  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.
