>An \(n\times p\) matrix where each row represents an individual observation</dd>
<dt>zm</dt>
<dd>An n-dimensional vector of group partition including the missing-label, denoted as NA.</dd>
<dt>g</dt>
<dd>Number of multivariate Gaussian groups.</dd>
<dt>par</dt>
<dd>An informative vector including <code>mu</code>, <code>pi</code>,<code>sigma</code> and <code>xi</code>.</dd>
<dt>ncov</dt>
<dd>Options of structure of sigma matrix; the default value is 2;
<code>ncov</code> = 1 for a common covariance matrix;
<code>ncov</code> = 2 for the unequal covariance/scale matrices.</dd>
<dt>type</dt>
<dd>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.</dd></dl>

Arguments

Negative objective function for gmmssl — neg_objective_function

<dl>

<dt>dat</dt>
<dd>An \(n\times p\) matrix where each row represents an individual observation</dd>


<dt>zm</dt>
<dd>An n-dimensional vector of group partition including the missing-label, denoted as NA.</dd>


<dt>g</dt>
<dd>Number of multivariate Gaussian groups.</dd>


<dt>par</dt>
<dd>An informative vector including <code>mu</code>, <code>pi</code>,<code>sigma</code> and <code>xi</code>.</dd>


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


<dt>type</dt>
<dd>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.</dd>

</dl>

neg_objective_function: Negative objective function for gmmssl

Description

Usage

Value

Arguments