Clustering and Latent Semantic Indexing Aspects of the Singular Value Decomposition

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used in clustering. And the second is to show that the two seemingly unrelated SVD aspects actually originate from the same source: related vertices tend to be more clustered in the graph representation of lower rank approximate matrix using the SVD than in the original semantic graph. Accordingly, the SVD can improve retrieval performance of an information retrieval system since queries made to the approximate matrix can retrieve more relevant documents and filter out more irrelevant documents than the same queries made to the original matrix. By utilizing this fact, we will devise an LSI algorithm that mimicks SVD capability in clustering related vertices. Convergence analysis shows that the algorithm is convergent and produces a unique solution for each input. Experimental results using some standard datasets in LSI research show that retrieval performances of the algorithm are comparable to the SVD's. In addition, the algorithm is more practical and easier to use because there is no need to determine decomposition rank which is crucial in driving retrieval performance of the SVD.