---
title: morpheus...........

output:
  pdf_document:
    number_sections: true
    toc_depth: 1
---

```{r setup,  results="hide", include=FALSE}
knitr::opts_chunk$set(echo = TRUE, include = TRUE,
  cache = TRUE, comment="", cache.lazy = FALSE,
  out.width = "100%", fig.align = "center")
```

0) Tell that we try to learn classification parameters in a non-EM way, using algebric manipulations.
1) Model.
2) Algorithm (as in article)
3) Experiments: show package usage

# Expériences

```{r, results="show", include=TRUE, echo=TRUE}
library(Rmixmod) #to get clustering probability matrix
library(ClusVis)
library(FactoMineR) #for PCA

plotPCA <- function(prob)
{
  par(mfrow=c(2,2), mar=c(4,4,2,2), mgp=c(2,1,0))
  partition <- apply(prob, 1, which.max)
  n <- nrow(prob)
  K <- ncol(prob)
  palette <- rainbow(K, s=.5)
  cols <- palette[partition]
  tmp <- PCA(rbind(prob, diag(K)), ind.sup=(n+1):(n+K), scale.unit=F, graph=F)
  scores <- tmp$ind$coord[,1:3] #samples coords, by rows
  ctrs <- tmp$ind.sup$coord #projections of indicator vectors (by cols)
  for (i in 1:2)
  {
    for (j in (i+1):3)
    {
      absc <- scores[,i]
      ords <- scores[,j]
      xrange <- range(absc)
      yrange <- range(ords)
      plot(absc, ords, col=c(cols,rep(colors()[215],K),rep(1,K)),
        pch=c(rep("o",n),rep(as.character(1:K),2)),
        xlim=xrange, ylim=yrange,
        xlab=paste0("Dim ", i, " (", round(tmp$eig[i,2],2), "%)"),
        ylab=paste0("Dim ", j, " (", round(tmp$eig[j,2],2), "%)"))
      ctrsavg <- t(apply(as.matrix(palette), 1,
        function(cl) c(mean(absc[cols==cl]), mean(ords[cols==cl]))))
			text(ctrsavg[,1], ctrsavg[,2], as.character(1:K), col=colors()[215])
			text(ctrs[,i], ctrs[,j], as.character(1:K), col=1)
			title(paste0("PCA ", i, "-", j, " / K=",K))
    }
  }
  # TODO:
  plot(0, xaxt="n", yaxt="n", xlab="", ylab="", col="white", bty="n")
}

plotClvz <- function(xem, alt=FALSE)
{
  par(mfrow=c(2,2), mar=c(4,4,2,2), mgp=c(2,1,0))
  if (alt) {
    resvisu <- clusvis(log(xem@bestResult@proba), xem@bestResult@parameters@proportions)
  } else {
    resvisu <- clusvisMixmod(xem)
  }
  plotDensityClusVisu(resvisu, positionlegend=NULL)
  plotDensityClusVisu(resvisu, add.obs=TRUE, positionlegend=NULL)
  # TODO:
  plot(0, xaxt="n", yaxt="n", xlab="", ylab="", col="white", bty="n")
  plot(0, xaxt="n", yaxt="n", xlab="", ylab="", col="white", bty="n")
}

grlplot <- function(x, K, alt=FALSE) #x: data, K: nb classes
{
  xem <- mixmodCluster(x, K, strategy=mixmodStrategy(nbTryInInit=500,nbTry=25))
  plotPCA(xem@results[[1]]@proba)
  plotClvz(xem, alt)
}
```

## Iris data

```{r, results="show", include=TRUE, echo=TRUE}
data(iris)
x <- iris[,-5] #remove class info
for (i in 3:5)
{
  print(paste("Resultats en", i, "classes"))
  grlplot(x, i)
}
```

### finance dataset (from Rmixmod package)
#
#This dataset has two categorical attributes (the year and financial status), and four continuous ones.
#
#Warnings, some probabilities of classification are exactly equal to zero then we cannot use ClusVis
#
#```{r, results="show", include=TRUE, echo=TRUE}
#data(finance)
#x <- finance[,-2]
#for (i in 3:5)
#{
#  print(paste("Resultats en", i, "classes"))
#  grlplot(x, i, TRUE)
#}
#```
#
### "Cathy dataset" (12 clusters)
#
#Warnings, some probabilities of classification are exactly equal to zero then we cannot use ClusVis
#
#```{r, results="hide", include=TRUE, echo=TRUE}
#cathy12 <- as.matrix(read.table("data/probapostCatdbBlocAtrazine-K12.txt"))
#resvisu <- clusvis(log(cathy12), prop = colMeans(cathy12))
#par(mfrow=c(2,2), mar=c(4,4,2,2), mgp=c(2,1,0))
#plotDensityClusVisu(resvisu, positionlegend = NULL)
#plotDensityClusVisu(resvisu,  add.obs = TRUE, positionlegend = NULL)
#plotPCA(cathy12)
#```
#
### Pima indian diabete
#
#[Source.](https://gist.github.com/ktisha/c21e73a1bd1700294ef790c56c8aec1f)
#
#```{r, results="show", include=TRUE, echo=TRUE}
#load("data/pimaData.rda")
#for (i in 3:5)
#{
#  print(paste("Resultats en", i, "classes"))
#  grlplot(x, i)
#}
#```
#
### Breast cancer
#
#[Source.](http://archive.ics.uci.edu/ml/datasets/breast+cancer+wisconsin+\%28diagnostic\%29)
#
#```{r, results="show", include=TRUE, echo=TRUE}
#load("data/wdbc.rda")
#for (i in 3:5)
#{
#  print(paste("Resultats en", i, "classes"))
#  grlplot(x, i)
#}
#```
#
### House-votes
#
#```{r, results="show", include=TRUE, echo=TRUE}
#load("data/house-votes.rda")
#for (i in 3:5)
#{
#  print(paste("Resultats en", i, "classes"))
#  grlplot(x, i)
#}
#```