Latent Ambiguity in Latent Semantic Analysis?

Latent Semantic Analyis (LSA) consists in the use of SVD-based dimensionality-reduction to reduce the high dimensionality of vector representations of documents, where the dimensions of the vectors correspond simply to word counts in the documents. We show that that there are two contending, inequivalent, formulations of LSA. The distinction between the two is not generally noted and while some work adheres to one formulation, other work adheres to the other formulation. We show that on both a tiny contrived data-set and also on a more substantial word-sense discovery data-set that the empirical outcomes achieved with LSA vary according to which formulation is chosen.