Transactions on Rough Sets XV

189 Pages·2012·9.13 MB·English

by  Andrzej Janusz (auth.)

Lecture Notes in Computer Science 7255
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
FriedemannMattern
ETHZurich,Switzerland
JohnC.Mitchell
StanfordUniversity,CA,USA
MoniNaor
WeizmannInstituteofScience,Rehovot,Israel
OscarNierstrasz
UniversityofBern,Switzerland
C.PanduRangan
IndianInstituteofTechnology,Madras,India
BernhardSteffen
TUDortmundUniversity,Germany
MadhuSudan
MicrosoftResearch,Cambridge,MA,USA
DemetriTerzopoulos
UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
MosheY.Vardi
RiceUniversity,Houston,TX,USA
GerhardWeikum
MaxPlanckInstituteforInformatics,Saarbruecken,Germany
James F. Peters Andrzej Skowron (Eds.)
Transactions on
Rough Sets XV
1 3
VolumeEditors
JamesF.Peters
UniversityofManitoba,Winnipeg,MB,Canada
E-mail:[email protected]
AndrzejSkowron
UniversityofWarsaw,Poland
E-mail:[email protected]
ISSN0302-9743(LNCS) e-ISSN1611-3349(LNCS)
ISSN1861-2059(TRS) e-ISSN1861-2067(TRS)
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DOI10.1007/978-3-642-31903-7
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Preface
Volume XV of the Transactions on Rough Sets (TRSXV) offers a number re-
search streams that have grown out of the seminal work by Zdzisl(cid:3)aw Pawlak1
during the first decade of the twenty-first century.
These research streams include work on a promising rough set approach in
machine learningby A. Janusz,the introductionofmulti-valued nearset theory
byM.E.AbdEl-Monsef,H.M.Abu-DoniaandE.A.Marei,theadventofacom-
plete system that supports a rough-near set approach to digital image analysis
by C.J. Henry, and an exhaustive study of the mathematics of vagueness by
A. Mani.
The first of these research streams focuses on an extension of the rule-based
similarity(RBS) thatis a dynamic rule-basedsimilarity (DRBS) framework,an
extension of the rule-basedsimilarity (RBS) model by A. Janusz.RBS is an ex-
tensionoftheA.Tverskyfeaturecontrastmodel,whereanobjectisrepresented
by a set of features,object comparisondepends on a feature matching function,
and the representation of similarity is based on the contrast of the measures of
objectfeatures2.DRBSrepresentsasignificantstepforwardinmachinelearning
inasmuch as DRBS makes it possible to learn a similarity relation from high-
dimensionaldata.AsignificantapplicationofDBRSis inDNA microarraydata
mining.
The second of the research streams represented by M.E. Abd El-Monsef,
H.M. Abu-Donia and E.A. Marei in TRSXV considers the nearness of objects
in terms of an extended approximation space model3 and a new approach to
near sets based on several types of neighborhoods that takes its cue from topo-
logical rough sets4. The main results in this paper are that a right (left) lower
neighborhoodcoverageisnearthecorrespondingright(left)upperneighborhood
coverageand that topologies are generated from families of neighborhoods.
The thirdresearchstreaminTRSXVis representedby C.J.Henry’snearset
evaluationandrecognition(NEAR)system.Itcanbeobservedthattheapproach
1 See, e.g.,Pawlak, Z., A Treatise on Rough Sets, Transactions on Rough Sets IV,
(2006), 1-17. See, also, Pawlak, Z., Skowron,A.: Rudimentsof rough sets, Informa-
tion Sciences 177 (2007) 3-27; Pawlak, Z., Skowron, A.: Rough sets: Some exten-
sions, Information Sciences 177 (2007) 28-40; Pawlak, Z., Skowron, A.: Rough sets
and Boolean reasoning, Information Sciences 177 (2007) 41-73.
2 A. Tversky, Features of similarity, Psych. Review 84 (1977), 327–352, especially
A. Tversky, D.H. Krantz, The dimensional representation and metric structure of
similarity data, J. Math. Psych.7 (1970), 572-597.
3 J.F.Peters,A.Skowron,J.Stepaniuk,Nearnessofobjects:Extensionofapproxima-
tion space model, Fund.Info. 79 (/4) (2007), 497-512.
4 A.Wiweger, On topological rough sets, Bull. Pol. Akad.,Math. 37 (1989), 89-93.
VI Preface
to describing the nearness of objects in terms of feature vectors is actually an
alternative to A. Tversky’s view of object similarity defined by sets of features
in representing objects. Henry carries forward the feature vector approach to
describing objects with the introduction of visual rough sets and an approach
to measuring the similarity of disjoint roughsets. Henry’s proposedapproachis
useful in digital image analysis as well as in content-based image retrieval.
