{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T06:13:47Z","timestamp":1790835227898,"version":"4.1.0"},"reference-count":36,"publisher":"National Academy of Sciences","issue":"47","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2007,11,20]]},"abstract":"\n We describe the use of a higher-order singular value decomposition (HOSVD) in transforming a data tensor of genes \u00d7 \u201c\n x<\/jats:italic>\n -settings,\u201d that is, different settings of the experimental variable\n x<\/jats:italic>\n \u00d7 \u201c\n y<\/jats:italic>\n -settings,\u201d which tabulates DNA microarray data from different studies, to a \u201ccore tensor\u201d of \u201ceigenarrays\u201d \u00d7 \u201c\n x<\/jats:italic>\n -eigengenes\u201d \u00d7 \u201c\n y<\/jats:italic>\n -eigengenes.\u201d Reformulating this multilinear HOSVD such that it decomposes the data tensor into a linear superposition of all outer products of an eigenarray, an\n x<\/jats:italic>\n - and a\n y<\/jats:italic>\n -eigengene, that is, rank-1 \u201csubtensors,\u201d we define the significance of each subtensor in terms of the fraction of the overall information in the data tensor that it captures. We illustrate this HOSVD with an integration of genome-scale mRNA expression data from three yeast cell cycle time courses, two of which are under exposure to either hydrogen peroxide or menadione. We find that significant subtensors represent independent biological programs or experimental phenomena. The picture that emerges suggests that the conserved genes\n YKU70<\/jats:italic>\n ,\n MRE11<\/jats:italic>\n ,\n AIF1<\/jats:italic>\n , and\n ZWF1<\/jats:italic>\n , and the processes of retrotransposition, apoptosis, and the oxidative pentose phosphate pathway that these genes are involved in, may play significant, yet previously unrecognized, roles in the differential effects of hydrogen peroxide and menadione on cell cycle progression. A genome-scale correlation between DNA replication initiation and RNA transcription, which is equivalent to a recently discovered correlation and might be due to a previously unknown mechanism of regulation, is independently uncovered.\n <\/jats:p>","DOI":"10.1073\/pnas.0709146104","type":"journal-article","created":{"date-parts":[[2007,11,14]],"date-time":"2007-11-14T21:19:01Z","timestamp":1195075141000},"page":"18371-18376","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":129,"title":["A tensor higher-order singular value decomposition for integrative analysis of DNA microarray data from different studies"],"prefix":"10.1073","volume":"104","author":[{"given":"Larsson","family":"Omberg","sequence":"first","affiliation":[{"name":"*Physics, and"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gene H.","family":"Golub","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Stanford University, Stanford, CA 94305"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Orly","family":"Alter","sequence":"additional","affiliation":[{"name":"Departments of \u2021Biomedical Engineering and"},{"name":"Institutes for Cellular and Molecular Biology and Computational Engineering and Sciences, University of Texas, Austin, TX 78712; 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