A decomposability index in logical analysis of data

Hirotaka Ono, Mutsunori Yagiura, Toshihide Ibaraki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Logical analysis of data (LAD) is one of the methodologies for extracting knowledge in the form of a Boolean function f from a given pair of data sets (T,F) on attributes set S of size n, in which T (resp., F) ⊆{0,1} n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge f has a decomposable structure; f(x)=g(x[S0], h(x[S1])) 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, however, it is considered that the sizes |T| and |F| must be sufficiently large. In this paper, based on probabilistic analysis, we provide an index for such indispensable number of examples to detect decomposability; we claim that there exist many deceptive decomposable structures of (T,F) if |T||F|≤2n-1. The computational results on synthetically generated data sets and real-world data sets show that the above index gives a good lower bound on the indispensable data size.

Original languageEnglish
Pages (from-to)165-180
Number of pages16
JournalDiscrete Applied Mathematics
Volume142
Issue number1-3 SPEC. ISS.
DOIs
Publication statusPublished - Aug 15 2004

Fingerprint

Decomposability
Boolean functions
Decomposable
Boolean Functions
Denote
Probabilistic Analysis
Computational Results
Attribute
Projection
Lower bound
Methodology

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

A decomposability index in logical analysis of data. / Ono, Hirotaka; Yagiura, Mutsunori; Ibaraki, Toshihide.

In: Discrete Applied Mathematics, Vol. 142, No. 1-3 SPEC. ISS., 15.08.2004, p. 165-180.

Research output: Contribution to journalArticle

Ono, H, Yagiura, M & Ibaraki, T 2004, 'A decomposability index in logical analysis of data', Discrete Applied Mathematics, vol. 142, no. 1-3 SPEC. ISS., pp. 165-180. https://doi.org/10.1016/j.dam.2004.02.001
Ono, Hirotaka ; Yagiura, Mutsunori ; Ibaraki, Toshihide. / A decomposability index in logical analysis of data. In: Discrete Applied Mathematics. 2004 ; Vol. 142, No. 1-3 SPEC. ISS. pp. 165-180.
@article{7fe2cc7a71d644a493b8bbd75e5c041d,
title = "A decomposability index in logical analysis of data",
abstract = "Logical analysis of data (LAD) is one of the methodologies for extracting knowledge in the form of a Boolean function f from a given pair of data sets (T,F) on attributes set S of size n, in which T (resp., F) ⊆{0,1} n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge f has a decomposable structure; f(x)=g(x[S0], h(x[S1])) 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, however, it is considered that the sizes |T| and |F| must be sufficiently large. In this paper, based on probabilistic analysis, we provide an index for such indispensable number of examples to detect decomposability; we claim that there exist many deceptive decomposable structures of (T,F) if |T||F|≤2n-1. The computational results on synthetically generated data sets and real-world data sets show that the above index gives a good lower bound on the indispensable data size.",
author = "Hirotaka Ono and Mutsunori Yagiura and Toshihide Ibaraki",
year = "2004",
month = "8",
day = "15",
doi = "10.1016/j.dam.2004.02.001",
language = "English",
volume = "142",
pages = "165--180",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "1-3 SPEC. ISS.",

}

TY - JOUR

T1 - A decomposability index in logical analysis of data

AU - Ono, Hirotaka

AU - Yagiura, Mutsunori

AU - Ibaraki, Toshihide

PY - 2004/8/15

Y1 - 2004/8/15

N2 - Logical analysis of data (LAD) is one of the methodologies for extracting knowledge in the form of a Boolean function f from a given pair of data sets (T,F) on attributes set S of size n, in which T (resp., F) ⊆{0,1} n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge f has a decomposable structure; f(x)=g(x[S0], h(x[S1])) 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, however, it is considered that the sizes |T| and |F| must be sufficiently large. In this paper, based on probabilistic analysis, we provide an index for such indispensable number of examples to detect decomposability; we claim that there exist many deceptive decomposable structures of (T,F) if |T||F|≤2n-1. The computational results on synthetically generated data sets and real-world 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 in the form of a Boolean function f from a given pair of data sets (T,F) on attributes set S of size n, in which T (resp., F) ⊆{0,1} n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge f has a decomposable structure; f(x)=g(x[S0], h(x[S1])) 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, however, it is considered that the sizes |T| and |F| must be sufficiently large. In this paper, based on probabilistic analysis, we provide an index for such indispensable number of examples to detect decomposability; we claim that there exist many deceptive decomposable structures of (T,F) if |T||F|≤2n-1. The computational results on synthetically generated data sets and real-world 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=3142528914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142528914&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2004.02.001

DO - 10.1016/j.dam.2004.02.001

M3 - Article

AN - SCOPUS:3142528914

VL - 142

SP - 165

EP - 180

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3 SPEC. ISS.

ER -