Problem $3.$ Write a Matlab program to create and train a multilayer perceptron using the backpropagation learning algorithm with momentum $($use matlab toolbox for this problem$).$ Use your network to classify the Iris dataset $($iris$3$class.mat$)$ provided with this homework. Divide your data into a training set and testing set in a $2$:$1$ ratio. Perform the following experiments with your network:

Experiment with the following values of the learning rate $()$ and momentum parameter $()$ and comment on your results. Determine the values of $$ and $$ that yield best classification accuracy.

$in[0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1,0\mathrm{.}25,0\mathrm{.}5]$

$in[0,0\mathrm{.}1,0\mathrm{.}5,0\mathrm{.}8,0\mathrm{.}99]$

Use the Levenberg$-$Marquardt variant of backpropagation to train your network and compare its performance with classical backpropagation.

Use the Nguyen$-$Widrow technique for weight initialization and compare the network's perfor$-$ mance to that using random weight initialization.

Use $3-$fold cross validation to test and train your network. Comment on the network's perfor$-$ mance.