Question

Briefly explain the relationship between LSI and SVD (Singular Value Decomposition).

(( data mining question ))

Answer 1

LSI (Latent Semantic Analysis) are used by the information retrieval community.It uses SVD to decompose the term document matrix-A into a term concept matrix U , a singular value matrix S and finally concept document matrix V which can be shown as - A = USV^I.

SVD is nothing but Singular value decomposition.It is very closely related to PCA (Principle component Analysis).For beginners, PCA is a eigen decomposition of the correlation.SVD is the generalization of eigen decomposition to non-square matrices.The singular values are the square root of the eigen values of the matrix multiplied by its transpose.

Example

Consider the matrix A^*A = AA^* in which the singular values are non - negative i.e., it is absolutely in a positive sign.If the singular values of the eigen values got change in sign it needs a rework or it needs to fix the thing that is especially with non-square matrices.