Neural Computing and Applications

, Volume 25, Issue 3–4, pp 859–869 | Cite as

Extracting the contribution of independent variables in neural network models: a new approach to handle instability

  • Juan de OñaEmail author
  • Concepción Garrido
Original Article


One of the main limitations of artificial neural networks (ANN) is their high inability to know in an explicit way the relations established between explanatory variables (input) and dependent variables (output). This is a major reason why they are usually called “black boxes.” In the last few years, several methods have been proposed to assess the relative importance of each explanatory variable. Nevertheless, it has not been possible to reach a consensus on which is the best-performing method. This is largely due to the different relative importance obtained for each variable depending on the method used. This importance also varies with the designed network architecture and/or with the initial random weights used to train the ANN. This paper proposes a procedure that seeks to minimize these problems and provides consistency in the results obtained from different methods. Essentially, the idea is to work with a set of neural networks instead of a single one. The proposed procedure is validated using a database collected from a customer satisfaction survey, which was conducted on the public transport system of Granada (Spain) in 2007. The results show that, when each method is applied independently, the variable’s importance rankings are similar and, in addition, coincide with the hierarchy established by researchers who have applied other techniques.


Instability Neural networks Black box Variables contribution’s methods Importance ranking 



Support from Consejería de Innovación, Ciencia y Economía of the Junta de Andalucía (Spain) (Research Project P08-TEP-03819, co-funded by FEDER) is gratefully acknowledged. The authors also acknowledge the Granada Consorcio de Transportes for making the data set available for this study.


