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 language | English |
|---|---|
| Pages (from-to) | 165-180 |
| Number of pages | 16 |
| Journal | Discrete Applied Mathematics |
| Volume | 142 |
| Issue number | 1-3 SPEC. ISS. |
| DOIs | |
| Publication status | Published - Aug 15 2004 |
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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 journal › Article
}
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.
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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 -