Support Vector Machine and MLP

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You will train and test Support Vector Machine (SVM) and Multi-layer Perceptron (MLP) classifiers that aim for minimum probability of classification error. You may use any standard library of your choice. The SVM should use a Gaussian (radial-basis) kernel. The MLP should be a single-hidden layer model with your choice of activation functions for all perceptrons.

Generate 1000 independent and identically distributed (iid) samples for training and 5000 iid samples for testing. All data for class L ∈ {0, 1}, which are equiprobable and two dimensional, should be generated as follows:

x = rL * [cos(θ) sin(θ)]T + n

where,

θ ∼ Uniform[−π, π],

n ∼ N(0, σ2I), Note: N represents the Gaussian distribution 

r0 = 2, r1 = 4, σ = 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.

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.

Show 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 dataset.

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.

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dFarzad

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