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. 2019 Jul 5;9:9747. doi: 10.1038/s41598-019-46059-1

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© The Author(s) 2019

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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Classification potential for decomposed gene sets. Classification accuracies for the full Hallmark gene sets (green) are compared to accuracies of the candidate genes identified by the combinatorial decomposition algorithm (yellow), non-candidate genes (blue), and random genes (red). The performance analysis for (A) Hedgehog Signaling, (B) Angiogenesis, (C) Notch Signaling, and (D) MYC Targets V2 Hallmark sets are shown for both GTEx and TCGA datasets. The number at the bottom of each bar denotes the size of the gene sets for that result.