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.

Student's answer$($Top$)$

library$($tidymodels$)$

# Set seed for reproducibility

set.seed$(1)$

# Create synthetic data

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$(150,50)))$

$)$

# Visualize the synthetic data

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

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

geom$\_$point$()$

# Create SVM specification with RBF kernel using parsnip

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

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

set$\_$engine$("$kernlab$")$

# Print the specification

svm$\_$rbf$\_$spec

Grade cell: cell$-66$b$70$e$8$f$71$c$4$b$8$acScore: $50\mathrm{.}0/50\mathrm{.}0($Top$)$

Hidden Tests Redacted

Congratulations! All test cases in this cell passed.

Now fit your model using fit$().$

Student's answer$($Top$)$

# Load required libraries

library$($tidymodels$)$

# Set seed for reproducibility

set.seed$(1)$

# Create synthetic data

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$(150,50)))$

$)$

# Visualize the synthetic data

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

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

geom$\_$point$()$

# Create SVM specification with RBF kernel using parsnip

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

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

set$\_$engine$("$kernlab$")$

# Print the specification

svm$\_$rbf$\_$spec

# Fit the SVM model

svm$\_$rbf$\_$fit $<-$ fit$($svm$\_$rbf$\_$spec, data $=$ sim$\_$data$2,$ formula $=$ y ~ x$1+$ x$2)$

# Print the fitted model

svm$\_$rbf$\_$fit

Grade cell: cell$-34$d$5$ed$07$e$423$b$2$cdScore: $50\mathrm{.}0/50\mathrm{.}0($Top$)$

Hidden Tests Redacted

Congratulations! All test cases in this cell passed.

Plot your model. What do you notice?

$$

$$

$$

$$

$$