The first three questions use the following matrix:

	Article 1	Article 2	Article 3	Article 4
Jean	7	-	8	7
Marie	6	5	-	2
Pierre	-	2	2	5
Luc	1	3	4	1
Guy	2	-	2	1

When you ask to complete the matrix, you are asking to predict the missing values (indicated by a dash).

1-Using Pearson's collaborative user-user correlation filtering, without similarity amplification, complete the matrix. Explain the details of your calculations and justify your approach.

2-Using Pearson's Collaborative User-User Correlation Filtering, with Similarity Amplification, complete the matrix.

Explain the details of your calculations and justify your approach.

3-sing Slope One collaboration filtering, with weighted average, complete the matrix. Explain the details of your calculations and justify your approach.

4-Taking Jean, Marie and Pierre as the first set and Luc and Guy as the "test" set, explain how many missing values must be predicted to calculate the cross-validation error (All-But-1 MAE) for the three algorithms used in questions 1, 2 and 3.