The fourth researchstream is represented by A. Mani in TRSXV in a study
of the mathematics of vagueness. Mani introduces a structure called a rough
Y-system that captures a minimum common fragment of different rough set
theories. The article by Mani in this volume is broad in scope inasmuch as it
considers the category Rough, Y. Yao’s information granule model, contamina-
tion of object perception by meta-level consideration of objects of all types vs.
classes of equivalent objects, objectivity in the computation by rough inclusion
methods,axiomaticapproachtoinformationgranules,variousformsofroughset
theory considered relative discernibility, and classification of rough set theories.
Theeditorsofthisspecialissuewouldliketoexpressgratitudetotheauthors
of all submitted papers. Special thanks are due to the following reviewers: Mo-
hua Banerjee, Jan Bazan, Jerzy Grzyma(cid:3)la-Busse, Davide Cuicci, Ivo Du¨ntsch,
HomaFashandi,AnnaGomolin´ska,ChristopherHenry,JouniJ¨arvinen,Andrzej
Janusz, Marcin Wolski, Wei-Zhi Wu and Wojciech Ziarko.
The editorsand authorsof this volumeextend their gratitude to Alfred Hof-
mann, Anna Kramer, Ursula Barth, Christine Reiss, and the LNCS staff at
Springer for their support in making this volume of the TRS possible.
The Editors-in-Chief were supported by the State Committee for Scientific
Researchofthe Republic ofPoland(KBN)researchgrantNN516077837,grant
2011/01/D/ST6/06981from the PolishNational Science Centre, the PolishNa-
tional Centre for Research and Development (NCBiR) under grant SP/I/1/
77065/10by the strategicscientific researchandexperimentaldevelopmentpro-
gram:“InterdisciplinarySystemforInteractiveScientificandScientific-Technical
Information,”anindividualresearchgrantbytheprogramHomingPlus,edition
3/2011, from the Foundation for Polish Science and the Natural Sciences and
EngineeringResearchCouncilofCanada(NSERC)researchgrant185986,Cana-
dian Network of Excellence (NCE), and a Canadian Arthritis Network (CAN)
grant SRI-BIO-05.
March 2012 James F. Peters
Andrzej Skowron
LNCS Transactions on Rough Sets
The Transactions on Rough Sets series has as its principal aim the fostering of
professional exchanges between scientists and practitioners who are interested
in the foundations and applications of rough sets. Topics include foundations
and applications of rough sets as well as foundations and applications of hybrid
methodscombiningroughsetswithotherapproachesimportantforthedevelop-
ment of intelligent systems. The journal includes high-quality research articles
accepted for publication on the basis of thorough peer reviews. Dissertations
and monographs up to 250 pages that include new research results can also be
considered as regular papers. Extended and revised versions of selected papers
from conferences can also be included in regularor special issues of the journal.
Editors-in-Chief: James F. Peters, Andrzej Skowron
Managing Editor: Sheela Ramanna
Technical Editor: Marcin Szczuka
Editorial Board
Mohua Banerjee Ewa Orl(cid:3)owska
Jan Bazan Sankar K. Pal
Gianpiero Cattaneo Lech Polkowski
Mihir K. Chakraborty Henri Prade
Davide Ciucci Sheela Ramanna
Chris Cornelis Roman Sl(cid:3)owin´ski
Ivo Du¨ntsch Jerzy Stefanowski
Anna Gomolin´ska Jaros(cid:3)law Stepaniuk
Salvatore Greco Zbigniew Suraj
Jerzy W. Grzymal(cid:3)a-Busse Marcin Szczuka
Masahiro Inuiguchi Dominik S´le¸zak
Jouni Ja¨rvinen Roman S´winiarski
Richard Jensen Shusaku Tsumoto
Boz˙ena Kostek Guoyin Wang
Churn-Jung Liau Marcin Wolski
PawanLingras Wei-Zhi Wu
Victor Marek Yiyu Yao
Mikhail Moshkov Ning Zhong
Hung Son Nguyen Wojciech Ziarko
Table of Contents
Dynamic Rule-Based Similarity Model for DNA MicroarrayData ...... 1
Andrzej Janusz
Multi-valued Approach to Near Set Theory.......................... 26
M.E. Abd El-Monsef, H.M. Abu-Donia, and E.A. Marei
Perceptual Indiscernibility, Rough Sets, Descriptively Near Sets, and
Image Analysis .................................................. 41
Christopher J. Henry
Dialectics of Counting and the Mathematics of Vagueness ............. 122
A. Mani
Author Index.................................................. 181
Dynamic Rule-Based Similarity Model
for DNA Microarray Data
Andrzej Janusz
Faculty of Mathematics, Informatics, and Mechanics, The Universityof Warsaw,
Banacha 2, 02-097 Warszawa, Poland
[email protected]
Abstract. Rules-based Similarity (RBS) is a framework in which con-
cepts from rough set theory are used for learning a similarity relation
from data. This paper presents an extension of RBS called Dynamic
Rules-based Similarity model (DRBS) which is designed to boost the
qualityofthelearnedrelationincaseofhighlydimensionaldata.Rules-
based Similarity utilizes a notion of a reduct to construct new features
whichcanbeinterpretedasimportantaspectsofasimilarityintheclas-
sification context. Having defined such features it is possible to utilize
the idea of Tversky’s feature contrast similarity model in order to de-
sign an accurate and psychologically plausible similarity relation for a
given domain of objects. DRBS tries to incorporate a broader array of
aspects of the similarity into themodel byconstructing many heteroge-
neoussetsoffeaturesfrommultipledecisionreducts.Toensurediversity,
the reducts are computed on random subsets of objects and attributes.