  1. 1.
    Akin D, Akbaç B (2010) A neural network (NN) model to predict intersection crashes based upon driver, vehicle and roadway surface characteristics. Sci Res Essays 5(19):2837–2847Google Scholar
  2. 2.
    Azadeh A, Rouzbahman M, Saberi M, Fam IM (2011) An adaptative neural network algorithm for assessment and improvement of job satisfaction with respect to HSE and ergonomics program: the case of a gas refinery. J Loss Prev Process Ind 24:361–370CrossRefGoogle Scholar
  3. 3.
    Beale MH, Hagan MT, Demuth HB (2007) Neural Network Toolbox 7. User’s Guide. MathWorks, Inc. 3 Apple Hill Drive Natic, MA 01760-2098Google Scholar
  4. 4.
    Cao M, Qiao P (2008) Neural network committee-based sensitivity analysis strategy for geotechnical engineering problems. Neural Comput Appl 17:509–519CrossRefGoogle Scholar
  5. 5.
    Cortez P, Embrechts MJ (2011) Opening black box data mining models using sensitivity analysis. IEEE symposium series in computational intelligence, Paris, France, 4, 2011Google Scholar
  6. 6.
    Cortez P, Embrechts MJ (2013) Using sensitivity analysis and visualization techniques to open black box data mining models. Inf Sci 225:1–17CrossRefGoogle Scholar
  7. 7.
    De Oña J, De Oña R, Calvo FJ (2012) A classification tree approach to identify key factors of transit service quality. Expert Syst Appl 39:11164–11171CrossRefGoogle Scholar
  8. 8.
    De Oña J, De Oña R, Eboli L, Mazzulla G (2013) Perceived service quality in bus transit service: a structural equation approach. Transp Policy 29:219–226CrossRefGoogle Scholar
  9. 9.
    Delen D, Sharda R, Bessonov M (2006) Identifying significant predictors of injury severity in traffic accidents using a series of artificial neural networks. Accid Anal Prev 38:434–444CrossRefGoogle Scholar
  10. 10.
    Dell’Olio L, Ibeas A, Cecín P (2010) Modelling user perception of bus transit quality. Transp Policy 17(6):388–397CrossRefGoogle Scholar
  11. 11.
    Dell’Olio L, Ibeas A, Cecín P (2011) The quality of service desired by public transport users. Transp Policy 18(1):217–227CrossRefGoogle Scholar
  12. 12.
    Dimopoulos Y, Bourret P, Lek S (1995) Use of some sensitivity criteria for choosing networks with good generalization ability. Neural Process Lett 2:1–4CrossRefGoogle Scholar
  13. 13.
    Eboli L, Mazulla G (2008) Willingness-to-pay of public transport users for improvement in service quality. Eur Transp 38:107–118Google Scholar
  14. 14.
    Eboli L, Mazulla G (2010) How to capture the passengers’ point of view on a transit service through rating and choice opinions. Transp Rev 30:435–450CrossRefGoogle Scholar
  15. 15.
    Engelbrecht AP, Cloete I, Zurada JM (1995) Determining the significance of input parameters using sensitivity analysis, from natural to artificial neural computation. In: proceedings of International Workshop on Artificial Neural Networks. Málaga-Torremolinos, Springer, Spain, pp 382–388Google Scholar
  16. 16.
    Funahashi KI (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192CrossRefGoogle Scholar
  17. 17.
    Garson GD (1991) Interpreting neural-network connection weights. Artif Intell Expert 6:47–51Google Scholar
  18. 18.
    Gedeon, T.D., Wong, P.M. & Harris, D., (1995). Balancing the bias and variance: network topology and pattern set reduction techniques. In: proceedings of International Workshop on Artificial Neural Networks, IWANN95, Torremolinos, España, pp 550–558Google Scholar
  19. 19.
    Gedeon TD (1997) Data mining of inputs: analyzing magnitude of functional measures. Int J Neural Syst 8(2):209–218MathSciNetCrossRefGoogle Scholar
  20. 20.
    Gevrey M, Dimopoulos I, Lek S (2003) Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecol Model 160:249–264CrossRefGoogle Scholar
  21. 21.
    Gevrey M, Dimopoulos I, Lek S (2006) Two-way interaction of input variables in the sensitivity analysis of neural network models. Ecol Model 195:43–50CrossRefGoogle Scholar
  22. 22.
    Goh ATC (1995) Back-propagation neural networks for modeling complex systems. Artif Intell Eng 9:143–151CrossRefGoogle Scholar
  23. 23.
    Hagan MT, Demuth HB, Beale MH (1996) Neural network design. Campus Publishing Service, Colorado University Bookstore, Colorado. ISBN 0-9717321-0-8Google Scholar
  24. 24.
    He F, Sung AH, Guo B (1997) A neural network for prediction of oil well cement bonding quality. In: proceedings of IASTED international conference on control, IASTED-ACTA Press, Cancun-Mexico, pp 417–420Google Scholar
  25. 25.
    Hunter A, Kennedy L, Henry J, Ferguson I (2000) Application of neural networks and sensitivity analysis to improved prediction of trauma survival. Comput Methods Progr Biomed 62:11–19CrossRefGoogle Scholar
  26. 26.
    Hornik K, Stichcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366CrossRefGoogle Scholar
  27. 27.
    Kemp SL, Zaradic P, Hansen F (2007) An approach for determining relative input parameter importance and significance in artificial neural networks. Ecol Model 204:326–334CrossRefGoogle Scholar
