Support Vector Machines

This assignment will build off of the previous ungraded assignment. However, here you will use a radial basis function for your kernel rather than a linear specification.

To begin, a synthetic data set has been provided below. It is normally distributed with an added offset to create two separate classes.

library$($tidymodels$)$

library$($ISLR$2)$

$$

set.seed$(1)$

sim$\_$data$2<-$ tibble$($

x$1=$ rnorm$(200)+$ rep$($c$(2,-2,0),$ c$(100,50,50)),$

x$2=$ rnorm$(200)+$ rep$($c$(2,-2,0),$ c$(100,50,50)),$

y $=$ factor$($rep$($c$(1,2),$ c$(150,50)))$

$)$

$$

sim$\_$data$2\%>\%$

ggplot$($aes$($x$1,$ x$2,$ color $=$ y$))+$

geom$\_$point$()$

Now, you will try an SVM using a radial basis function $($RBF$).$ RBF should allow you to capture the non$-$linearity in the data. To create the specification, you should use svm$\_$rbf$().$ Be sure to pass in classification as the mode and kernlab as the engine. Save your output to svm$\_$rbf$\_$spec.

# YOUR CODE HERE

set.seed$(1)$

# svm$\_$rbf$\_$spec $<-$

# your code here

$$

svm$\_$rbf$\_$spec $<-$ svm$\_$rbf$()\%>\%$

set$\_$mode$("$classification$")\%>\%$

set$\_$engine$("$kernlab$",$ scaled $=$ FALSE$)$

$$

Now fit your model using fit$().$

# your code here

svm$\_$rbf$\_$fit$=$ function$()\{$

fit$($svm$\_$rbf$\_$spec, data $=$ sim$\_$data$2)$

$\}$

$$

Plot your model. What do you notice?

library$($kernlab$)$

$$

# YOUR CODE HERE

$$

# fit$\_$plot $<-$

$$

# your code here

fit$\_$plot $<-$ plot$($svm$\_$rbf$\_$fit$)$

fit$\_$plot

Error in x$($x$)$: unused argument $($x$)$

Traceback:

$1.$ plot$($svm$\_$rbf$\_$fit$)$

$2.$ plot$($svm$\_$rbf$\_$fit$)$

$3.$ plot.function$($svm$\_$rbf$\_$fit$)$

$4.$ curve$($expr $=$ x$,$ from $=$ from, to $=$ to$,$ xlim $=$ xlim$,$ ylab $=$ ylab,

$....)$

$5.$ eval$($expr$,$ envir $=$ ll$,$ enclos $=$ parent.frame$())$

$6.$ eval$($expr$,$ envir $=$ ll$,$ enclos $=$ parent.frame$())$

$$

Now, let's see how well this model generalizes to new data from the sam generating process.

set.seed$(2)$

sim$\_$data$2\_$test $<-$ tibble$($

x$1=$ rnorm$(200)+$ rep$($c$(2,-2,0),$ c$(100,50,50)),$

x$2=$ rnorm$(200)+$ rep$($c$(2,-2,0),$ c$(100,50,50)),$

y $=$ factor$($rep$($c$(1,2),$ c$(150,50)))$

$)$

augment$($svm$\_$rbf$\_$fit, new$\_$data $=$ sim$\_$data$2\_$test$)\%>\%$

conf$\_$mat$($truth $=$ y$,$ estimate $=.$pred$\_$class$)$

Error: No augment method for objects of class function

Traceback:

$1.$ augment$($svm$\_$rbf$\_$fit, new$\_$data $=$ sim$\_$data$2\_$test$)\%>\%$ conf$\_$mat$($truth $=$ y$,$

$.$ estimate $=.$pred$\_$class$)$

$2.$ eval$($lhs$,$ parent, parent$)$

$3.$ eval$($lhs$,$ parent, parent$)$

$4.$ augment$($svm$\_$rbf$\_$fit, new$\_$data $=$ sim$\_$data$2\_$test$)$

$5.$ augment.default$($svm$\_$rbf$\_$fit, new$\_$data $=$ sim$\_$data$2\_$test$)$

$6.$ stop$("$No augment method for objects of class $",$ class$($x$)[1],$

$.$ call. $=$ FALSE$)$

What do you notice?