شناسایی اماری الگو

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شرح پروژه

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 tentime-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)

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