EMMIXSSL (version 1.1.1)

Classifier_Bayes: Classifier based on Bayes rule

Description

A classifier based on Bayes rule, that is maximum a posterior probabilities of class membership

Usage

Classifier_Bayes(dat, n, p, g, pi, mu, sigma, ncov = 2)

Value

cluster

A vector of the class membership.

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

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.

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. The Bayes' Classifier of allocation assigns an entity with feature vector \(y_j\) to Class \(C_k\) if $$ k= arg max_i \tau_i(y_j;\theta). $$

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,ncov=2)
cluster<-Classifier_Bayes(dat=dat$Y,n=150,p=3,g=4,mu=mu,sigma=sigma,pi=pi,ncov=2)