A link that shows that SVD analysis minimizes the approximation error

[Subbarao Kambhampati <rao@parichaalak.eas.asu.edu>]

Yesterday, in the class, I talked about how doing SVD and taking the
top K singular values and reconstructing the matrix will lead to an
approximation of the original that is closest to the original matrix
of all the k-rank matrices. 

The link below discusses the development of this derivation and might
make interesting reading for those who like linear algebra and calculus.

http://rakaposhi.eas.asu.edu/cse494/notes/pplcomps.pdf

Notice that the following terms are all refer basically to the same
technique:

1. Karhounen-Loueve Transform (used in image processing literature)
2. Latent Semantic Indexing  (used in IR literature)
3. Principal Component Analysis (used in pattern  recognition/Statistics literature)
  
Singular value decompositionis the technique underlyign all three
ideas.

Rao