Question $1$ Please PROVIDE FULL CODE and OUTPUT, Please do not use AI GENERATED ANSWER

Train and test Support Vector Machine $($SVM$)$ and Multi$-$layer Perceptron $($MLP$)$ classifiers

that aim for minimum probability of classification error $($i$.$e$.$ we are using $0-1$ loss; all error in$-$

stances are equally bad$).$ You may use a trusted implementation of training, validation, and testing

in your choice of programming language. The SVM should use a Gaussian $($sometimes called

radial$-$basis$)$ kernel. The MLP should be a single$-$hidden layer model with your choice of activa$-$

tion functions for all perceptrons.

Generate $1000$ independent and identically distributed $($iid$)$ samples for training and $10000$ iid

samples for testing. All data for class l in$\{-1,+1\}$ should be generated as follows:

x$=$r$\_($l$)[[$cos$($theta$)],[$sin$($theta$)]]+$n

where theta$$ Uniform $[-$pi$,$pi$]$ and n$$N$(0,$sigma$^(2)$I$).$ Use r$\_(-1)=2,$r$\_(+1)=4,$sigma$=1.$

Note: The two class sample sets will be highly overlapping two concentric disks, and due

to angular symmetry, we anticipate the best classification boundary to be a circle between the

two disks. Your SVM and MLP models will try to approximate it$.$ Since the optimal boundary is

expected to be a quadratic curve, quadratic polynomial activation functions in the hidden layer of

the MLP may be considered as to be an appropriate modeling choice. If you have time $($optional$,$

not needed for assignment$),$ experiment with different activation function selections to see the effect

of this choice.

Use the training data with $10-$fold cross$-$validation to determine the best hyperparameters $($box

constraints parameter and Gaussian kernel width for the SVM$,$ number of perceptrons in the hidden

layer for the MLP$).$ Once these hyperparameters are set, train your final SVM and MLP classifier

using the entire training data set. Apply your trained SVM and MLP classifiers to the test data set

and estimate the probability of error from this data set.

Report the following: $(1)$ visual and numerical demonstrations of the K$-$fold cross$-$validation

process indicating how the hyperparameters for SVM and MLP classifiers are set; $(2)$ visual and

numerical demonstrations of the performance of your SVM and MLP classifiers on the test data

set. It is your responsibility to figure out how to present your results in a convincing fashion to

indicate the quality of training procedure execution, and the test performance estimate.

Hint: For hyperparameter selection, you may show the performance estimates for various

choices and indicate where the best result is achieved. For test performance, you may show the

data and classification boundary superimposed, along with an estimated probability of error from

the samples. Modify and supplement these ideas as you see appropriate.