# gmm16G: Weighted GMM by Gebru et al. (2016) In T4cluster: Tools for Cluster Analysis

## Description

When each observation x_i is associated with a weight w_i > 0, modifying the GMM formulation is required. Gebru et al. (2016) proposed a method to use scaled covariance based on an observation that

\mathcal{N}≤ft(x\vert μ, Σ\right)^w \propto \mathcal{N}≤ft(x\vert μ, \frac{Σ}{w}\right)

by considering the positive weight as a role of precision. Currently, we provide a method with fixed weight case only while the paper also considers a Bayesian formalism on the weight using Gamma distribution.

## Usage

 1 gmm16G(data, k = 2, weight = NULL, ...) 

## Arguments

 data an (n\times p) matrix of row-stacked observations. k the number of clusters (default: 2). weight a positive weight vector of length n. If NULL (default), uniform weight is set. ... extra parameters including maxiterthe maximum number of iterations (default: 10). usediaga logical; covariances are diagonal if TRUE, or full covariances are returned for FALSE (default: FALSE).

## Value

a named list of S3 class T4cluster containing

cluster

a length-n vector of class labels (from 1:k).

mean

a (k\times p) matrix where each row is a class mean.

variance

a (p\times p\times k) array where each slice is a class covariance.

weight

a length-k vector of class weights that sum to 1.

loglkd

log-likelihood of the data for the fitted model.

algorithm

name of the algorithm.

## References

\insertRef

gebru_em_2016T4cluster

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 # ------------------------------------------------------------- # clustering with 'iris' dataset # ------------------------------------------------------------- ## PREPARE data(iris) X = as.matrix(iris[,1:4]) lab = as.integer(as.factor(iris[,5])) ## EMBEDDING WITH PCA X2d = Rdimtools::do.pca(X, ndim=2)$Y ## CLUSTERING WITH DIFFERENT K VALUES cl2 = gmm16G(X, k=2)$cluster cl3 = gmm16G(X, k=3)$cluster cl4 = gmm16G(X, k=4)$cluster ## VISUALIZATION opar <- par(no.readonly=TRUE) par(mfrow=c(1,4), pty="s") plot(X2d, col=lab, pch=19, main="true label") plot(X2d, col=cl2, pch=19, main="gmm16G: k=2") plot(X2d, col=cl3, pch=19, main="gmm16G: k=3") plot(X2d, col=cl4, pch=19, main="gmm16G: k=4") par(opar) 

T4cluster documentation built on Aug. 16, 2021, 9:07 a.m.