Problem $9$

Implementing and Applying Support Vector Machines $($SVM$)$

Part $1$: Implementing SVM with Synthetic Data

Implement a linear SVM classifier using CVXpy$.$

Create a synthetic dataset with two features and a binary target variable. En$-$

sure that the data is linearly separable. Visualize the dataset using a scatter plot,

distinguishing the two classes with different colors.

Your implementation should include the formulation of the hard and soft SVM

optimization problem. Apply the SVM model to the synthetic data and find the

optimal hyperplane.

Visualize the optimal hyperplane along with the margin and support vectors on the

scatter plot of the synthetic dataset. Discuss the role of support vectors in SVM$.$

Calibrate the $$ parameter $($soft formulation$).$

Part $2($bonus credit$)$: Applying SVM to a Real$-$World Dataset

Choose a well$-$known dataset that is suitable for binary classification. Examples

include the Iris dataset $($selecting two of the three species$)$ or the Breast Cancer

Wisconsin $($Diagnostic$)$ dataset.

Preprocess the dataset as necessary.

Apply the SVM model implemented in Part $1$ to the selected dataset.

Evaluate the model's performance using appropriate metrics such as accuracy, pre$-$

cision, and recall. Compare these results with a baseline model, such as logistic

regression.Implement a linear SVM classifier using CVXpy$.$

Create a synthetic dataset with two features and a binary target variable. En$-$

sure that the data is linearly separable. Visualize the dataset using a scatter plot,

distinguishing the two classes with different colors.

$$ Your implementation should include the formulation of the hard and soft SVM

optimization problem. Apply the SVM model to the synthetic data and find the

optimal hyperplane.

$$ Visualize the optimal hyperplane along with the margin and support vectors on the

scatter plot of the synthetic dataset. Discuss the role of support vectors in SVM$.$

$$ Calibrate the $\backslash$lambda parameter $($soft formulation$)$