Title: Clustering and latent semantic indexing aspects of the singular value decomposition

Authors: Andri Mirzal

Addresses: Computer Science Department, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman

Abstract: This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purposes of this paper are two-fold. The first is to give a review on how and why the singular vectors can be used in clustering. And the second is to show that the two seemingly unrelated 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. By utilising this fact, we devise an LSI algorithm that mimics SVD capability in grouping related vertices. The proposed 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. Moreover, convergence analysis shows that the algorithm is convergent and produces a unique solution. Experimental results using some standard datasets in LSI research show that retrieval performances of the algorithm are comparable to retrieval performances of the SVD.

Keywords: eigenvector; Ky Fan theorem; latent semantic indexing; LSI; matrix completion; singular value decomposition; SVD; spectral clustering.

DOI: 10.1504/IJIDS.2016.075790

International Journal of Information and Decision Sciences, 2016 Vol.8 No.1, pp.53 - 72

Available online: 05 Apr 2016

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