  28. 28.
    Kewley R, Embrechts M, Breneman C (2000) Data strip mining for the virtual design of pharmaceuticals with neural networks. IEEE Trans Neural Netw 11(3):668–679CrossRefGoogle Scholar
  29. 29.
    Lek S, Beland A, Dimopoulos I, Lauga J, Moreau J (1995) Improved estimation, using neural networks, of the food consumption of fish populations. Mar Freshw Res 46(8):1229–1236CrossRefGoogle Scholar
  30. 30.
    Lek S, Delacoste M, Baran P, Dimopoulos I, Lauga J, Aulagnier S (1996) Application of neural networks to modeling nonlinear relationships in ecology. Ecol Model 90:39–52CrossRefGoogle Scholar
  31. 31.
    Lek S, Beland A, Baran P, Dimopoulos I, Delacoste M (1996) Role of some environmental variables in trout abundance models using neural networks. Aquat Living Resour 9:23–29CrossRefGoogle Scholar
  32. 32.
    Lin Y, Cunningham GA (1995) A new approach to fuzzy-neural system modeling. IEEE Trans Fuzzy Syst 3(2):190–198CrossRefGoogle Scholar
  33. 33.
    Martín del Bío B, Sanz Molina A (2006) Neural networks and fuzzy systems. Editorial RA-MAGoogle Scholar
  34. 34.
    Masters T (1993) Practical neural networks recipes in C ++. Academic Press, WalthamGoogle Scholar
  35. 35.
    Moghaddam FR, Afandizadeh S, Ziyadi M (2010) Prediction of accident severity using artificial neural networks. Int J Civ Eng 9:1Google Scholar
  36. 36.
    Mohammadipour AH, Alavi SH (2009) The optimization of the geometric cross-section dimensions of raised pedestrian crosswalks: a case of study in Qazvin. Accid Anal Prev 41:314–326CrossRefGoogle Scholar
  37. 37.
    Mussone L, Ferrari A, Oneta M (1999) An analysis of urban collisions using an artificial intelligence model. Accid Anal Prev 31:705–718CrossRefGoogle Scholar
  38. 38.
    Olden JD, Jackson DA (2002) Illuminating the “black-box”: a randomization approach for understanding variable contributions in artificial neural networks. Ecol Model 154:135–150CrossRefGoogle Scholar
  39. 39.
    Olden JD, Joy MK, Death RG (2004) An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. Ecol Model 178:389–397CrossRefGoogle Scholar
  40. 40.
    Özesmi SL, Özesmi U (1999) An artificial neural network approach to spatial habitat modeling with interspecific interaction. Ecol Model 116:15–31CrossRefGoogle Scholar
  41. 41.
    Paliwal M, Kumar UA (2011) Assessing the contribution of variables in feed forward neural network. Appl Soft Comput 11:3690–3696CrossRefGoogle Scholar
  42. 42.
    Palmer A, Montaño JJ (2002a) Redes neuronales artificiales aplicadas al análisis de datos. Doctoral Dissertation. University of Palma de MallorcaGoogle Scholar
  43. 43.
    Palmer A, Montaño JJ (2002) Redes neuronales artificiales: abriendo la caja negra. Metodología de las ciencias del comportamiento 4(1):77–93Google Scholar
  44. 44.
    Palmer A, Montaño JJ (2003) Numeric sensitivity analysis applied to feed forward neural networks. Neural Comput Appl 12:119–125CrossRefGoogle Scholar
  45. 45.
    Rzempoluk EJ (1998) Neural network data analysis using simulnet. Springer, New YorkCrossRefGoogle Scholar
  46. 46.
    Rumelhart DE, McClelland JL (1986) Parallel distributed processing, vol 1: foundations. MIT Press, CambridgeGoogle Scholar
  47. 47.
    Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by backpropagation errors. Nature 323:533–536CrossRefGoogle Scholar
  48. 48.
    Scardi M, Harding LW (1999) Developing an empirical model of phytoplankton primary production: a neural networks case study. Ecol Model 120(2–3):213–223CrossRefGoogle Scholar
  49. 49.
    Sung AH (1998) Ranking importance of input parameters of neural networks. Expert Syst Appl 15:405–411CrossRefGoogle Scholar
  50. 50.
    Watts MJ, Worner SP (2008) Using artificial neural networks to determine the relative contribution of abiotic factors influencing the establishment of insect pest species. Ecol Inform 3:64–74CrossRefGoogle Scholar
  51. 51.
    Werbos PJ (1974) Beyond regression: new tools for prediction and analysis in behavioral sciences. Doctoral Dissertation. Applied Mathematics, Harvard UniversityGoogle Scholar
  52. 52.
    Yao J, Teng N, Poh HL, Tan CL (1998) Forecasting and analysis of marketing data using neural networks. J Inf Sci Eng 14:843–862Google Scholar
  53. 53.
    Yeh I, Cheng W (2010) First and second order sensitivity analysis of MLP. Neurocomputing 73:2225–2233CrossRefGoogle Scholar
  54. 54.
    Zhou ZH, Wu J, Tang W (2002) Ensembling neural networks: many could be better than all. Artif Intell 137(1–2):239–263zbMATHMathSciNetCrossRefGoogle Scholar
  55. 55.
    Zurada JM, Malinowski A, Cloete I (1994) Sensitivity analysis for minimization of input data dimensión for feed forward neural network. In: proceedings of IEEE international symposium on circuits and systems, IEEE Press, LondonGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.TRYSE Research Group, Department of Civil EngineeringUniversity of GranadaGranadaSpain

Personalised recommendations