- #1

joshmccraney

Gold Member

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Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot of data, if we arrange it in a matrix, we can filter out the important pieces from the unimportant pieces.

Evidently, any matrix

**##A##**can be decomposed into

**##U \Sigma V^T##**where

**##U##**is an orthonormal basis for the row space of

**##A##**and

**##V^T##**is an orthogonal basis for column space of

**##A##**.

**##\Sigma##**is a diagonal matrix whose trace is the eigenvalues of

**##A##**in descending order. Apparently the values of

**##\Sigma##**report the "importance" of each component of

**##A##**.

I've read some articles dealing with the unit sphere and they make some sense, but I'm still not sure how to interpret what these orthogonal and diagonal vectors give me and how they filter data.

Can anyone add to this intuition and perhaps give me an example (not how to calculate SVD but how to interpret it)?

Thanks!