This approach is particularly well-suited for dealing with“few-objects-
many-attributes”problem,suchasminingofDNAmicroarraydata.The
induced similarity relation and the resulting similarity function can be
used to perform an accurate classification of previously unseen objects
inacase-basedfashion.Experiments,whoseresultsarealsopresentedin
thepaper,show thattheproposed modelcan successfully competewith
other state-of-the-art algorithms such as RandomForest or SVM.
1 Introduction
A notion of similarity plays an important role in both the rough set theory
and data analysis in general. Since its introduction in [1], rough sets have been
usedinconjunctionwiththeconceptofsimilarityandnumeroussimilarityfunc-
tions to perform classification (e.g. [2], [3]) or clustering of data (e.g. [4], [5]).
The similarity itself has been used for generalization of rough sets by defining
more natural lower and upper approximations ([2], [6], [7]). It has also been
applied in the process of data granulation for the purpose of granular comput-
ing approaches([8]). In statistical learning clustering algorithms grouptogether
objects that are similar in some sense. For this purpose, many methods make
a use of predefined similarity models (e.g. distance-based similarity as in the
classic k-means algorithm). Moreover, in domains such as information retrieval
J.F.PetersandA.Skowron(Eds.):TransactionsonRoughSetsXV,LNCS7255,pp.1–25,2012.
(cid:2)c Springer-VerlagBerlinHeidelberg2012
2 A.Janusz
or case-based reasoning the concept of similarity is essential as it is being used
in every phase of the case-basedreasoning cycle ([9]).
In the most of those examples, the utilized models of the similarity are given
a priori and their properties are dictated by the design. However, researchers
who investigated human perception of similar objects noticed that in real life
the features of the similarity are strongly dependent on a domain of considered
objects andalso ona context([10], [11]). Due to this fact, in confrontationwith
many real-life problems the similarity model cannot be given by an expert but
has to be learned from available data ([12]).
There have been many attempts to develop a similarity learning model that
would fit to a wide range of applications. Among them, a huge share consists
of methods that try to optimize weights of distance-based local similarities and
aggregate them into a global similarity function ([13], [14], [15], [16], [17]). Al-
though the distance-based similarity learning models differ in a way they hone
a similarity function, they all enforce certain properties on resulting similarity
relation(suchassymmetryortriangularinequity)andthatmaybeundesirable.
Rules-based Similarity (RBS) model was developed as an alternative to the
distance-basedapproaches([18]). It may be seenas a roughsetextensionto the
psychologicallyplausible feature contrastmodel (see [10]) proposedby Tversky.
Hearguedthatdistancemetricsarenotsuitableformodelinghumanperception
of resemblance since they enforce some undesirable properties and they neglect
a context in which the objects are compared. Instead, he proposed to measure
the similarity by examining whether the objects share some binary features.
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Fig.1. A general construction schema of the RBSmodel
In RBS, a similarity between two objects in a context set by a decision at-
tributeisalsoexpressedintermsoftheircommonanddistinctivefeatures.Those
features correspond to higher-level characteristics of examined samples and are
automatically derived from data using a decision rule mining algorithm. This
approach is different from other rough set case-based classification models (e.g.
[2], [3]) as it does not need to consider all pairs of available training samples
and it does not assume existence of any predefined local similarity measures.
Experiments conducted with the use of the original RBS showed that it can