This question is to compare different classifiers and their performance for multi-class classifications on the complete MNIST dataset at http://yann.lecun.com/exdb/mnist/. You can find the data file mnist 10digits.mat in the homework folder. The MNIST database of handwritten digits has a training set of 60,000 examples and a test set of 10,000 examples. Use the number of clusters K = 10. We suggest you "standardize" the features (pixels in this case) by dividing the values of the features by 255 (thus mapping the range of the features from [0, 255] to [0, 1]). We are going to use purity score as a performance metric: each cluster is assigned to the class which is most frequent in the cluster, and then the accuracy of this assignment is measured by the number of correlated assigned samples and divided by the size of the cluster:

purity(i) = number of most frequent label in cluster(i) / size of cluster(i)

e.g in cluster9, if the most frequent digit is 8, then

purity(cluster9) = (number of 8's in cluster9)/ size of cluster 9

1. Use the squared-`2 norm as a metric for clustering (you may base it on the code you had Report the purity score for each cluster by using a python K means clustering code.