# A Fuzzy Approach to Discriminant Analysis based on the Results of an Iterative Fuzzy k-Means Method

### Francesco Campobasso, Annarita Fanizzi

#### Abstract

The common classification techniques are designed for a rigid (even if probabilistic) allocation of each unit into one of several groups. Nevertheless the dissimilarity among combined units often leads to consider the opportunity of assigning each of them to more than a single group with different degrees of membership. In previous works we proposed a fuzzy approach to discriminant analysis, structured by linearly regressing the degrees of membership of each unit to every groups on the same variables used in a preliminary clustering. In this work we show that non-linear regression models can be used more profitably than linear ones. The applicative case concerns the entrepreneurial propensity of provinces in Central and Southern Italy, even if our methodological proposal was initially conceived to assign new customers to defined groups for Customer Relationship Management (CRM) purposes.

#### References

- Bezdek, J. C., 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York.
- Campobasso, F., Fanizzi, A., 2013. A Proposal for a Discriminant Analysis Based on the Results of a Preliminary Fuzzy Clustering. In Computational Science and Its Applications - ICCSA 2013, LNCS, vol. 7974, pp. 444-456. Springer, Heidelberg.
- Campobasso, F., Fanizzi, A., 2013. A fuzzy approach to Ward's method of classification: an application case to the Italian university system. In Statistical Methods for spatial planning and monitoring, pp.31-46. SpringerVerlag, Berlin Heidelberg.
- Campobasso, F., Fanizzi, A., Perchinunno, P., 2008. Homogenous urban poverty clusters within the city of Bari. In Computational Science and its Applications - ICCSA 2008, Part I. LNCS, vol. 5072, pp. 232-244. Springer, Heidelberg.
- Kaufman, L., Rousseau, P. J., 1990. Finding Groups in Data - An Introduction to Cluster Analysis. John Wiley and Sons, New York.
- Watada J., H. Tanaka, K. Asai. 1986. Fuzzy discriminant analysis in fuzzy groups. In Fuzzy Sets and Systems, vol. 19, pp. 261-271. Elsevier, The Netherlands.
- Wu H. X., J. J. Zhou. 2006. Fuzzy discriminant analysis with kernel methods. Pattern Recognition, vol. 39, pp. 2236-2239. Elsevier, The Netherlands.
- Song X., X. Yang, J. Yang, X. Wu, Y. Zheng. 2010. Discriminant analysis approach using fuzzy fourfold subspaces model. In Neurocomputing, vol. 73, pp. 255-2265. Elsevier, The Netherlands.
- Zhao M., T. W. S. Chow, Z. Zhang. 2012. Random walkbased fuzzy linear discriminant analysis for dimensionality reduction. In Soft Computing, vol. 16, pp. 1393-1409. Springer-Verlag, Berlin, Heidelberg.

#### Paper Citation

#### in Harvard Style

Campobasso F. and Fanizzi A. (2013). **A Fuzzy Approach to Discriminant Analysis based on the Results of an Iterative Fuzzy k-Means Method** . In *Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)* ISBN 978-989-8565-77-8, pages 257-264. DOI: 10.5220/0004553802570264

#### in Bibtex Style

@conference{fcta13,

author={Francesco Campobasso and Annarita Fanizzi},

title={A Fuzzy Approach to Discriminant Analysis based on the Results of an Iterative Fuzzy k-Means Method},

booktitle={Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)},

year={2013},

pages={257-264},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004553802570264},

isbn={978-989-8565-77-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)

TI - A Fuzzy Approach to Discriminant Analysis based on the Results of an Iterative Fuzzy k-Means Method

SN - 978-989-8565-77-8

AU - Campobasso F.

AU - Fanizzi A.

PY - 2013

SP - 257

EP - 264

DO - 10.5220/0004553802570264