An index for the data size to extract decomposable structures in LAD

Hirotaka Ono, Mut Unori Yagiura, Toshihide Ibaraki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Logical analysis of data (LAD)is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T,F)on attributes set S of size n in whch T (resp.,F)0 , 1n denotes a set of positive (resp.,negative)examples for the phenomenon under cons deration.In this paper,we consider the case n which extracted knowledge has a decomposable structure;i.e.,f is described as aform f (x)=g(x[S0],h x[S 1]))for some S0,S1 .S and Boolean functions g and h where x[I]denotes the projection of vector x on I In order to detect meaningful decomposable structures,it is expected that the sizes |T|and |F| must be sufficiently large.In this paper,we provide an index for such indispensable number of examples,based on probabilistic analysis.Using p = |T|/|T|+ |F|)and q = |F|/|T|+|F|),we claim that there exist many deceptive decomposable structures of (T,F) if |T|+|F| ≤√2n-1 /pq The computat onal results on synthetically generated data sets show that the above index gives a good lower bound on the indispensable data size.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings
Pages279-290
Number of pages12
DOIs
Publication statusPublished - Dec 1 2001
Event12th International Symposium on Algorithms and Computation, ISAAC 2001 - Christchurch, New Zealand
Duration: Dec 19 2001Dec 21 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2223 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th International Symposium on Algorithms and Computation, ISAAC 2001
CountryNew Zealand
CityChristchurch
Period12/19/0112/21/01

Fingerprint

Boolean functions
Decomposable
Boolean Functions
Denote
Probabilistic Analysis
Attribute
Projection
Lower bound
Methodology
Knowledge

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ono, H., Yagiura, M. U., & Ibaraki, T. (2001). An index for the data size to extract decomposable structures in LAD. In Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings (pp. 279-290). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS). https://doi.org/10.1007/3-540-45678-3_25

An index for the data size to extract decomposable structures in LAD. / Ono, Hirotaka; Yagiura, Mut Unori; Ibaraki, Toshihide.

Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings. 2001. p. 279-290 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2223 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ono, H, Yagiura, MU & Ibaraki, T 2001, An index for the data size to extract decomposable structures in LAD. in Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2223 LNCS, pp. 279-290, 12th International Symposium on Algorithms and Computation, ISAAC 2001, Christchurch, New Zealand, 12/19/01. https://doi.org/10.1007/3-540-45678-3_25
Ono H, Yagiura MU, Ibaraki T. An index for the data size to extract decomposable structures in LAD. In Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings. 2001. p. 279-290. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45678-3_25
Ono, Hirotaka ; Yagiura, Mut Unori ; Ibaraki, Toshihide. / An index for the data size to extract decomposable structures in LAD. Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings. 2001. pp. 279-290 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{1b1e2b918a6340a3844a0e4bd6365d2f,
title = "An index for the data size to extract decomposable structures in LAD",
abstract = "Logical analysis of data (LAD)is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T,F)on attributes set S of size n in whch T (resp.,F)0 , 1n denotes a set of positive (resp.,negative)examples for the phenomenon under cons deration.In this paper,we consider the case n which extracted knowledge has a decomposable structure;i.e.,f is described as aform f (x)=g(x[S0],h x[S 1]))for some S0,S1 .S and Boolean functions g and h where x[I]denotes the projection of vector x on I In order to detect meaningful decomposable structures,it is expected that the sizes |T|and |F| must be sufficiently large.In this paper,we provide an index for such indispensable number of examples,based on probabilistic analysis.Using p = |T|/|T|+ |F|)and q = |F|/|T|+|F|),we claim that there exist many deceptive decomposable structures of (T,F) if |T|+|F| ≤√2n-1 /pq The computat onal results on synthetically generated data sets show that the above index gives a good lower bound on the indispensable data size.",
author = "Hirotaka Ono and Yagiura, {Mut Unori} and Toshihide Ibaraki",
year = "2001",
month = "12",
day = "1",
doi = "10.1007/3-540-45678-3_25",
language = "English",
isbn = "3540429859",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "279--290",
booktitle = "Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings",

}

TY - GEN

T1 - An index for the data size to extract decomposable structures in LAD

AU - Ono, Hirotaka

AU - Yagiura, Mut Unori

AU - Ibaraki, Toshihide

PY - 2001/12/1

Y1 - 2001/12/1

N2 - Logical analysis of data (LAD)is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T,F)on attributes set S of size n in whch T (resp.,F)0 , 1n denotes a set of positive (resp.,negative)examples for the phenomenon under cons deration.In this paper,we consider the case n which extracted knowledge has a decomposable structure;i.e.,f is described as aform f (x)=g(x[S0],h x[S 1]))for some S0,S1 .S and Boolean functions g and h where x[I]denotes the projection of vector x on I In order to detect meaningful decomposable structures,it is expected that the sizes |T|and |F| must be sufficiently large.In this paper,we provide an index for such indispensable number of examples,based on probabilistic analysis.Using p = |T|/|T|+ |F|)and q = |F|/|T|+|F|),we claim that there exist many deceptive decomposable structures of (T,F) if |T|+|F| ≤√2n-1 /pq The computat onal results on synthetically generated data sets show that the above index gives a good lower bound on the indispensable data size.

AB - Logical analysis of data (LAD)is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T,F)on attributes set S of size n in whch T (resp.,F)0 , 1n denotes a set of positive (resp.,negative)examples for the phenomenon under cons deration.In this paper,we consider the case n which extracted knowledge has a decomposable structure;i.e.,f is described as aform f (x)=g(x[S0],h x[S 1]))for some S0,S1 .S and Boolean functions g and h where x[I]denotes the projection of vector x on I In order to detect meaningful decomposable structures,it is expected that the sizes |T|and |F| must be sufficiently large.In this paper,we provide an index for such indispensable number of examples,based on probabilistic analysis.Using p = |T|/|T|+ |F|)and q = |F|/|T|+|F|),we claim that there exist many deceptive decomposable structures of (T,F) if |T|+|F| ≤√2n-1 /pq The computat onal results on synthetically generated data sets show that the above index gives a good lower bound on the indispensable data size.

UR - http://www.scopus.com/inward/record.url?scp=70350640692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350640692&partnerID=8YFLogxK

U2 - 10.1007/3-540-45678-3_25

DO - 10.1007/3-540-45678-3_25

M3 - Conference contribution

AN - SCOPUS:70350640692

SN - 3540429859

SN - 9783540429852

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 279

EP - 290

BT - Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings

ER -