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. © 2001 Springer Berlin Heidelberg.
CITATION STYLE
Ono, H., Yagiura, M. U., & Ibaraki, T. (2001). An index for the data size to extract decomposable structures in LAD. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2223 LNCS, pp. 279–290). https://doi.org/10.1007/3-540-45678-3_25
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