In this context, we consider two forms of normalization, term and document normalization, which can also be considered as row/column normalizations of X.
a straightforward approach to normalization is to normalize each column of X to obtain a matrix as follows: If we calculate X T X = Y then we get that the (i, j)-th element of Y is: 4 In the experiments in the next section we discarded 4.2% of documents at N1 = 1000 and 47% of documents at N1 = 5000 the diagonal of Y consists of ones only and due to the Cauchy-Schwarz inequality we have that |y ij | ≤ 1, with the result that the matrix Y is already close to I.