Dimensionality Reduction Using Graph Weighted Subspace Learning for Bankruptcy Prediction

  • Bernardete RibeiroEmail author
  • Ning Chen
Part of the Annals of Information Systems book series (AOIS, volume 17)


Bankruptcy prediction is an extremely actual and important topic in the world. In this complex problem, dimensionality reduction becomes important easing both tasks of visualization and classification. Despite the different motivations, these algorithms can be cast in a graph embedding framework. In this paper we address weighted graph subspace learning methods for dimensionality reduction of bankruptcy data. The rationale behind re-embedding the data in a lower dimensional space that would be better filled is twofold: to get the most compact representation (visualization) and to make subsequent processing of data more easy (classification). To achieve this, two graph weighted subspace learning models are investigated, namely graph regularized non-negative matrix factorization (GNMF) and spatially smooth subspace learning (SSSL). Through an affinity weight graph matrix, the geometric properties are embedded explicitly into the submanifold lying in the high-dimensional data, consequently, the resulting subspace models allow compact representations able to enhance visualization, clustering and classification. The experimental results on a real world database of French companies show that the graph weighted subspace learning models used in a supervised learning manner are very effective for bankruptcy prediction.


Support Vector Machine Credit Risk Generalize Regression Neural Network Rand Index Local Linear Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Aha, H., Kim, K.: Bankruptcy prediction modeling with hybrid case-based reasoning and genetic algorithms approach. Appl. Soft Comput. 9(2), 599–607 (2009)CrossRefGoogle Scholar
  2. 2.
    Altman, E.: Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J. Financ. 23(4), 589–609 (1968)CrossRefGoogle Scholar
  3. 3.
    Altman, E.: Corporate Financial Distress and Bankruptcy: A Complete Guide to Predicting and Avoiding Distress and Profiting from Bankruptcy, 2nd edn. Wiley, New York (1993)Google Scholar
  4. 4.
    Atiya, A.: Bankruptcy prediction for credit risk using neural networks: A survey and new results. IEEE Trans. Neural Netw. 12(4), 929–935 (2001)CrossRefGoogle Scholar
  5. 5.
    Baek, J., Cho, S.: Bankruptcy prediction for credit risk using an auto-associative neural network in Korean firms. In: Proceedings of International Conference on Computational Intelligence for Financial Engineering, Hong Kong, pp. 25–29. IEEE (2003)Google Scholar
  6. 6.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems 14, pp. 585–591. MIT Press, Cambridge, MA (2002)Google Scholar
  7. 7.
    Bellovary, J., Giacomino, D., Akers, M.: A review of bankruptcy prediction studies: 1930 to present. J. Financ. Educ. 33(4), 1–43 (2007)Google Scholar
  8. 8.
    Boyacioglu, M., Kara, Y., Baykan, O.: Predicting bank financial failures using neural networks, support vector machines and multivariate statistical methods: A comparative analysis in the sample of savings deposit insurance fund (SDIF) transferred banks in Turkey. Expert Syst. Appl. 36(2, Part 2), 3355–3366 (2009)CrossRefGoogle Scholar
  9. 9.
    Cai, D., He, X., Han, J.: Document clustering using locality preserving indexing. IEEE Trans. Knowl. Data Eng. 17(12), 1624–1637 (2005)CrossRefGoogle Scholar
  10. 10.
    Cai, D., He, X., Hu, Y., Han, J., Huang, T.: Learning a spatially smooth subspace for face recognition. In: Proceedings of International Conference on Computer Vision and Pattern Recognition Machine Learning (CVPR'07), Rio de Janeiro, Brazil, pp. 1–7. IEEE (2007)Google Scholar
  11. 11.
    Cai, D., He, X., Han, J., Huang, T.S.: Graph regularized non-negative matrix factorization for data representation. IEEE Trans. Pattern Anal. Mach. Intell. 33(8), 1548–1560 (2011)CrossRefGoogle Scholar
  12. 12.
    Cao, Y.: Aggregating multiple classification results using Choquet integral for financial distress early warning. Expert Syst. Appl. 39(2), 1830–1836 (2012)CrossRefGoogle Scholar
  13. 13.
    Chandra, D., Ravi, V., Ravisankar, P.: Support vector machine and wavelet neural network hybrid: Application to bankruptcy prediction in banks. Int. J. Data Min. Model. Manag. 2(9), 1–21 (2010)Google Scholar
  14. 14.
    Charalambous, C., Charitou, A., Kaourou, F.: Application of feature extractive algorithm to bankruptcy prediction. In: Proceedings of International Joint Conference on Neural Networks, Como, Italy, vol. 5, pp. 303–308. IEEE (2000)Google Scholar
  15. 15.
    Chen, N., Vieira, A.: Bankruptcy prediction based on independent component analysis. In: Proceedings of International Conference on Agents and Artificial Intelligence (ICAART09), pp. 150–155 (2009)Google Scholar
  16. 16.
