Skip to main content
SpringerLink
Log in

A survival ensemble of extreme learning machine

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Due to the fast learning speed, simplicity of implementation and minimal human intervention, extreme learning machine has received considerable attentions recently, mostly from the machine learning community. Generally, extreme learning machine and its various variants focus on classification and regression problems. Its potential application in analyzing censored time-to-event data is yet to be verified. In this study, we present an extreme learning machine ensemble to model right-censored survival data by combining the Buckley-James transformation and the random forest framework. According to experimental and statistical analysis results, we show that the proposed model outperforms popular survival models such as random survival forest, Cox proportional hazard models on well-known low-dimensional and high-dimensional benchmark datasets in terms of both prediction accuracy and time efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. David C R (1972) Regression models and life tables (with discussion). J R Stat Soc 34:187–220

    Google Scholar 

  2. Cox D R, Oakes D (1984) Analysis of survival data, vol 21. CRC Press, Cleveland

    Google Scholar 

  3. Tibshirani R et al (1997) The lasso method for variable selection in the cox model. Stat Med 16(4):385–395

    Article  Google Scholar 

  4. Gui J, Li H (2005) Penalized cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21(13):3001–3008

    Article  Google Scholar 

  5. Simon N, Friedman J H, Hastie T, Tibshirani R (2011) Regularization paths for cox’s proportional hazards model via coordinate descent. J Stat Softw 39(5):1–13

    Article  Google Scholar 

  6. Faraggi D, Simon R (1995) A neural network model for survival data. Stat Med 14(1):73–82

    Article  Google Scholar 

  7. Biganzoli E, Boracchi P, Mariani L, Marubini E (1998) Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach. Stat Med 17(10):1169– 1186

    Article  Google Scholar 

  8. LeBlanc M, Crowley J (1995) A review of tree-based prognostic models. In: Recent advances in clinical trial design and analysis. Springer, Berlin, pp 113–124

  9. Bou-Hamad I, Larocque D, Ben-Ameur H (2011) A review of survival trees. Stat Surv 5:44–71

    Article  MathSciNet  MATH  Google Scholar 

  10. Hothorn T, Bühlmann P, Dudoit S, Molinaro A, Van Der Laan M J (2006) Survival ensembles. Biostatistics 7(3):355–373

    Article  MATH  Google Scholar 

  11. Ishwaran H, Kogalur U B, Blackstone E H, Lauer M S (2008) Random survival forests. Ann Appl Stat 2(3):841–860

    Article  MathSciNet  MATH  Google Scholar 

  12. Lu W, Li L (2008) Boosting method for nonlinear transformation models with censored survival data. Biostatistics 9(4):658–667

    Article  Google Scholar 

  13. Ravdin P M, Clark G M (1992) A practical application of neural network analysis for predicting outcome of individual breast cancer patients. Breast Cancer Res Treat 22(3):285–293

    Article  Google Scholar 

  14. Ebell M H (1993) Artificial neural networks for predicting failure to survive following in-hospital cardiopulmonary resuscitation. J Fam Pract 36(3):297–304

    Google Scholar 

  15. Liestbl K, Andersen P K, Andersen U (1994) Survival analysis and neural nets. Stat Med 13(12):1189–1200

    Article  Google Scholar 

  16. Lisboa P J, Wong H, Harris P, Swindell R (2003) A bayesian neural network approach for modelling censored data with an application to prognosis after surgery for breast cancer. Artif Intell Med 28(1):1–25

    Article  Google Scholar 

  17. Biganzoli E M, Boracchi P, Ambrogi F, Marubini E (2006) Artificial neural network for the joint modelling of discrete cause-specific hazards. Artif Intell Med 37(2):119–130

    Article  Google Scholar 

  18. Ambrogi F, Lama N, Boracchi P, Biganzoli E (2007) Selection of artificial neural network models for survival analysis with genetic algorithms. Comput Stat Data Anal 52(1):30–42

    Article  MathSciNet  MATH  Google Scholar 

  19. Lisboa P J, Etchells T A, Jarman I H, Aung M H, Chabaud S, Bachelot T, Perol D, Gargi T, Bourdès V, Bonnevay S et al (2008) Time-to-event analysis with artificial neural networks: an integrated analytical and rule-based study for breast cancer. Neural Netw 21(2):414–426

    Article  Google Scholar 

  20. Xiang A, Lapuerta P, Ryutov A, Buckley J, Azen S (2000) Comparison of the performance of neural network methods and cox regression for censored survival data. Computat Stat Data Anal 34(2):243–257

    Article  MATH  Google Scholar 

  21. Huang G -B, Zhu Q -Y, Siew C -K (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1):489– 501

    Article  Google Scholar 

  22. Huang G -B, Zhou H, Ding X, Zhang R (2012) Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern Part B (Cybern) 42(2):513–529

    Article  Google Scholar 

  23. Huang G -B, Chen L, Siew C K et al (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892

    Article  Google Scholar 

  24. Wang Y, Cao F, Yuan Y (2011) A study on effectiveness of extreme learning machine. Neurocomputing 74(16):2483–2490

    Article  Google Scholar 

  25. Buckley J, James I (1979) Linear regression with censored data. Biometrika 66:429–436

    Article  MATH  Google Scholar 

  26. Wang S, Nan B, Zhu J, Beer D G (2008) Doubly penalized buckley–james method for survival data with high-dimensional covariates. Biometrics 64(1):132–140

