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Math Tools

Math Tools. Remember these?. Singular Value Decomposition (SVD). M = U S V T. Orthogonal. Orthogonal. (“Rotate”). (“Rotate”). Diagonal. (“Stretch”). SVD. S. U. V T. Output. Scaling. Input. A simple case. V=. U. S. V T. u 2. O. S. I. x. Outer Product!. v 2. u 1.

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Math Tools

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  1. Math Tools

  2. Remember these?

  3. Singular Value Decomposition (SVD) M = U S VT Orthogonal Orthogonal (“Rotate”) (“Rotate”) Diagonal (“Stretch”)

  4. SVD S U VT Output Scaling Input

  5. A simple case V= U S VT u2 O S I x Outer Product! v2 u1 v1

  6. SVD can be interpreted as • A sum of outer products! • Decomposing the matrix into a sum of scaled outer products. • Key insight: The operations on respective dimensions stay separate from each other, all the way – through v, s and u. • They are grouped, each operating on another piece of the input.

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