    Chen, N., Vieira, A., Ribeiro, B., Duarte, J., Neves, J.: A stable credit rating model based on learning vector quantization. Int. J. Intell. Data Anal. 15(2), 237–250 (2011)Google Scholar
  17. 17.
    Chung, F.: Spectral Graph Theory, 1st edn. American Mathematical Society, Providence (1997)Google Scholar
  18. 18.
    Cox, T., Cox, M.: Multidimensional Scaling, 1st edn. Chapman & Hall, London (1994)Google Scholar
  19. 19.
    Demsar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)Google Scholar
  20. 20.
    Garcia, S., Fernandez, A., Luengo, J., Herrera, F.: Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Inf. Sci. 180(10), 2044–2064 (2010)CrossRefGoogle Scholar
  21. 21.
    Gestel, T., Baesens, B., Suykens, J., Poel, D., Baestaens, D.E., Willekens, M.: Bayesian kernel based classification for financial distress detection. Eur. J. Oper. Res. 172(3), 979–1003 (2006)CrossRefGoogle Scholar
  22. 22.
    Hadsell, R., Chopra, S., LeCun, Y.: Dimensionality reduction by learning an invariant mapping. In: Proceedings of Computer Vision and Pattern Recognition Conference (CVPR'06), pp. 1735–1742. IEEE (2006)Google Scholar
  23. 23.
    Ham, J., Lee, D., Mika, S., Scholkopf, B.: A kernel view of the dimensionality reduction of manifolds. In: Proceedings of International Conference on Machine Learning, Alberta, Canada, pp. 47–54 (2004)Google Scholar
  24. 24.
    He, X., Niyogi, P.: Locality preserving projections. In: Thrun, S., Saul, L., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems 16, pp. 153–160. MIT Press, Cambridge (2004)Google Scholar
  25. 25.
    Huang, F.: A genetic fuzzy neural network for bankruptcy prediction in chinese corporations. In: Proceedings of International Conference on Risk Management & Engineering Management (ICRMEM08), pp. 542–546 (2008)Google Scholar
  26. 26.
    Huang, Z., Chen, H., Hsu, C., Chen, W., Wu, S.: Credit rating analysis with support vector machines and neural networks: a market comparative study. Decis. Support Syst. 37(4), 543–558 (2004)CrossRefGoogle Scholar
  27. 27.
    Huang, K., Kuo, Y., Yeh, I.: A novel fitness function in genetic algorithm to optimize neural networks for imbalanced data sets. In: Proceedings of 8th International Conference on Intelligent Systems Design and Applications. pp. 647–650 (2008)Google Scholar
  28. 28.
    Hung, C., Chen, J.: A selective ensemble based on expected probabilities for bankruptcy prediction. Expert Syst. Appl. 36(3), 5297–5303 (2009)CrossRefGoogle Scholar
  29. 29.
    Kima, M., Kang, D.: Ensemble with neural networks for bankruptcy prediction. Expert Syst. Appl. 37(4), 3373–3379 (2010)CrossRefGoogle Scholar
  30. 30.
    Kumar, P.R., Ravi, V.: Bankruptcy prediction in banks and firms via statistical and intelligent techniques - a review. Eur. J. Oper. Res. 180(1), 1–28 (2007)CrossRefGoogle Scholar
  31. 31.
    Lee, D., Seung, H.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems 13. pp. 556–562. MIT Press, Cambridge, MA (2001)Google Scholar
  32. 32.
    Lin, S., Shiue, Y., Chen, S., Cheng, H.: Applying enhanced data mining approaches in predicting bank performance: A case of taiwanese commercial banks. Expert Syst. Appl. 36(9), 11543–11551 (2009)CrossRefGoogle Scholar
  33. 33.
    Min, J., Lee, Y.: Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters. Expert Syst. Appl. 28(4), 603–614 (2005)CrossRefGoogle Scholar
  34. 34.
    Min, S., Lee, J., Han, I.: Hybrid genetic algorithms and support vector machines for bankruptcy prediction. Expert Syst. Appl. 31(3), 652–660 (2006)CrossRefGoogle Scholar
  35. 35.
    Min, J., Jeong, C., Kim, M.: Tuning the architecture of support vector machine - the case of bankruptcy prediction. Int. J. Manag. Sci. 17(1), 1–116 (2011)Google Scholar
  36. 36.
    Pai, G.R., Annapoorani, R., Pai, G.V.: Performance analysis of a statistical and an evolutionary neural network based classifier for the prediction of industrial bankruptcy. In: Proceedings of International Conference on Cybernetics and Intelligent Systems, vol. 2, Singapore, pp. 1033–1038. IEEE (2004)Google Scholar
  37. 37.
    Rafiei, M., Manzari, S., Bostanian, S.: Financial health prediction models using artificial neural networks, genetic algorithm and multivariate discriminant analysis: Iranian evidence. Expert Syst. Appl. 38(8), 10210–10217 (2011)CrossRefGoogle Scholar
  38. 38.
