The partial singular value decomposition approximates the DTM using three matrices: U, S, and V‘. The relationship between these matrices is defined as follows:
DTMU * S * V‘
Define nDoc as the number of documents (rows) in the DTM, nTerm as the number of terms (columns) in the DTM, and nVec as the specified number of singular vectors. Note that nVec must be less than or equal to min(nDoc, nTerm). It follows that U is an nDoc by nVec matrix that contains the left singular vectors of the DTM. S is a diagonal matrix of dimension nVec. The diagonal entries in S are the singular values of the DTM. V‘ is an nVec by nTerm matrix. The rows in V‘ (or columns in V) are the right singular vectors.
The DTM, by default, is centered, scaled, and divided by nDoc minus 1 before the singular value decomposition is carried out. This analysis is equivalent to a PCA of the correlation matrix of the DTM.
You can also specify Centered or Uncentered in the Specifications window. If you specify Centered, the DTM is centered and divided by nDoc minus 1 before the singular value decomposition. This analysis is equivalent to a PCA of the covariance matrix of the DTM. If you specify Uncentered, the DTM is divided by nDoc before the singular value decomposition. This analysis is equivalent to a PCA of the unscaled DTM.

Help created on 7/12/2018