Latent Semantic Analysis via Truncated ULV Decomposition

Abstract

Latent semantic analysis (LSA) usually uses the singular value decomposition (SVD) of the term-document matrix for discovering the latent relationships within the document collection. With the SVD, by disregarding the smaller singular values of the term-document matrix a vector space cleaned from noises that distort the meaning is obtained. The latent semantic structure of the terms and documents is obtained by examining the relationship of representative vectors in the vector space. However, the computational time of re-computing or updating the SVD of the term-document is high when adding new terms and/or documents to pre-existing document collection. Thus, the need a method not only has low computational complexity but also creates the correct semantic structure when updating the latent semantic structure is arisen. This study shows that the truncated ULV decomposition is a good alternative to the SVD in LSA modelling about cost and producing the correct semantic structure.