We discussed the dynamic rescaling of LSI. Let's discuss the dynamic rescaling of COV. Here too, we follow a similar approach as we did with the LSI and LSI-rescaling. In COV-rescale, the residual of the covariance matrix is computed. The Covariance matrix was given by the function C = V E Vt where V is the
orthogonal matrix that diagnolizes C so that the diagonal entries of E are in monotone decreasing order going from top to bottom. Vt is the document
attribute matrix m x n with m row vectors representing documents. V is calculated as the matrix [aiq, ai2, ai3, .. ain]. V and Vt seem to be the left and
right singular vectors of the singular values of document vectors.
So the algorithm repeats the following steps for each of the k dimensions :
First, the max of the residual vector for the documents r1, r2, r3, ... rm is calculated.
Second, the value of the rescale factor is determined as a function of this value obtained from the step above.
Third, the residual matrix is computed as the magnitude of the residual term raised to the rescale factor combined with the corresponding component residual
vector. This is expressed as [(|r1|^q)r1, (|r2|^q)r2, (|r3|^q)r3, ... (|rn|^q)rn].
Fourth, we generate the Covariance matrix based on the residual matrix above.  The covariance matrix function is given above.
Fifth, we perform the singular value decomposition of the covariance matrix. This is a factorization of the real matrix that we get with the step above. The SVD decomposes the covariance matrix into three simple transformations, a rotation V followed by the scaling with E and another rotation Vt
Then we take the first row vector of Vt and perform a Gram-Schmidt transformation on the same.
We then recompute the residual matrix as R-R.b.bt
Then we repeat the iteration with the next k.
Generally speaking the COV-rescaling performs better than LSI, COV and LSI-Rescaling.