{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T05:17:30Z","timestamp":1791868650764,"version":"4.3.4"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>In today's vector space information retrieval systems, dimension reduction is imperative for efficiently manipulating the massive quantity of data. To be useful, this lower-dimensional representation must be a good approximation of the full document set. To that end, we adapt and extend the discriminant analysis projection used in pattern recognition. This projection preserves cluster structure by maximizing the scatter between clusters while minimizing the scatter within clusters. A common limitation of trace optimization in discriminant analysis is that one of the scatter matrices must be nonsingular, which restricts its application to document sets in which the number of terms does not exceed the number of documents. We show that by using the generalized singular value decomposition (GSVD), we can achieve the same goal regardless of the relative dimensions of the term-document matrix. In addition, applying the GSVD allows us to avoid the explicit formation of the scatter matrices in favor of working directly with the data matrix, thus improving the numerical properties of the approach. Finally, we present experimental results that confirm the effectiveness of our approach.<\/jats:p>","DOI":"10.1137\/s0895479801393666","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"165-179","source":"Crossref","is-referenced-by-count":140,"title":["Structure Preserving Dimension Reduction for Clustered Text Data Based on the Generalized Singular Value Decomposition"],"prefix":"10.1137","volume":"25","author":[{"given":"Peg","family":"Howland","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moongu","family":"Jeon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haesun","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/1037127"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971484"},{"key":"R3","unstructured":"W. B. Frakes and R. Baeza\u2010Yates,\n                      Information Retrieval: Data Structures and Algorithms\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1992."},{"key":"R4","volume-title":"Introduction to statistical pattern recognition","author":"Fukunaga Keinosuke","year":"1990"},{"key":"R5","volume-title":"Matrix computations","author":"Golub Gene","year":"1996"},{"key":"R6","unstructured":"P. Howland and H. Park,\n                      Extension of discriminant analysis based on the generalized singular value decomposition\n                      , in Proceedings of the Second SIAM International Conference on Data Mining\/Text Mining Workshop, SIAM, Philadelphia, 2002."},{"key":"R7","volume-title":"Algorithms for clustering data","author":"Jain Anil","year":"1988"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"M. Jeon, H. Park, and J. B. Rosen,\n                      Dimension reduction based on centroids and least squares for efficient processing of text data\n                      , in Proceedings of the First SIAM International Conference on Data Mining, CD\u2010ROM, SIAM, Philadelphia, 2001.","DOI":"10.1137\/1.9781611972719.21"},{"key":"R9","unstructured":"G. Kowalski,\n                      Information Retrieval Systems: Theory and Implementation\n                      , Kluwer Academic, Dordrecht, The Netherlands, 1997."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971217"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0718026"},{"key":"R12","unstructured":"H. Park, M. Jeon, and J. B. Rosen,\n                      Lower dimensional representation of text data based on centroids and least squares\n                      , BIT, to appear."},{"key":"R13","unstructured":"G. Salton,\n                      The SMART Retrieval System\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1971."},{"key":"R14","unstructured":"G. Salton and M. J. McGill,\n                      Introduction to Modern Information Retrieval\n                      , McGraw\u2013Hill, New York, 1983."},{"key":"R15","unstructured":"S. Theodoridis and K. Koutroumbas,\n                      Pattern Recognition\n                      , Academic Press, New York, 1999."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/0713009"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479801393666","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:41:02Z","timestamp":1787334062000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479801393666"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479801393666"],"URL":"https:\/\/doi.org\/10.1137\/s0895479801393666","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}