$1.$ Based on the following confusion matrix

a$)$ Compute the entropy and purity of each cluster and the overall clustering. Purity is computed as counting the number of the class which is the most frequent in the cluster dividing by the total number.

b$)$ Compute the precision of the class "Sports" with respect to each cluster and overall clustering. Precision measures the proportion of the correct pages returned to all the pages returned.

c$)$ Compute the recall of the class "Entertainment" with respect to each cluster and overall clustering. Recall measures the proportion of the correct pages returned to all the correct pages available on the Web.

Hint: Definitions from handout$1,$

Precision measures the proportion of the correct pages returned to all the pages returned, Recall measures the proportion of the correct pages returned to all the correct pages available on the Web.

How to calculate the recall of the overall clusters, SUM $($the cluster total number$/$overall total $*$ recall in each cluster$)$