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polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive grids.
Experimental results present cardinality of the set of association rules constructed for information system and lower bound on minimum possible cardinality of rule set based on the information obtained during algorithm work as well as obtained results for length.
datasets representing Boolean functions with 10 variables.
point of view of classification – exact or approximate; and (ii) which order of optimization gives better results of classifier work: length, length+coverage, coverage, or coverage+length. Experimental results show that, on average, classifiers based on exact rules are better than classifiers based on approximate rules, and sequential optimization (length+coverage or coverage+length) is better than the ordinary optimization (length or coverage).
Experimental results for data sets from UCI Machine Learning Repository and randomly generated tables are presented. We make a comparative study of the depth and average depth of the constructed decision trees for proposed approach and approach based on generalized decision. The obtained results show that the proposed approach can be useful from the point of view of knowledge representation and algorithm construction.
relative to length, we obtain a graph Λ(T) which describes all nonredundant inhibitory rules with minimum length.
wyniku procedury optymalizacji względem długości, na podstawie grafu Λ(T) można opisać cały zbiór nienadmiarowych reguł wzbraniających o minimlanej długości.
attached to this row. We consider bounds on the precision of this algorithm relative to the cardinality of tests.
of rows with the most common decision for T. For a nonnegative real number , we consider γ-decision rules (partial decision rules) that localize rows in subtables of T with uncertainty at most γ. Presented algorithm constructs a directed acyclic graph Δ(T) which nodes are subtables of the decision table T given by systems of equations of the kind "attribute = value". This algorithm finishes the partitioning of a subtable when its uncertainty is at most . The graph Δ(T) allows us to describe the whole set of so-called irredundant γ-decision rules. We can optimize such set of rules according to length or coverage. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository.
decision tables.
systems are investigated. Systems from these classes are best from the point of view of time complexity and space complexity of deterministic as well as nondeterministic decision trees. In proofs methods of test theory and rough set theory are used.
this case a decision tree which recognizes some words may be interpreted as an algorithm for the recognition of images which are defined by considered words. The classification of all regular languages depending on the growth of minimal depth of decision trees for language word recognition with the growth of the word length is obtained. In proofs methods of test theory and rough set theory are used.
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