Abstract
The selection of features that describe samples in sets of data is a typical problem in data mining. A crucial issue is to select a maximal set of pertinent features, because the scarce knowledge of the problem under study often leads to consider features which do not provide a good description of the corresponding samples. The concept of consistent biclustering of a set of data has been introduced to identify such a maximal set. The problem can be modeled as a 0–1 linear fractional program, which is NP-hard. We reformulate this optimization problem as a bilevel program, and we prove that solutions to the original problem can be found by solving the reformulated problem. We also propose a heuristic for the solution of the bilevel program, that is based on the meta-heuristic Variable Neighborhood Search (VNS). Computational experiments show that the proposed heuristic outperforms previously proposed heuristics for feature selection by consistent biclustering.
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
Belotti, P.: Couenne: a user’s manual. Technical report, Lehigh University (2009)
Busygin, S., Prokopyev, O.A., Pardalos, P.M.: Feature selection for consistent biclustering via fractional 0–1 programming. Journal of Combinatorial Optimization 10, 7–21 (2005)
Hitt, B.A., Levine, P.J., Fusaro, V.A., Steinberg, S.M., Mills, G.B., Simone, C., Fishman, D.A., Kohn, E.C., Liotta, L.A., Petricoin III, E.F., Ardekani, A.M.: Use of proteomic patterns in serum to identify ovarian cancer. The Lancet 359, 572–577 (2002)
Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Brooks/Cole Publishing Company, Cengage Learning (2002)
Hansen, P., Mladenovic, N.: Variable neighborhood search: Principles and applications. European Journal of Operational Research 130(3), 449–467 (2001)
Hartigan, J.: Clustering Algorithms. John Wiles & Sons, New York (1975)
Ilog cplex solver, http://www.ilog.com/products/cplex/
Kent ridge database, http://datam.i2r.a-star.edu.sg/datasets/krbd/
Kundakcioglu, O.E., Pardalos, P.M.: The complexity of feature selection for consistent biclustering. In: Butenko, S., Pardalos, P.M., Chaovalitwongse, W.A. (eds.) Clustering Challenges in Biological Networks. World Scientific Publishing (2009)
Mladenovic, M., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)
Mucherino, A.: Extending the definition of β-consistent biclustering for feature selection. In: Proceedings of the Federated Conference on Computer Science and Information Systems, FedCSIS 2011. IEEE (2011)
Mucherino, A., Cafieri, S.: A new heuristic for feature selection by consistent biclustering. Technical Report arXiv:1003.3279v1 (March 2010)
Mucherino, A., Papajorgji, P., Pardalos, P.M.: Data Mining in Agriculture. Springer (2009)
Mucherino, A., Papajorgji, P., Pardalos, P.M.: A survey of data mining techniques applied to agriculture. Operational Research: An International Journal 9(2), 121–140 (2009)
Mucherino, A., Urtubia, A.: Consistent biclustering and applications to agriculture. In: Proceedings of the Industrial Conference on Data Mining, ICDM 2010, Workshop on Data Mining and Agriculture DMA 2010, IbaI Conference Proceedings, pp. 105–113. Springer, Berlin (2010)
Mucherino, A., Urtubia, A.: Feature selection for datasets of wine fermentations. In: Proceedings of the 10th International Conference on Modeling and Applied Simulation, MAS 2011. I3A (2011)
Nahapatyan, A., Busygin, S., Pardalos, P.M.: An improved heuristic for consistent biclustering problems, vol. 102, pp. 185–198. Springer
Notterman, D.A., Alon, U., Sierk, A.J., Levine, A.J.: Transcriptional gene expression profiles of colorectal adenoma, adenocarcinoma, and normal tissue examined by oligonucleotide arrays. Cancer Research 61, 3124–3130 (2001)
Sahinidis, N.V., Tawarmalani, M.: BARON 9.0.4: Global Optimization of Mixed-Integer Nonlinear Programs. User’s Manual (2010)
Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Mathematical Programming 103, 225–249 (2005)
Notterman, D.A., Gish, K., Ybarra, S., Mack, D., Levine, A.J., Alon, U., Barkai, N.: Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. PNAS 96, 6745–6750 (1999)
Urtubia, A., Perez-Correa, J.R., Meurens, M., Agosin, E.: Monitoring large scale wine fermentations with infrared spectroscopy. Talanta 64(3), 778–784 (2004)
Urtubia, A., Perez-Correa, J.R., Soto, A., Pszczolkowski, P.: Using data mining techniques to predict industrial wine problem fermentations. Food Control 18, 1512–1517 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mucherino, A., Liberti, L. (2013). A VNS-Based Heuristic for Feature Selection in Data Mining. In: Talbi, EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-30671-6_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30670-9
Online ISBN: 978-3-642-30671-6
eBook Packages: EngineeringEngineering (R0)