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

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

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

$$

# your code here

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$$

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Now fit your model using fit$().$

# your code here

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

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

$\}$

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Plot your model. What do you notice?

library$($kernlab$)$

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# YOUR CODE HERE

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