Artículos

A Supervised Discretization Method for Quantitative and Qualitative Ordered Variables

Un método de Discretización Supervisada para Variables Cuantitativas y Cualitativas Ordenadas

Francisco J. Ruiz¹, Cecilio Angulo¹ and Núria Agell²

1 Knowledge Engineering Research Group. Universitat Politècnica de Catalunya
Av. Víctor Balaguer s/n. 08800 Vilanova i la Geltrú (Spain)
francisco.javier.ruiz@upc.edu, cecilio.angulo@upc.edu

2 Department of Quantitative Methods Management. ESADE–Universitat Ramon Llull
Av. Pedralbes 62–65. 08034 Barcelona (Spain)
nuria.agell@esade.edu

Article received on November 15, 2005; accepted on January 01,2006

Abstract

In this work, a new technique to define cut–points in the discretization process of a continuous attribute is presented. This method is used as a prior step in a regression problem, considered as a learning problem in which the output variable can be either quantitative (continuous or discreet) or qualitative defined over an ordinal scale. The proposed method emphasizes the concept of location to determine discretization cut–points. In the case of continuous outputs, the method is based on the maximization of the difference between distributions by using intervalar distances. In the case of qualitative outputs, a qualitative distance is defined over a structure of absolute orders of magnitude. The main characteristics of the method presented are illustrated through three examples, two for continuous outputs and the last for a qualitative output.

Keywords: Supervised Discretization, Regression, Qualitative Reasoning, Intervalar distance.

Resumen

En este trabajo se presenta una nueva técnica para definir las fronteras en el proceso de discretización de una variable continua. Este método es usado como paso previo en un problema de regresión, considerado como un problema de aprendizaje en el cual la variable de salida puede ser cuantitativa (continua o discreta) o cualitativa definida sobre una escala ordinal. El método propuesto enfatiza el concepto de "localidad" para determinar las fronteras de las discretización. En el caso de variables continuas, el método se basa en la maximización de la diferencia entre distribuciones usando distancias intercalares, y en el caso de salidas cualitativas, en una distancia definida sobre una estructura de órdenes de magnitud absolutos. La principal característica del método se ilustra con tres ejemplos, dos para salidas continuas y un último con salidas cualitativas.

Palabras Clave: Discretización Supervisada, Regresión, Razonamiento Cualitativo, Distancia Intervalar.

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Acknowledgements

This work has been partially supported by the coordinated project MERITO (analysis and development of innovative soft–computing techniques integrating expert knowledge: an application to the measure of financial credit risk), funded by the Spanish Ministry of Science and Technology (TIC2002–04371–C02).

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