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. First, a quick introduction to this dataset, since you will encounter it in other assignments as well. The MNIST database of handwritten digits has a training set of 60,000 examples and a test set of 10,000 examples. This split will be become particularly important when we explore supervised methods, but for this case, only focus on the training set. Use the number of clusters K = 10. Also, 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 correctly assigned samples divided by the size of the cluster: 

purity = (correctly assigned samples) / (size of cluster)     for the cluster i. 

 

1. Use the squared-ℓ2 norm as a metric for clustering Report the purity score for each cluster with python code.