Really not LSI but SVD (Singular Value Decomposition) was used.
In other words Matrix of NN_Profiles that consists of n documents in vector space with dimention d, let it will be M [nxd], was replaced by left-singular matrix U from Singular Value Decomposition.

SVD of M can be defined as M = U*S*V'.
U [nxn] and V [dxd] are unitary matrices :
U'*U = n-by-n identity matrix
V'*V = d-by-d identity matrix.
S [nxd] - diagonal matrix of the same dimension as M with nonnegative diagonal elements in decreasing order, which are called singular values.
Singular values are defined as nonnegative sqare roots of eigenvalues of M*M'.

Library that calculates SVD was based on SVDPACKC Version 1.0 (ANSI-C) by University of Tennessee.
Adapting for oasis usage by Igor Kuralenok.

Questions and comments send to Dimitrij Petoukhov.