Apply logistic regression to the data set ` vehicle.mat`^{2}. The task is to classify a given silhouette as one of two types of vehicles, i.e. SAAB and BUS, using a set of features extracted from the silhouette. You are required to use MATLAB for this assignment.

- a)
Use the MATLAB command

`mapstd`to normalize the values of each feature so that the mean is 0 and the variance is 1.- b)
- [1 P]
Perform gradient descent on the

*cross-entropy error function*. Initialize the weights to small non-zero values (use the MATLAB command`randn`). Adjust the learning rate used for the weight update step - c)
- [1 P]
Perform linear regression using the

*Moore-Penrose pseudo-inverse*of the design matrix . Compare the resulting*cross-entropy error*to the one obtained in b). - d)
- [1 P]
Apply the

*iterative reweighted least squares algorithm*to the dataset. Report the performance after 100 epochs and the number of epochs needed to reach close to optimal performance. Hand in a plot showing the dependence of the error on the number of epochs. Compare the results to the one obtained in b).