SVM models are a varied model that can work for both regression and classification. They work to find a hyperplance between points and increase the margin. We will leave the math to a different post, but a benifit of this algorithm is it no

For this tutorial, we will use the Boston data set which includes
housing data with features of the houses and their prices. We would like
to predict the `medv`

column or the medium value.

```
library(MASS)
data(Boston)
str(Boston)
```

```
## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
```

To create a basic svm regression in r, we use the `svm`

method from the
`e17071`

package. We supply two parameters to this method. The first
parameter is a formula `medv ~ .`

which means model the medium value
parameter by all other parameters. Then, we supply our data set, Boston.

`library(e1071)`

`## Warning: package 'e1071' was built under R version 4.0.5`

```
model = svm(medv ~ ., data = Boston)
print(model)
```

```
##
## Call:
## svm(formula = medv ~ ., data = Boston)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 1
## gamma: 0.07692308
## epsilon: 0.1
##
##
## Number of Support Vectors: 334
```

We will now see how to model a linear regression using the `Caret`

package. We will use this library as it provides us with many features
for real life modeling.

To do this, we use the `train`

method. We pass the same parameters as
above, but in addition we pass the `method = 'svmRadial'`

model to tell
Caret to use a svm model. Caret also provides us with the fllowing svm
options: “svmRadial”, “svmLinear”, or “svmPoly”.

```
set.seed(1)
library(caret)
```

```
## Loading required package: lattice
## Loading required package: ggplot2
```

`library(kernlab)`

```
##
## Attaching package: 'kernlab'
## The following object is masked from 'package:ggplot2':
##
## alpha
```

```
model <- train(
medv ~ .,
data = Boston,
method = 'svmRadial'
)
model
```

```
## Support Vector Machines with Radial Basis Function Kernel
##
## 506 samples
## 13 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 506, 506, 506, 506, 506, 506, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 4.698854 0.7612310 2.757942
## 0.50 4.292711 0.7923997 2.554691
## 1.00 3.970728 0.8170827 2.421873
##
## Tuning parameter 'sigma' was held constant at a value of 0.09566003
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.09566003 and C = 1.
```

One feature that we use from Caret is preprocessing. Often in real life
data science we want to run some pre processing before modeling. We will
center and scale our data by passing the following to the train method:
`preProcess = c("center", "scale")`

.

```
set.seed(1)
model2 <- train(
medv ~ .,
data = Boston,
method = 'svmRadial',
preProcess = c("center", "scale")
)
model2
```

```
## Support Vector Machines with Radial Basis Function Kernel
##
## 506 samples
## 13 predictor
##
## Pre-processing: centered (13), scaled (13)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 506, 506, 506, 506, 506, 506, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 4.698854 0.7612310 2.757942
## 0.50 4.292711 0.7923997 2.554691
## 1.00 3.970728 0.8170827 2.421873
##
## Tuning parameter 'sigma' was held constant at a value of 0.09566003
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.09566003 and C = 1.
```

Often when we are modeling, we want to split our data into a train and
test set. This way, we can check for overfitting. We can use the
`createDataPartition`

method to do this. In this example, we use the
target `medv`

to split into an 80/20 split, `p = .80`

.

This function will return indexes that contains 80% of the data that we should use for training. We then use the indexes to get our training data from the data set.

```
set.seed(1)
inTraining <- createDataPartition(Boston$medv, p = .80, list = FALSE)
training <- Boston[inTraining,]
testing <- Boston[-inTraining,]
```

```
set.seed(1)
model3 <- train(
medv ~ .,
data = training,
method = 'svmRadial',
preProcess = c("center", "scale")
)
model3
```

```
## Support Vector Machines with Radial Basis Function Kernel
##
## 407 samples
## 13 predictor
##
## Pre-processing: centered (13), scaled (13)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 407, 407, 407, 407, 407, 407, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 5.006385 0.7263591 2.959711
## 0.50 4.532278 0.7641084 2.724318
## 1.00 4.183087 0.7908114 2.576319
##
## Tuning parameter 'sigma' was held constant at a value of 0.1106087
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.1106087 and C = 1.
```

Now, we want to check our data on the test set. We can use the `subset`

method to get the features and test target. We then use the `predict`

method passing in our model from above and the test features.

Finally, we calculate the RMSE and r2 to compare to the model above.

```
test.features = subset(testing, select=-c(medv))
test.target = subset(testing, select=medv)[,1]
predictions = predict(model3, newdata = test.features)
# RMSE
sqrt(mean((test.target - predictions)^2))
```

`## [1] 3.825048`

```
# R2
cor(test.target, predictions) ^ 2
```

`## [1] 0.8495157`

In practice, we don’t normal build our data in on training set. It is
common to use a data partitioning strategy like k-fold cross-validation
that resamples and splits our data many times. We then train the model
on these samples and pick the best model. Caret makes this easy with the
`trainControl`

method.

We will use 10-fold cross-validation in this tutorial. To do this we
need to pass three parameters `method = "repeatedcv"`

, `number = 10`

(for 10-fold). We store this result in a variable.

```
set.seed(1)
ctrl <- trainControl(
method = "cv",
number = 10,
)
```

Now, we can retrain our model and pass the `trainControl`

response to
the `trControl`

parameter. Notice the our call has added
`trControl = set.seed`

.

```
set.seed(1)
model4 <- train(
medv ~ .,
data = testing,
method = 'svmRadial',
preProcess = c("center", "scale"),
trCtrl = ctrl
)
model4
```

```
## Support Vector Machines with Radial Basis Function Kernel
##
## 99 samples
## 13 predictors
##
## Pre-processing: centered (13), scaled (13)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 99, 99, 99, 99, 99, 99, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 6.374356 0.5756692 3.771028
## 0.50 5.883662 0.6228022 3.435913
## 1.00 5.455462 0.6646681 3.224363
##
## Tuning parameter 'sigma' was held constant at a value of 0.08959179
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.08959179 and C = 1.
```

This results seemed to have improved our accuracy for our training data. Let’s check this on the test data to see the results.

```
test.features = subset(testing, select=-c(medv))
test.target = subset(testing, select=medv)[,1]
predictions = predict(model4, newdata = test.features)
# RMSE
sqrt(mean((test.target - predictions)^2))
```

`## [1] 3.819472`

```
# R2
cor(test.target, predictions) ^ 2
```

`## [1] 0.8647817`

To tune a svm model, we can give the model different values of `C`

which
represents cost and sigma. Caret will retrain the model using different
lambdas and select the best version.

```
set.seed(1)
tuneGrid <- expand.grid(
C = c(0.25, .5, 1),
sigma = 0.1
)
model5 <- train(
medv ~ .,
data = training,
method = 'svmRadial',
preProcess = c("center", "scale"),
trControl = ctrl,
tuneGrid = tuneGrid
)
model5
```

```
## Support Vector Machines with Radial Basis Function Kernel
##
## 407 samples
## 13 predictor
##
## Pre-processing: centered (13), scaled (13)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 367, 366, 367, 366, 365, 367, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 4.803438 0.7503886 2.924299
## 0.50 4.258538 0.7930483 2.620436
## 1.00 3.820902 0.8247794 2.409192
##
## Tuning parameter 'sigma' was held constant at a value of 0.1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.1 and C = 1.
```

Finally, we can again plot the model to see how it performs over different tuning parameters.

`plot(model5)`