### 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 , 1^{n} 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[S_{0}],h x[S _{1}]))for some S_{0},S_{1} .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| ≤√2^{n-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 language | English |
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Title of host publication | Algorithms and Computation - 12th International Symposium, ISAAC 2001, Proceedings |

Pages | 279-290 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Dec 1 2001 |

Event | 12th International Symposium on Algorithms and Computation, ISAAC 2001 - Christchurch, New Zealand Duration: Dec 19 2001 → Dec 21 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2223 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Symposium on Algorithms and Computation, ISAAC 2001 |
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Country | New Zealand |

City | Christchurch |

Period | 12/19/01 → 12/21/01 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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.

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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 -