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A Role of (Not) Crisp Discernibility in Rough Set Approach to Numeric Feature Selection

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Advanced Machine Learning Technologies and Applications (AMLTA 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 322))

Abstract

We investigate the rough-set-based framework for feature selection in decision tables with numeric attributes. We compare functions evaluating subsets of attributes with respect to their potential in determining the distinguished decision attribute by means of two alternative methods: discernibility-based functions over discretized numeric data, as well as distance-based functions often used in the fuzzy-rough approaches to feature selection. In both cases, the idea is to compare objects belonging to different decision classes, by verifying whether they can be distinguished from each other by using discretized attributes or measuring distances between their values over original numeric attributes. We draw a correspondence between functions evaluating subsets of numeric attributes according to both methodologies. For a subset of numeric attributes, we consider a function measuring the amount of pairs of objects belonging to different decision classes that are not discerned by discretized attributes, averaged over all possible choices of binary discretization cuts over the attribute ranges. We prove that such a function can be rewritten by means of distances between the original numeric attributes. Namely, it is equal to the average fuzzy indiscernibility function computed by using the product t-norm combining indiscernibility degrees obtained over particular attributes.

Supported by the Polish National Science Centre grant 2011/01/B/ST6/03867.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Dominik Ślęzak & Paweł Betliński

  2. Infobright Inc., Krzywickiego 34 pok. 219, 02-078, Warsaw, Poland

    Dominik Ślęzak

Authors
  1. Dominik Ślęzak
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  2. Paweł Betliński
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Editors and Affiliations

  1. Cairo University, Egypt

    Aboul Ella Hassanien  & Rabie Ramadan  & 

  2. Ain Shams University, Cairo, Egypt

    Abdel-Badeeh M. Salem

  3. University of Tasmania, TAS, Australia

    Tai-hoon Kim

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Ślęzak, D., Betliński, P. (2012). A Role of (Not) Crisp Discernibility in Rough Set Approach to Numeric Feature Selection. In: Hassanien, A.E., Salem, AB.M., Ramadan, R., Kim, Th. (eds) Advanced Machine Learning Technologies and Applications. AMLTA 2012. Communications in Computer and Information Science, vol 322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35326-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-35326-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35325-3

  • Online ISBN: 978-3-642-35326-0

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