{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T04:59:14Z","timestamp":1778129954435,"version":"3.51.4"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Cancer is a heterogeneous progressive disease caused by perturbations of the underlying gene regulatory network that can be described by dynamic models. These dynamics are commonly modeled as Boolean networks or as ordinary differential equations. Their inference from data is computationally challenging, and at least partial knowledge of the regulatory network and its kinetic parameters is usually required to construct predictive models.<\/jats:p>\n               <jats:p>Results: Here, we construct Hopfield networks from static gene-expression data and demonstrate that cancer subtypes can be characterized by different attractors of the Hopfield network. We evaluate the clustering performance of the network and find that it is comparable with traditional methods but offers additional advantages including a dynamic model of the energy landscape and a unification of clustering, feature selection and network inference. We visualize the Hopfield attractor landscape and propose a pruning method to generate sparse networks for feature selection and improved understanding of feature relationships.<\/jats:p>\n               <jats:p>Availability: Software and datasets are available at http:\/\/acb.qfab.org\/acb\/hclust\/<\/jats:p>\n               <jats:p>Contact: \u00a0m.ragan@uq.edu.au<\/jats:p>\n               <jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btt773","type":"journal-article","created":{"date-parts":[[2014,1,10]],"date-time":"2014-01-10T02:04:52Z","timestamp":1389319492000},"page":"1273-1279","source":"Crossref","is-referenced-by-count":29,"title":["Characterizing cancer subtypes as attractors of Hopfield networks"],"prefix":"10.1093","volume":"30","author":[{"given":"Stefan R.","family":"Maetschke","sequence":"first","affiliation":[{"name":"1 The University of Queensland, Institute for Molecular Bioscience, Brisbane, QLD 4072, Australia and 2Australian Research Council Centre of Excellence in Bioinformatics, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark A.","family":"Ragan","sequence":"additional","affiliation":[{"name":"1 The University of Queensland, Institute for Molecular Bioscience, Brisbane, QLD 4072, Australia and 2Australian Research Council Centre of Excellence in Bioinformatics, Australia"},{"name":"1 The University of Queensland, Institute for Molecular Bioscience, Brisbane, QLD 4072, Australia and 2Australian Research Council Centre of Excellence in Bioinformatics, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2014,1,8]]},"reference":[{"key":"2023012710502247900_btt773-B1","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1016\/j.mehy.2007.03.043","article-title":"Cancer as robust intrinsic state of endogenous molecular-cellular network shaped by evolution","volume":"70","author":"Ao","year":"2008","journal-title":"Med. 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Clin. Bioinforma."},{"key":"2023012710502247900_btt773-B46","doi-asserted-by":"crossref","first-page":"8257","DOI":"10.1073\/pnas.1017017108","article-title":"Quantifying the Waddington landscape and biological paths for development and differentiation","volume":"108","author":"Wang","year":"2011","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2023012710502247900_btt773-B47","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1080\/01621459.1963.10500845","article-title":"Hierarchical grouping to optimize an objective function","volume":"58","author":"Ward","year":"1963","journal-title":"J. Am. Stat. 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