R Notebook

# HLCM vs MCLUST vs MDA

experiment to asses the different classes found by each method discusing about the individual observations predicted by each

Sonar Dataset

data(Sonar, package = "mlbench")
Sonar$Class <- 1*(Sonar$Class == "M")

Compare.df <- as.data.frame( Sonar$Class)

FRESA HLCM fitting and extraction of classes found

Meta-algorithm that finds lattent classes by EM

• by getting the classification on every lattent class 2* lattentclass + 1*(testResult >= 0.5) [one per diferent classification for different latent class ]

set.seed(42)

sonarHlcm <- HLCM_EM(Class ~., Sonar,hysteresis = 0.1)

## [+++++-][++--][+++++++]( 50 )[+++-][++++-]( 22 )[++-][+++++-]( 11 )[+++--][++++++---]( 14 )[++-][++++-]( 10 )[++-][++-+--]( 16 )[++-][+++-]( 15 )[++-][+++-]( 14 )[+--][+++-]( 22 )[+-][+++++-]( 4 )< 168 , 160 , 106 , 5 >

predict.latentClass <- function(model,data){
  testResult <-  predict(model,data)
  #eliminate the first column because it isnt a class
  prbclass <- attr(testResult,"probabilities")[,-1] 
  latentclass <- apply(prbclass,1,which.max)
  result <- list(classification = 2*latentclass + 1*(testResult >= 0.5),
                 outcome=testResult,
                 latentclass=latentclass)
  
  return(result)
}


prd.Hlcm <- predict.latentClass(sonarHlcm,Sonar)

#2. get the classification per class 2* lattentclass + 1*(testResult >= 0.5) 
# [one per diferent classification for different latent class]
prd.Hlcm.2 <- prd.Hlcm$classification


Compare.df <- cbind(Compare.df,prd.Hlcm.2 )
Compare.df$`Sonar$Class` <- NULL 

mclustDA fitting and extraction of classes found

Finite Gaussian mixture modelling fitted via EM algorithm for model-based clustering, classification, and density estimation, including Bayesian regularization and dimension reduction.

• the lattent classes or components are estimated with a model for each label in the target variable

SonarMclustDA <- MclustDA(data =Sonar ,class = Sonar$Class)

MclustDA.getclass  <- function(MclustDA.obj) {
  models <-MclustDA.obj$models
  print( paste("classes found: ", length(MclustDA.obj$models)) )
  predicted <- c()
  i= 1
  G = 0 #number of components found in previous model 
  for (model in models){
    print( paste("components found in class (",i,"): ",model$G),sep ="" )
    predicted <- c(predicted,model$classification +G)
    G = model$G + G # to differenciate from components with same label but different class
    i = i+1
    }
  return(predicted)
}

prd.mclust <- MclustDA.getclass(SonarMclustDA) 

## [1] "classes found:  2"
## [1] "components found in class ( 1 ):  5"
## [1] "components found in class ( 2 ):  1"

#summary(SonarMclustDA)

Compare.df <- cbind(Compare.df,prd.mclust)

MDA fitting and extraction of classes found

Mixture discriminant analysis.

• this approach same as the MclustDA generates two classes (one per label in the target variable) and then it creates 3 components by default

sonarMDA <- mda(Class ~ ., Sonar)

MDA.getclass  <- function(MDA.obj) {
  print( paste("classes found: ", length(MDA.obj$weights)) )
  predicted <- c()
  i= 1
  G = 0 #number of components found in previous model 
  for (weights in MDA.obj$weights){
    print( paste("components found in class (",i,"): ",dim(weights)[2] ))
    print( paste("observations found in class (",i,"): ",dim(weights)[1] ))
    component <-  apply(weights,1,which.max) # get the component which has max prob
    predicted <- c(predicted,component+G)
    G = dim(weights)[2] + G # to differenciate from components with same label but different class
    i = i+1 
  }
  return(predicted)
}

#Number of subclasses per class, default is 3. Can be a vector with a number for each class.
prd.MDA <- MDA.getclass(sonarMDA) # abbreviations are allowed

## [1] "classes found:  2"
## [1] "components found in class ( 1 ):  3"
## [1] "observations found in class ( 1 ):  97"
## [1] "components found in class ( 2 ):  3"
## [1] "observations found in class ( 2 ):  111"

Compare.df <- cbind(Compare.df, prd.MDA)

hlcm.vs.mclust <- jaccardMatrix(Compare.df[,1], Compare.df[,2])
hlcm.vs.mda <- jaccardMatrix(Compare.df[,1], Compare.df[,3])
mclust.vs.mda <- jaccardMatrix(Compare.df[,2], Compare.df[,3])


hlcm.vs.mclust$balancedMeanJaccard

## [1] 0.3264524

hlcm.vs.mda$balancedMeanJaccard

## [1] 0.3704139

mclust.vs.mda$balancedMeanJaccard

## [1] 0.384201