پروژه پایتون 50134

شرح پروژه

سلام یه تمرین برا درس شناسایی آماری الگو،svmهست میتونید انجام بدید؟

In this exercise, you will be using support vector machines (SVMs) with various example 2D datasets. Experimenting with
these datasets will help you gain an intuition of how SVMs work and how to use a Gaussian kernel with SVMs. (You can use
optimizer libaraies for this part)
• You will try using different values of the C parameter with SVMs. Informally, the C parameter is a positive value that
controls the penalty for misclassified training examples. A large C parameter tells the SVM to try to classify all the
examples correctly.
• Train the SVM using three different values of the penalty parameter (C=1 and C=100 and C=1000) on
“Dataset1.mat”.
• Plot the train and test data with the decision boundary and marginal boundary on “Dataset1.mat”.
• Report the train and test accuracies for C=1, 100 and 1000 on “Dataset1.mat”.
• In the next part by using the Gaussian kernel with the SVM, you will be able to learn a non-linear decision boundary that
can perform reasonably well for the dataset. In general, SVM is a linear classifier. When data are not linearly separable,
Kernel SVM can be used. Here, you will utilize SVM with RBF kernel for non-linear classification. Perform the following
step for “Dataset2.mat” and “Dataset1.mat” datasets.
• Train SVM with the penalty parameter C and the standard deviation σ for RBF kernel. Your task is to use the ten time-ten-fold cross-validation set to determine the best C parameter to use.
• In the next part you should find the best value for both C and σ simountinously, we suggest trying values in
multiplicative steps (e.g., 0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30). Note that you should try all possible pairs of
values for C and σ (e.g., C = 0.3 , and σ = 0.1). For example, if you try each of the 8 values listed above for C and for
σ, you would end up training and evaluating (on the cross-validation set) a total of 8
2 = 64 different models to
select the best model.
• Plot train and test accuracies and their corresponding variances of ten-time-ten-fold cross-validation for different
values of C and 𝜎.
• Plot the train and test data and the non-linear decision boundary for both datasets (for the best model)
• Report the train and test accuracies using the selected model for both datasets (best C and 𝜎)boundary

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