A decomposability index in logical analysis of data

Hirotaka Ono, Mutsunori Yagiura, Toshihide Ibaraki

Research output: Contribution to journalArticlepeer-review

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

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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