Correction to: Enhancing SVM for survival data using local invariances and weighting
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CORRECTION
Open Access
Correction to: Enhancing SVM for survival data using local invariances and weighting Hector Sanz1*, Ferran Reverter1,2 and Clarissa Valim3,4 The original article can be found online at https://doi.org/10.1186/ s12859-020-3481-2. * Correspondence: hsrodenas@ gmail.com 1 Department of Genetics, Microbiology and Statistics, Faculty of Biology, Universitat de Barcelona, Diagonal, 643, 08028 Barcelona, Catalonia, Spain Full list of author information is available at the end of the article
Correction to: BMC Bioinformatics 21, 193 (2020) https://doi.org/10.1186/s12859-020-3481-2 Following publication of the original article [1], the authors identified errors in the equations. The correct equations are given below. Equation (7) ðtiþzÞ
S zðtiÞ ¼ SSðtiÞ
Equation (8) n X 1 ξi ðkwk2 þ γkw k2 Þ þ C 2 i¼1
minimize w;w ;b;b
subject to ξ i ¼ ðhw ; xi i þ b Þ; yi ðhw; xi i þ bÞ ≥ 1−ðhw ðhw
; xi i
i ¼ 1; …; n
; xi i
þ b Þ;
þ b Þ ≥ 0;
i ¼ 1; …; n i ¼ 1; …; n
Equation (10) minimize w;b
1 kwk2 2
subject to yi ðhw; xi i ¼ bÞ ≥ 1; z−i ≤ hw; xi i
þ
i ¼ 1; …; n
b ≤zþ i ;
i ¼ n þ 1; …; m
Re-expression of Equation (10) minimize − þ w;ξ;ξ ;ξ ;b
n m X X 1 ~ ξi þ C ðξ −i þ ξ þ kwk2 þ C i Þ 2 i¼1 i¼nþ1
subject to yi ðhw; xi i þ bÞ ≥ 1−ξ i ; z−i −ξ −i ≤ hw; xi i
ξ i ≥ 0; ξ −i ≥ 0;
ξþ i ≥ 0;
þ
b ≤ zþ i
i ¼ 1; …; n þ
ξþ i ;
i ¼ n þ 1; …; m i ¼ 1; …; n i ¼ n þ 1; …; m i ¼ n þ 1; …; m
© The Author(s). 2020 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
Sanz et al. BMC Bioinformatics
(2020) 21:371
Page 2 of 2
Equation (11) 1 kwk2 2
minimize w;b
subject to yi ðhw; xi i þ bÞ ≥ 1; z−i ≤hw; xi i þ b≤ zþ i ;
i ¼ 1; …; n i ¼ n þ 1; …; m
Equation (13) n X 1 W iξ i kwk2 þ C 2 i¼1
minimize w;ξ
subject to yi ðhw; xi i þ bÞ ≥ 1−ξ i ; ξ i ≥ 0;
i ¼ 1; …; n i ¼ 1; …; n
Equation (16) j
zxi; j ðxÞ ¼ σ12 ðx j −xi Þ expð− 2σ1 2 kx ¼ xi k2 Þ The original article has been corrected. Author details 1 Department of Genetics, Microbiology and Statistics, Faculty of Biology, Universitat de Ba
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