Abstract
In the recent financial crisis the incidence of important cases of bankruptcy led to a growing interest in corporate bankruptcy prediction models. In addition to building appropriate financial distress prediction models, it is also of extreme importance to devise dimensionality reduction methods able to extract the most discriminative features. Here we show that Non-Negative Matrix Factorization (NMF) is a powerful technique for successful extraction of features in this financial setting. NMF is a technique that decomposes financial multivariate data into a few basis functions and encodings using non-negative constraints. We propose an approach that first performs proper initialization of NMF taking into account original data using K-means clustering. Second, builds a bankruptcy prediction model using the discriminative financial ratios extracted by NMF decomposition. Model predictive accuracies evaluated in real database of French companies with statuses belonging to two classes (healthy and distressed) are illustrated showing the effectiveness of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)
Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002)
Paatero, P., Tapper, U.: Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126 (1994)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing 13 (Proc. NIPS 2000). MIT Press, Cambridge (2001)
Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. Journal of Machine Learning Research 5, 1457–1469 (2004)
Zhang, Z.Y., Zhang, X.S.: Two improvements of NMF used for tumor clustering. In: The First International Symposium on Optimization and Systems Biology (OSB 2007), pp. 242–249 (2007)
Carmona-Saez, P., Pascual-Marqui, R.D., Tirado, F., Carazo, J., Pascual-Montano, A.: Biclustering of gene expression data by non-smooth non-negative matrix factorization. BMC Bioinformatics (2006)
Fogel, P., Young, S., Hawkins, D.M., Ledirac, N.: Inferential, robust non-negative matrix factorization analysis of microarray data. BMC Bioinformatics 23(1), 44–49 (2007)
Brunet, J.P., Tamayo, P., Golub, T.R., Mesirov, J.P.: Metagenes and molecular pattern discovery using matrix factorization. In: National Academy of Science, vol. 101 (2004)
Guimet, F., Boqué, R., Ferré, J.: Application of non-negative matrix factorization combined with fisher’s linear discriminant analysis for classification of olive oil excitationemission fluorescence spectra. Chemometrics and Intelligent Laboratory Systems 81(2006), 94–106 (2006)
Stefan, W., James, C., Anne, D.: Motivating non-negative matrix factorization. In: Eighth SIAM Conference on Applied Linear Algebra, Williamsburg, VA (2003)
Cooper, M., Foote, J.: Summarizing video using non-negative similarity matrix factorization. In: IEEE Workshop on Multimedia Signal Processing, pp. 25–28 (2002)
Pauca, V., Shahmazand, F., Berry, M.W., Plemmons, R.: Text mining using nonnegative matrix factorization. In: SIAM International Conference on Data Mining, pp. 452–456 (2004)
Berry, M., Browne, M., Langville, A., Pauca, V., Plemmons, R.: Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics & Data Analysis 52(1), 155–173 (2007)
Xu, W., Liu, X., Gong, Y.: Document clustering based on non-negative matrix factorization. In: SIGIR 2003: Proceedings of the 26th annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 267–273. ACM, New York (2003)
Drakakis, K., Rickard, S., de Frein, R., Cichocki, A.: Analysis of financial data using non-negative matrix factorization. International Mathematical Forum 3, 1853–1870 (2008)
Vandendorpe, A., Ho, N.D., Vanduffel, S., Dooren, P.V.: On the parameterization of the CreditRisk+ model for estimating credit portfolio risk. Mathematics and Economics 42, 736–745 (2008)
Guyon, I., Gunn, S., Nikravesh, M., Zadeh, L.: Feature Extraction: Foundations And Applications. In: Studies in Fuzziness and Soft Computing. Physica Verlag, Heidelberg (2006)
Lin, C.-J.: Projected gradient methods for nonnegative matrix factorization. Neural Computation 19(10), 2756–2779 (2007)
Hofmann, T.: Probabilistic latent semantic indexing. In: Twenty-Second Annual International SIGIR Conference on Research and Development in Information Retrieval (1999)
Lin, C.J.: On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Transactions on Neural Networks 6(18), 1589–1596 (2007)
Chu, M., Plemmons, R.J.: Nonnegative matrix factorization and applications. Image 34, 1–5 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ribeiro, B., Silva, C., Vieira, A., Neves, J. (2009). 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. ICANNGA 2009. Lecture Notes in Computer Science, vol 5495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04921-7_55
Download citation
DOI: https://doi.org/10.1007/978-3-642-04921-7_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04920-0
Online ISBN: 978-3-642-04921-7
eBook Packages: Computer ScienceComputer Science (R0)