Dependency Analysis and Attribute Reduction in the Probabilistic Approach to Rough Sets - Feature Selection for Data and Pattern Recognition - page 89

Chapter 6
Dependency Analysis and Attribute
Reduction in the Probabilistic Approach
to Rough Sets

Wojciech Ziarko

Abstract Two probabilistic approaches to rough sets are discussed in this chapter:
the variable precision rough set model and the Bayesian rough set model, as they
apply to data dependencies detection, analysis and their representation. The focus
is on the analysis of data co-occurrence-based dependencies appearing in classifi-
cation tables and probabilistic decision tables acquired from data. In particular, the
notion of attribute reduct, in the framework of probabilistic approach, is of interest in
the chapter. The reduct allows for information-preserving elimination of redundant
attributes from classification tables and probabilistic decision tables. The chapter
includes two efficient reduct computation algorithms.

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Keywords Variable precision rough set model Bayesian rough set model Depen-

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dency analysis Reduct

6.1 Introduction

The chapter reviews the basics of the variable precision rough set [ 2 , 3 , 7 , 13 , 15 , 26 ,
28 , 30 , 32 , 34 , 35 ] and the Bayesian rough set [ 13 ] approaches to data dependencies
detection, analysis and their optimal representation. The variable precision rough set
and the Bayesian rough set theories are extensions of the rough set theory, as intro-
duced by Pawlak [ 10 , 11 ]. They are among many extensions and generalizations of
the rough set approach, which inspired significant research interest worldwide (see,
for example [ 5 , 12 , 17 , 18 , 22 ]). The primary motivation behind the research aimed
at extending rough set approach is the imperfections of gathered practical applica-
tion data. In particular, application data often suffer from presence of measurement
noise, leading to lack of consistency and resulting difficulty to form data classifi-
cations and set approximations of the rough set model. In addition, the data often
are real-valued, for example in pattern recognition or control applications, requiring