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Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?

Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?
Transcribed Image Text:Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?
If the new user's known movie ratings are all the same as another known user X, then the new user will be recommended all the movies that X rated highly. If the new user has rated only movies of a certain genre, and rated them all much higher than the average score, then the new user will be recommended all the movies in this genre. O If the new user tends to rate movies much differently than the average score a movie receives, then the recommendations that the new user receives are likely to be inaccurate.
Transcribed Image Text:If the new user's known movie ratings are all the same as another known user X, then the new user will be recommended all the movies that X rated highly. If the new user has rated only movies of a certain genre, and rated them all much higher than the average score, then the new user will be recommended all the movies in this genre. O If the new user tends to rate movies much differently than the average score a movie receives, then the recommendations that the new user receives are likely to be inaccurate.
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