I. Vector Space Model Consider 2 sets of Facebook users: U1-A,B,C,D] and U2-E,F,G,H). Each member of U1 is a friend of all members of U2. Table 1 shows the number of comments posted by each member of U2 to each member of U1. For instance, E has posted 75 comments in total to A's posts. Table 1 75 90 40 95 100 25 10 20 30 30 10 Table 2 represents the total number of friends for each member of U2. Assume each member of U2 has posted at least 1 comment on the posts of each of their friends. Assume the total number of users in Facebook is 10000 Table 2 Users of U2 Number of Friends 200 60 100 a. (15 points) Assume i) the number of comments made by a user X on another user Y's posts denotes the significance of X to Y and ii) if a user X makes comments on less friends' posts than another user Z, then X's comments are considered to be more significant than Z's. Based on these two assumptions, find out the significance of each member of U2 to each member of U1. In solving the problem, use TF-IDF weighting and base-10 logarithms. Consider the users of U1 and U2 as documents and terms, respectively. Each user in U1 is modeled as a vector using U2 as the features. In other words, a user is represented by their friends who comment on their posts. b. (15 points) Find out which user in U1 is most similar to A. Use cosine similarity as the similarity measure I. Vector Space Model Consider 2 sets of Facebook users: U1-A,B,C,D] and U2-E,F,G,H). Each member of U1 is a friend of all members of U2. Table 1 shows the number of comments posted by each member of U2 to each member of U1. For instance, E has posted 75 comments in total to A's posts. Table 1 75 90 40 95 100 25 10 20 30 30 10 Table 2 represents the total number of friends for each member of U2. Assume each member of U2 has posted at least 1 comment on the posts of each of their friends. Assume the total number of users in Facebook is 10000 Table 2 Users of U2 Number of Friends 200 60 100 a. (15 points) Assume i) the number of comments made by a user X on another user Y's posts denotes the significance of X to Y and ii) if a user X makes comments on less friends' posts than another user Z, then X's comments are considered to be more significant than Z's. Based on these two assumptions, find out the significance of each member of U2 to each member of U1. In solving the problem, use TF-IDF weighting and base-10 logarithms. Consider the users of U1 and U2 as documents and terms, respectively. Each user in U1 is modeled as a vector using U2 as the features. In other words, a user is represented by their friends who comment on their posts. b. (15 points) Find out which user in U1 is most similar to A. Use cosine similarity as the similarity measure