Latent Semantic Indexing is an Optimal Special Case of Multidimensional Scaling.

Brian T. Bartell, Garrison W. Cottrell, Richard K. Belew: Latent Semantic Indexing is an Optimal Special Case of Multidimensional Scaling. SIGIR 1992: 161-167

@inproceedings{DBLP:conf/sigir/BartellCB92,
  author    = {Brian T. Bartell and
               Garrison W. Cottrell and
               Richard K. Belew},
  editor    = {Nicholas J. Belkin and
               Peter Ingwersen and
               Annelise Mark Pejtersen},
  title     = {Latent Semantic Indexing is an Optimal Special Case of Multidimensional
               Scaling},
  booktitle = {Proceedings of the 15th Annual International ACM SIGIR Conference
               on Research and Development in Information Retrieval. Copenhagen,
               Denmark, June 21-24, 1992},
  publisher = {ACM},
  year      = {1992},
  isbn      = {0-89791-523-2},
  pages     = {161-167},
  ee        = {db/conf/sigir/BartellCB92.html},
  crossref  = {DBLP:conf/sigir/92},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

BibTeX

Abstract

Latent Semantic Indexing (LSI) is a technique for representing documents, queries, and terms as vectors in a multidimensional real-valued space. The representtions are approximations to the original term space encoding, and are found using the matrix technique of Singular Value Decomposition. In comparison Multidimensional Scaling (MDS) is a class of data analysis techniques for representing data points as points in a multidimensional real-valued space. The objects are represented so that inter-point similarities in the space match inter-object similarity information provided by the researcher. We illustrate how the document representations given by LSI are equivalent to the optimal representations found when solving a particular MDS problem in which the given inter-object similarity information is provided by the inner product similarities between the documents themselves. We further analyze a more general MDS problem in which the interdocument similarity information, although still in inner product form is arbitrary with respect to the vector space encoding of the documents.

Copyright © 1992 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.

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BibTeX

Printed Edition

Nicholas J. Belkin, Peter Ingwersen, Annelise Mark Pejtersen (Eds.): Proceedings of the 15th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. Copenhagen, Denmark, June 21-24, 1992. ACM 1992, ISBN 0-89791-523-2
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