A comparison of latent semantic analysis and correspondence analysis of document-term matrices

Abstract

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 and dense vectors 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 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 two tasks, a document classification task in English and an authorship attribution task 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.

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ORCID for Peter Van Der Heijden: orcid.org/0000-0002-3345-096X

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