1 Cross Validation Data Design
The Iris dataset is composed of 150 samples of 4dimensional vectors with 1 integer label. There are 3
distinct labels, and there are exactly 50 samples per label. We first want to 5fold cross validation as
follows:
For class 1, split data into 5 folds: sample numbers 110, 1120, 2130, 3140, and 4150, and they
are named as f11, f12, f13, f14, and f15, respectively.

For class 2, its folds are f21, f22, f23, f24, and f25.

For class 3, its folds are f31, f32, f33, f34, and f35.

Create a training data set by R1 = {f11, . . ., f14, f21, . . ., f24, f31, . . ., f34 }, and a test set by T1 = {f15, f25, f35 }.

Use R1 to train the above 6 Gaussian classifiers, calculate the accuracy on T1.

Repeat the above with R2R5 and T2T5, to obtain 5 accuracies.

Find the average accuracies, and determine the best Gaussian classifier for Iris dataset.
2 Gaussian Classifier Design
There are 6 different types of unimodel Gaussian classifiers.

Σc = σ2I

Σc = Σ = diag (σ1, . . ., σm**)**

Σc = Σ

Σc = σc2I (alpha C suare I)

Σc1 /= Σc2 – general case

Σc1 /= Σc2, Σc = diag (σc,1, . . ., σc,m**) – diagonal covariance case**
For given data in the form of matrix, (dimension) × (number of samples), or (number of samples) ×
(dimension), depending on your implementation, write 6 methods (functions) to estimate mean and
covariance matrix of the above 6 techniques.
Perform 5fold crossvalidation experiments for all 6 methods
Evaluate the average performace
Determine which is the best out of 6 methods
You may use python with numpy, scikitlearn, etc.
3 Support Vector Machines
The hyperparamters of SVM are C (nonseparability) and kernelspecific parameters. Use 5fold cross
validation to
Determine the best C and degree (order, rank, etc.) of the polynomial kernel functions.
Determine the best C and the standard deviation of the Gaussian kernel function (or called
paramter of RBF kernel).
These hyperparameter selection process is called grid search because the combinations of discrete param
eter selection constitute a grid in a multidimensional vector space, and we look into every grid to find
the optimal hyperparameter set.
The critical design issue is the selection of discretizing continuous parameter space: for example, the
usual choice of C = {1, 10, 100, . . .}.