PCA Notes
نویسنده
چکیده
1.1 Power iteration We would like to recover the largest singular value σ 1 , and corresponding singular vectors u 1 and v 1. To simplify the discussion, assume that σ 2 < σ 1 We consider the following optimization problem min p∈R n ,q∈R m A − pq T 2 F s.t.p 2 = 1 Let f (p, q) = A − pq T 2 F. The optimizers are shown to be (p * , q *) = (u 1 , σ 1 v 1) (up to a sign change). This problem can be solved using a block coordinate descent algorithm. Assume p is fixed, and such that p 2 = 1, and consider the partial optimization over q. The optimal q satisfies stationarity
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