{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T15:49:20Z","timestamp":1781106560332,"version":"3.54.1"},"reference-count":21,"publisher":"National Academy of Sciences","issue":"49","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2005,12,6]]},"abstract":"<jats:p>We describe the use of the matrix eigenvalue decomposition (EVD) and pseudoinverse projection and a tensor higher-order EVD (HOEVD) in reconstructing the pathways that compose a cellular system from genome-scale nondirectional networks of correlations among the genes of the system. The EVD formulates a genes \u00d7 genes network as a linear superposition of genes \u00d7 genes decorrelated and decoupled rank-1 subnetworks, which can be associated with functionally independent pathways. The integrative pseudoinverse projection of a network computed from a \u201cdata\u201d signal onto a designated \u201cbasis\u201d signal approximates the network as a linear superposition of only the subnetworks that are common to both signals and simulates observation of only the pathways that are manifest in both experiments. We define a comparative HOEVD that formulates a series of networks as linear superpositions of decorrelated rank-1 subnetworks and the rank-2 couplings among these subnetworks, which can be associated with independent pathways and the transitions among them common to all networks in the series or exclusive to a subset of the networks. Boolean functions of the discretized subnetworks and couplings highlight differential, i.e., pathway-dependent, relations among genes. We illustrate the EVD, pseudoinverse projection, and HOEVD of genome-scale networks with analyses of yeast DNA microarray data.<\/jats:p>","DOI":"10.1073\/pnas.0509033102","type":"journal-article","created":{"date-parts":[[2005,11,28]],"date-time":"2005-11-28T20:34:10Z","timestamp":1133210050000},"page":"17559-17564","update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":45,"title":["Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations"],"prefix":"10.1073","volume":"102","author":[{"given":"Orly","family":"Alter","sequence":"first","affiliation":[{"name":"Department of Biomedical Engineering and Institute for Cellular and Molecular Biology, University of Texas, Austin, TX 78712; and Scientific Computing and Computational Mathematics Program and Department of Computer Science, Stanford University, Stanford, CA 94305"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gene H.","family":"Golub","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering and Institute for Cellular and Molecular Biology, University of Texas, Austin, TX 78712; and Scientific Computing and Computational Mathematics Program and Department of Computer Science, Stanford University, Stanford, CA 94305"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2005,11,28]]},"reference":[{"key":"e_1_3_2_1_2","doi-asserted-by":"publisher","DOI":"10.1091\/mbc.9.12.3273"},{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.287.5454.873"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1075090"},{"key":"e_1_3_2_4_2","first-page":"86","volume":"22","year":"2002","unstructured":"Ihmels, J., Levy, R. & Barkai, N. 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