rolandyekple415

what is eigen value and eigen vector

For the following ratings given to items by the users, perform the tasks below:
 
           Item 1 Item 2 Item 3 Item 4 Item 5 
User 1   ?           3         ?         3          4 
User 2   4           ?         ?         2          ? 
User 3   ?           ?         3         ?          ? 
User 4   3          ?         4        ?           3 
User 5   4          3         ?        4          4

Note: '?' means user has not rated that item.

For all of these tasks, use Pearson Correlation Coefficient as similarity measure and mean-centered prediction function.
Show your working clearly for :
a) Find nearest neighbors of user 1 for k=2.
b) Apply user-based Collaborative Filtering to predict R(U1, I3) (read: rating for user 1 and item 3).
c) Apply item-based Collaborative Filtering to predict R(U3, I2) and R(U4, I4). (HINT: USE CASCADING)
d) Say we had an option of using mode-centered prediction function instead of using mean. What do you think would be the effect of using mode as a baseline instead of average? Can using mode ever improve the performance of recommender system?

The revenue from selling q items is R(q)= 125q-q^2 , and the totalcost is C(q)= 150+3q . Write a function that gives the total profitearned, and find the quantity which maximizes the profit.