{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T10:14:12Z","timestamp":1771841652491,"version":"3.50.1"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"20","license":[{"start":{"date-parts":[[2018,4,27]],"date-time":"2018-04-27T00:00:00Z","timestamp":1524787200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology of Taiwan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001868","name":"NSC","doi-asserted-by":"publisher","award":["97-2118-M-032-001"],"award-info":[{"award-number":["97-2118-M-032-001"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001868","name":"NSC","doi-asserted-by":"publisher","award":["98-3112-B-001-027"],"award-info":[{"award-number":["98-3112-B-001-027"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001868","name":"NSC","doi-asserted-by":"publisher","award":["99-3112-B-001-029"],"award-info":[{"award-number":["99-3112-B-001-029"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research Program for Genomic Medicine"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,10,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Motivation<\/jats:title><jats:p>Heatmap is a popular visualization technique in biology and related fields. In this study, we extend heatmaps within the framework of matrix visualization (MV) by incorporating a covariate adjustment process through the estimation of conditional correlations. MV can explore the embedded information structure of high-dimensional large-scale datasets effectively without dimension reduction. The benefit of the proposed covariate-adjusted heatmap is in the exploration of conditional association structures among the subjects or variables that cannot be done with conventional MV.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>For adjustment of a discrete covariate, the conditional correlation is estimated by the within and between analysis. This procedure decomposes a correlation matrix into the within- and between-component matrices. The contribution of the covariate effects can then be assessed through the relative structure of the between-component to the original correlation matrix while the within-component acts as a residual. When a covariate is of continuous nature, the conditional correlation is equivalent to the partial correlation under the assumption of a joint normal distribution. A test is then employed to identify the variable pairs which possess the most significant differences at varying levels of correlation before and after a covariate adjustment. In addition, a z-score significance map is constructed to visualize these results. A simulation and three biological datasets are employed to illustrate the power and versatility of our proposed method.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>GAP is available to readers and is free to non-commercial applications. The installation instructions, the user\u2019s manual, and the detailed tutorials can be found at http:\/\/gap.stat.sinica.edu.tw\/Software\/GAP.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary Data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/bty335","type":"journal-article","created":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T06:44:44Z","timestamp":1524638684000},"page":"3529-3538","source":"Crossref","is-referenced-by-count":13,"title":["Covariate-adjusted heatmaps for visualizing biological data via correlation decomposition"],"prefix":"10.1093","volume":"34","author":[{"given":"Han-Ming","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Statistics, National Taipei University, New Taipei City, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yin-Jing","family":"Tien","sequence":"additional","affiliation":[{"name":"Digital Transformation Institute, Institute for Information Industry, Taipei, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng-Ru","family":"Ho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai-Gwo","family":"Hwu","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, National Taiwan University Hospital and College of Medicine, Taipei, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-chang","family":"Lin","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Sciences, Academia Sinica, Taipei, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mi-Hua","family":"Tao","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Sciences, Academia Sinica, Taipei, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun-houh","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,4,26]]},"reference":[{"key":"2023012712420384300_bty335-B10","volume-title":"Diagnostic and Statistical Manual of Mental Disorders DSM-IV, Fourth Edition","author":"American Psychiatric Association","year":"1996"},{"key":"2023012712420384300_bty335-B1","volume-title":"The Scale for the Assessment of Negative Symptoms (SANS)","author":"Andreasen","year":"1983"},{"key":"2023012712420384300_bty335-B2","volume-title":"The Scale for the Assessment of Positive Symptoms (SANS)","author":"Andreasen","year":"1984"},{"key":"2023012712420384300_bty335-B3","volume-title":"Semiologie Graphique, Paris: Editions Gauthier-Villars, 1967. 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