  Latent semantic analysis (LSA) and correspondence analysis (CA) are two
techniques that use a singular value decomposition (SVD) for dimensionality
reduction. LSA has been extensively used to obtain low-dimensional
representations that capture relationships among documents and terms. In this
article, we present a theoretical analysis and comparison of the two techniques
in the context of document-term matrices. We show that CA has some attractive
properties as compared to LSA, for instance that effects of margins, i.e. sums
of row elements and column elements, arising from differing document-lengths
and term-frequencies are effectively eliminated, so that the CA solution is
optimally suited to focus on relationships among documents and terms. A
unifying framework is proposed that includes both CA and LSA as special cases.
We empirically compare CA to various LSA based methods on text categorization
in English and authorship attribution on historical Dutch texts, and find that
CA performs significantly better. We also apply CA to a long-standing question
regarding the authorship of the Dutch national anthem Wilhelmus and provide
further support that it can be attributed to the author Datheen, amongst
several contenders.