    Article  MathSciNet  MATH  Google Scholar 

  27. Breiman L (2001) Random forests. Mach Learn 45(1):5–32

    Article  MATH  Google Scholar 

  28. Kaplan E L, Meier P (1958) Nonparametric estimation from incomplete observations. J Amer Stat Assoc 53(282):457– 481

    Article  MathSciNet  MATH  Google Scholar 

  29. Breiman L (1996) Bagging predictors. Mach Learn 24(2):123–140

    MathSciNet  MATH  Google Scholar 

  30. Ho T K (1998) The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell 20(8):832– 844

    Article  Google Scholar 

  31. Breiman L, Friedman J, Stone C J, Olshen R A (1984) Classification and regression trees. CRC Press, Cleveland

    MATH  Google Scholar 

  32. Fernández-Delgado M, Cernadas E, Barro S, Amorim D (2014) Do we need hundreds of classifiers to solve real world classification problems. J Mach Learn Res 15(1):3133–3181

    MathSciNet  MATH  Google Scholar 

  33. Ren Y, Zhang L, Suganthan P N (2016) Ensemble classification and regression-recent developments, applications and future directions [review article]. IEEE Comput Intell Mag 11(1):41– 53

    Article  Google Scholar 

  34. Jia L, Liao S (2009) Accurate probabilistic error bound for eigenvalues of kernel matrix. In: Asian conference on machine learning. Springer, Berlin, pp 162–175

  35. Polikar R (2006) Ensemble based systems in decision making. Circs Syst Mag IEEE 6(3):21–45

    Article  Google Scholar 

  36. Melville P, Mooney R J (2003) Constructing diverse classifier ensembles using artificial training examples. In: Proceedings of the 18th international joint conference on artificial intelligence, IJCAI’03. Morgan Kaufmann Publishers Inc., San Francisco, pp 505–510

  37. Harrell F E, Lee K L, Mark D B (1996) Tutorial in biostatistics multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Stat Med 15:361–387

    Article  Google Scholar 

  38. Dietterich T G (1998) Approximate statistical tests for comparing supervised classification learning algorithms. Neural Comput 10(7):1895–1923

    Article  Google Scholar 

  39. Demṡar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  Google Scholar 

  40. Hsu C W, Chang CC, Lin CJ (2016) A practical guide to support vector classification, Tech. rep., National Taiwan University. http://www.csie.ntu.edu.tw/cjlin/papers/guide/guide.pdf. Accessed 22 May 2017

  41. R Core Team (2016) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. https://www.R-project.org/

  42. Pohlert T (2014) The pairwise multiple comparison of mean ranks package (PMCMR). R package. http://CRAN.R-project.org/package=PMCMR. Accessed 22 May 2017

  43. Wright M, Ziegler A (2017) ranger: a fast implementation of random forests for high dimensional data in c++ and r. J Stat Softw 77(1):1–17. https://doi.org/10.18637/jss.v077.i01

    Article  Google Scholar 

  44. Ridgeway G (2017) gbm: generalized boosted regression models. R package. http://CRAN.R-project.org/package=gbm Accessed 22 May 2017

  45. Mersmann O (2015) microbenchmark: accurate timing functions. R package. https://CRAN.R-project.org/package=microbenchmark. Accessed 22 May 2017

  46. Deng W, Zheng Q, Chen L (2009) Regularized extreme learning machine. In: IEEE Symposium on computational intelligence and data mining, 2009. CIDM’09. IEEE, New York, pp 389– 395

  47. Liu N, Wang H (2010) Ensemble based extreme learning machine. IEEE Signal Process Lett 17(8):754–757

    Article  Google Scholar 

  48. Lu H-J, An C-L, Zheng E-H, Lu Y (2014) Dissimilarity based ensemble of extreme learning machine for gene expression data classification. Neurocomputing 128:22–30

    Article  Google Scholar 

  49. Yu Q, Van Heeswijk M, Miche Y, Nian R, He B, Séverin E, Lendasse A (2014) Ensemble delta test-extreme learning machine (dt-elm) for regression. Neurocomputing 129:153– 158

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Social Science Foundation of China (17BTJ019), Social Science Foundation for Young Scholars of Ministry of Education of China (15YJCZH166), Hunan Provincial Social Science Foundation of China (16YBA367), the scholarship from China Scholarship Council (CSC201606375129), China Postdoctoral Science Foundation (2017M612574) and Postgraduates Education Reform Fund (2016JGB25) at Central South University, China.

The funders had no role in the preparation of this article.

Author information

Authors and Affiliations

  1. School of Information Sciences and Engineering, Central South University, Changsha, China

    Hong Wang & Jianxin Wang

  2. School of Mathematics and Statistics, Central South University, Changsha, China

    Hong Wang

  3. School of Economics and Management, Changsha University, Changsha, China

    Lifeng Zhou

Authors
  1. Hong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianxin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lifeng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianxin Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, H., Wang, J. & Zhou, L. A survival ensemble of extreme learning machine. Appl Intell 48, 1846–1858 (2018). https://doi.org/10.1007/s10489-017-1063-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-017-1063-4

Keywords

Search

Navigation