For each question, write down your procedure for getting the answer $($each

value can be kept to two decimal places$)$;

Question $1(80$ points$)$

Consider the following rating matrix for a set of six users $($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ and a set of six

items $($Item$1,$ Item$2,$ Item$3,$ Item$4,$ Item$5,$ Item$6)$:

Answer the following FOUR questions:

a$.$ Predict User A$\text{'}$s rating for Item $5,$ and User C$\text{'}$s rating for Item $3,$ through the user$-$

based kNN with means based on Pearson Correlation. $(20$ points$)$

b$.$ Make the predictions for the same user$-$item pairs $($i$.$e$.,($User A$,$ Item $5),($User C$,$ Item

$)$ through the user$-$based kNN with means based on Cosine Similarity. $(20$ points$)$

c$.$ Make the predictions for the same user$-$item pairs through the item$-$based kNN with

means based on Cosine Similarity. $(20$ points$)$

Note: for each question above $($a$-$c$),$ you need to choose a proper neighborhood selection

method by yourself and provide your justification.

d$.$ Discuss the differences among the above three calculation methods with their

respective pros and cons. $(20$ points$)$