Text categorization: given the following document$-$term matrix: $($the value in the

matrix represents the frequency of a specific term in that document$)$

Assume that documents have been manually assigned to two pre$-$specified categories

as follows: Class$\_1=\{$Doc$1,$ Doc$2,$ Doc$5\},$ Class$\_2=\{$Doc$3,$ Doc$4,$ Doc$6,$ Doc$7\}$

$($a$)$ Using Na$$ve Bayes Multinomial Model to respectively calculate how Doc $8$ and

Doc $9$ given above will be classified. Please use add$-$one smoothing to process the

conditional probabilities in the calculation.

Feature Selection: given the following document$-$term matrix the above problem: $(1)$

calculate the mutual information between each term and the two the classes and select

the top four most important terms $($features$)$ for each class; $(2)$ use the top four

features selected for each class, re$-$categorize Doc$8$ and Doc$9$ based on Na$$ve

Bayes Multinomial Model.