    Ravi, V., Kurniawan, H., Thai, P.N.K., Kumar, P.R.: Soft computing system for bank performance prediction. Appl. Soft Comput. 8(1), 305–315 (2008)CrossRefGoogle Scholar
  39. 39.
    Ribeiro, B., Chen, N.: Graph weighted subspace learning models in bankruptcy. In: Proceedings of International Joint Conference on Neural Networks (IJCNN), San Jose, USA, pp. 2055–2061. IEEE (2011)Google Scholar
  40. 40.
    Ribeiro, B., Silva, C., Neves, J.: Sparse Bayesian models: Bankruptcy-predictors of choice? In: Proceedings of International Joint Conference on Neural Networks, Vancouver, Canada, pp. 3377–3381. IEEE (2006)Google Scholar
  41. 41.
    Ribeiro, B., Vieira, A., Carvalho das Neves, J.: Supervised isomap with dissimilarity measures in embedding learning. In: Ruiz-Shulcloper, J., Kropatsch, W. (eds.) Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science, vol. 5197, pp. 389–396. Springer, Berlin (2008)Google Scholar
  42. 42.
    Ribeiro, B., Silva, C., Vieira, A., Neves, J.: Extracting discriminative features using non-negative matrix factorization in financial distress data. In: Kolehmainen, M., Toivanen, P., Beliczynski, B. (eds.) Adaptive and Natural Computing Algorithms, Lecture Notes in Computer Science, vol. 5495, pp. 537–547. Springer, Berlin (2009)Google Scholar
  43. 43.
    Ribeiro, B., Vieira, A., Duarte, J., Silva, C., das Neves, J., Liu, Q., Sung, A.: Learning manifolds for bankruptcy analysis. In: Köppen, M., Kasabov, N., Coghill, G. (eds.) Advances in Neuro-Information Processing, Lecture Notes in Computer Science, vol. 5506, pp. 723–730. Springer, Berlin (2009)Google Scholar
  44. 44.
    Ribeiro, B., Silva, C., Chen, N., Vieira, A., Neves, J.: Enhanced default risk models with SVM+. Expert Syst. Appl. 39(11), 10140–10152 (2012)CrossRefGoogle Scholar
  45. 45.
    Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  46. 46.
    Shin, K., Han, I.: A case-based approach using inductive indexing for corporate bond rating. Decis. Support Syst. 32(1), 41–52 (2001)CrossRefGoogle Scholar
  47. 47.
    Sun, J., Li, H.: Listed companies financial distress prediction based on weighted majority voting combination of multiple classifiers. Expert Syst. Appl. 35(3), 818–827 (2008)CrossRefGoogle Scholar
  48. 48.
    Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)CrossRefGoogle Scholar
  49. 49.
    Tsai, C.F.: Feature selection in bankruptcy prediction. Knowl. Based Syst. 22(2), 120–127 (2009)CrossRefGoogle Scholar
  50. 50.
    Tsai, C.F., Wu, J.W.: Using neural network ensembles for bankruptcy prediction and credit scoring. Expert Syst. Appl. 34(4), 2639–2649 (2008)CrossRefGoogle Scholar
  51. 51.
    Tseng, F., Hu, Y.: Comparing four bankruptcy prediction models: Logit, quadratic interval logit, neural and fuzzy neural networks. Expert Syst. Appl. 37(3), 1846–1853 (2010)CrossRefGoogle Scholar
  52. 52.
    Vapnik, V., Vashist, A.: A new learning paradigm: Learning using privileged information. Neural Netw. 22(5–6), 544–557 (2009)CrossRefGoogle Scholar
  53. 53.
    Verikas, A., Kalsyte, Z., Bacauskiene, M., Gelzinis, A.: Hybrid and ensemble-based soft computing techniques in bankruptcy prediction: A survey. Soft Comput. Fus. Found. Methodol. Appl. 14(9), 995–1010 (2010)Google Scholar
  54. 54.
    Verleysen, M.: Learning high-dimensional data. In: Limitations and Future Trends in Neural Computation, pp. 141–162. IOS, Netherlands (2003)Google Scholar
  55. 55.
    Yan, S., Liu, J., Tang, X., Huang, T.: A parameter-free framework for general supervised subspace learning. IEEE Trans. Inf. Forensics Secur. 2(1), 69–76 (2007)CrossRefGoogle Scholar
  56. 56.
    Yan, S., Xu, D., Zhang, B., Zhang, H., Yang, Q., Lin, S.: Graph embedding and extensions: A general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 29(1), 40–51 (2007)CrossRefGoogle Scholar
  57. 57.
    Yang, Z., You, W., Ji, G.: Using partial least squares and support vector machines for bankruptcy prediction. Expert Syst. Appl. 38(7), 8336–8342 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.GECADInstituto Superior de Engenharia do PortoPortoPortugal

Personalised recommendations