Generate data in two classes, with two features. These features are all independent Gaussian variates with standard deviation 1. Their mean vectors are (-1, -1) in class 1 and (1, 1) in class 2. To each feature vector apply a random rotation of angle θ, θ chosen uniformly from 0 to 2π. Generate 50 observations from each class to form the training set, and 500 in each class as the test set. Apply four different classifiers:

1. Nearest-neighbors.

2. Nearest-neighbors with hints: ten randomly rotated versions of each data point are added to the training set before applying nearestneighbors.

3. Invariant metric nearest-neighbors, using Euclidean distance invariant to rotations about the origin.

4. Tangent distance nearest-neighbors. In each case choose the number of neighbors by tenfold cross-validation. Compare the results.