mixture.example {ElemStatLearn} | R Documentation

## Mixture Example

### Description

This is a simulated mixture example with 200 instances and two classes. 100 members in each class.

### Usage

    data(mixture.example)

### Format

The format is: List of 8 $ x : 200 x 2 matrix of training predictors $ y : 200 x 2 matrix of class labels, 0==green, 1==red $ xnew : matrix [1:6831, 1:2] -2.6 -2.5 -2.4 -2.3 -2.2 ... ..- attr(*, "class")= chr "matrix" ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:6831] "1" "2" "3" "4" ... .. ..$ : chr [1:2] "x1" "x2" : matrix 6831 x 2 of lattice points in predictor space $ prob : atomic [1:6831] 3.55e-05 3.05e-05 2.63e-05 2.27e-05 1.96e-05 ... ..- attr(*, ".Names")= chr [1:6831] "1" "2" "3" "4" ... vector of 6831 probabilities (of class RED) at each lattice point $ marginal: atomic [1:6831] 6.65e-15 2.31e-14 7.62e-14 2.39e-13 7.15e-13 ... ..- attr(*, ".Names")= chr [1:6831] "1" "2" "3" "4" ... : marginal probability at each lattice point $ px1 : 69 lattice coordinates for x.1 $ px2 : 99 lattice values for x.2 (69*99=6831) $ means : num [1:20, 1:2] : 20 x 2 matrix of the mixture centers, first ten for one class, next ten for the other

### Examples

    str(mixture.example)
    if(interactive())par(ask=TRUE)
    x <- mixture.example$x
     g <- mixture.example$y
     x.mod <- lm( g ~ x)
     plot(x, col=ifelse(g==1,"red", "green"), xlab="x1", ylab="x2")
     coef(x.mod)
     abline( (0.5-coef(x.mod)[1])/coef(x.mod)[3], -coef(x.mod)[2]/coef(x.mod)[3])
     ghat <- ifelse( fitted(x.mod)>0.5, 1, 0)
     length(ghat)

     sum(ghat == g)

     1 - sum(ghat==g)/length(g)
     #[1] 0.27
     # Training misclassification rate
     xnew <- mixture.example$xnew
     dim(xnew)
     colnames(xnew)

     library(class)

     mod15 <- knn(x, xnew, g, k=15, prob=TRUE)
     summary(mod15)

     plot(x, col=ifelse(g==1,"red", "green"),xlab="x1", ylab="x2")

     str(mod15)
     prob <- attr(mod15, "prob")
     prob <- ifelse( mod15=="1", prob, 1-prob) # prob is voting fraction for winning class!
                                               # Now it is voting fraction for red==1

     px1 <- mixture.example$px1
     px2 <- mixture.example$px2

     prob15 <- matrix(prob, length(px1), length(px2))
     contour(px1, px2, prob15, levels=0.5, labels="", xlab="x1", ylab="x2", main=
               "15-nearest neighbour")
     # adding the points to the plot:
     points(x, col=ifelse(g==1, "red", "green"))

     ghat15 <- ifelse(knn(x,x,k=15, cl=g)=="1", 1, 0)
     sum(ghat15==g)
     # [1] 169
     1 - sum(ghat15==g)/length(g)
     # [1] 0.155
     # Misclassification rate for knn(, k=15)

     # Then we want the plot for knn with k=1:

     mod1 <- knn(x, xnew, k=1, cl=g, prob=TRUE)
     prob <- attr(mod1, "prob")
     prob <- ifelse( mod1=="1", prob, 1-prob) # prob now is voting
                                              # fraction for "red"
     prob1 <- matrix(prob, length(px1), length(px2) )
     contour(px1, px2, prob1, level=0.5, labels="", xlab="x1", ylab="x2", main=
                    "1-nearest neighbour")
     # Adding the points to the plot:
     points(x, col=ifelse(g==1, "red", "green"))

     # Reproducing figure 2.4, page 17 of the book:
     # The data do not contain a test sample, so we make one,
     # using the description of the oracle page 17 of the book: The centers
     # is in the means component of mixture.example, with green(0) first,
     # so red(1).  For a test sample of size 10000 we simulate
     # 5000 observations of each class.

     library(MASS)
        set.seed(123)
        centers <- c(sample(1:10, 5000, replace=TRUE),
                     sample(11:20, 5000, replace=TRUE))
        means <- mixture.example$means
        means <- means[centers, ]
        mix.test <- mvrnorm(10000, c(0,0), 0.2*diag(2))
        mix.test <- mix.test + means
        cltest <- c(rep(0, 5000), rep(1, 5000))

        ks <- c(1,3,5,7,9,11,15,17,23,25,35,45,55,83,101,151 )
        # nearest neighbours to try
        nks <- length(ks)
        misclass.train <- numeric(length=nks)
        misclass.test  <- numeric(length=nks)
        names(misclass.train) <- names(misclass.test) <- ks
        for (i in seq(along=ks)) {
          mod.train <- knn(x,x,k=ks[i],cl=g)
          mod.test  <- knn(x, mix.test,k= ks[i],cl= g)
          misclass.train[i] <- 1 - sum(mod.train==factor(g))/200
          misclass.test[i] <- 1 - sum(mod.test==factor(cltest))/10000
        }
        print(cbind(misclass.train, misclass.test))

    # Using package mclust02

     if(require(mclust02)){
     x <- mixture.example$x
     g <- mixture.example$y
     xnew <- mixture.example$xnew
     px1 <- mixture.example$px1
     px2 <- mixture.example$px2

     mix.mclust <- mclustDA(x, g, xnew, G=1:6, verbose=TRUE)
     mix.mclust
    }

[Package ElemStatLearn version 0.1-4 Index]