Question

4. Applying the Matrix Cookbook (See Lecture 3 Slide 16) Consider a movie rating data from Netflix (480,000 users × 17,700 movies). Ifa user ui rates a movie mu as 4 stars, then we consider a user-movie matrix A with cell Ax has value 4. To capture the whole matrix, there are 480,000 × 17,700 matrix cells to store, which is too big. We attempt to decompose the matrix A WH, where W is 480,000 × r and H is r x 17,700. When r is small, the space is saved. For this goal, we attempt to minimize sum-of-squares error: One solution is to fix W, and minimize fby changing H; and then fix H, and minimize by changing W. This is repeated till a small /is reached. See the algorithm at Page 18 of http://meyer.math.ncsu.edu/Meyer/Talks/SAS 6 9 05 NmfWorkshop.pdfłpage l8 Please justify the update functions of W and H (10 points × 2).

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