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. 2017 Oct 17;7:13356. doi: 10.1038/s41598-017-13470-5

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Four matrices constructed for each gene j and each condition, i.e., a specific cancer stage. Y represents the vector of expression changes of gene j in the corresponding cancer patients under this condition; X ₁ represents the matrix of background adjustment factors (CNV and DNA methylation); R represents a RS vector that contains the regulatory scores of all r ₁ TF- and r ₂ miRNA- regulators of gene j; P is the matrix that includes all the expression changes of each regulator in each patient under the corresponding condition.