Matrix Factorization and Latent Semantic Indexing Low-Rank Approximation LoW-rank approximation SVD can be used to compute optimal low-rank approximations Approximation problem: Find Ak of rank k such that Frobenius norm A|=∑∑ Ak and X are both mxn matrices Typically, want k <<rMatrix Factorization and Latent Semantic Indexing 19 ▪ SVD can be used to compute optimal low-rank approximations. ▪ Approximation problem: Find Ak of rank k such that Ak and X are both mn matrices. Typically, want k << r. Low-rank Approximation F Frobenius norm Xrank Xk Ak = A−X : min ()= Low-Rank Approximation