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[Big Data] Week 4A (Basic)

Data Basic Big Week
2023-09-14 09:00:56 时间

Question 1

Here is a table of 1-5 star ratings for five movies (M, N, P. Q. R) by three raters (A, B, C).

 

 MNPQR
A 1 2 3 4 5
B 2 3 2 5 3
C 5 5 5 3 2

Normalize the ratings by subtracting the average for each row and then subtracting the average for each column in the resulting table. Then, identify the true statement about the normalized table.

 
Your Answer ScoreExplanation
There are more -1's than 0's.      
The smallest element is (A,M).      
The entry (B,M) is -1/3. Correct 1.00  
The entry (B,N) is -1/3.      
Total   1.00 / 1.00  

Question 2

Below is a table giving the profile of three items.

 

A 1 0 1 0 1 2
B 1 1 0 0 1 6
C 0 1 0 1 0 2

The first five attributes are Boolean, and the last is an integer "rating." Assume that the scale factor for the rating is α. Compute, as a function of α, the cosine distances between each pair of profiles. For each of α = 0, 0.5, 1, and 2, determine the cosine of the angle between each pair of vectors. Which of the following is FALSE?

 
Your Answer ScoreExplanation
For α = 0, B is closer to C than A is.      
For α = 0.5, C is closer to B than A is. Correct 1.00  
For α = 0, B is closer to A than C is.      
For α = 0.5, B is closer to C than A is.      
Total   1.00 / 1.00

Answer: Reference page 316 Chapter 9 Recommendation Systems, 9.2.4 Representing Item Profiles, Example 9.2

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