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1
Content available remote On Average Depth of Decision Trees Implementing Boolean Functions
100%
Chikalov I.
Fundamenta Informaticae
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2002
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tom Vol. 50, nr 3,4
265-284
EN
The article considers the representation of Boolean functions in the form of decision trees. It presents the bounds on average time complexity of decision trees for all classes of Boolean functions that are closed over substitution, and the insertion and deletion of unessential variables (the structure of these classes is described in the book by Jablonsky, Gavrilov and Kudriavtzev [5]). The obtained results are compared with the results developed by Moshkov in [6] that describe the worst case time complexity of decision trees.
2
Content available remote On algorithm for constructing of decision trees with minimal depth
63%
Moshkov M. , Chikalov I.
Fundamenta Informaticae
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2000
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tom Vol. 41, Nr 3
295-299
EN
An algorithm is considered which for a given decision table constructs a decision tree with minimal depth. The class of all information systems (finite and infinite) is described for which this algorithm has polynomial time complexity depending on the number of columns (attributes) in decision tables.
3
Content available remote Classifiers Based on Optimal Decision Rules
51%
Amin T. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2013
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tom Vol. 127, nr 1-4
151--160
EN
Based on dynamic programming approach we design algorithms for sequential optimization of exact and approximate decision rules relative to the length and coverage [3, 4]. In this paper, we use optimal rules to construct classifiers, and study two questions: (i) which rules are better from the 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).
4
Content available remote Relationships between Average Depth and Number of Misclassifications for Decision Trees
51%
Chikalov I. , Hussain S. , Moshkov M.
Fundamenta Informaticae
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2014
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tom Vol. 129, nr 1/2
15--26
EN
This paper presents a new tool for the study of relationships between the total path length or the average depth and the number of misclassifications for decision trees. In addition to algorithm, the paper also presents the results of experiments with datasets from UCI ML Repository [9] and datasets representing Boolean functions with 10 variables.
5
Content available remote A Greedy Algorithm for Construction of Decision Trees for Tables with Many-Valued Decisions : A Comparative Study
51%
Azad M. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2013
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tom Vol. 128, nr 1-2
1--15
EN
In the paper, we study a greedy algorithm for construction of decision trees. This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. 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.
6
Optimization of inhibitory decision rules relative to length
51%
Alsolami F. , Chikalov I. , Moshkov M. , Zielosko B.
Studia Informatica
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2012
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tom Vol. 33, nr 2A
395-406
EN
The paper is devoted to the study of an algorithm for optimization of inhibitory rules relative to the length. Such rules on the right-hand side have a relation "attribute ≠ value". The considered algorithm is based on an extension of dynamic programming. After the procedure of optimization relative to length, we obtain a graph Λ(T) which describes all nonredundant inhibitory rules with minimum length.
PL
W artykule przedstawiono algorytm dla optymalizacji reguł wzbraniających względem długości. Reguły te w prawej części mają relację "atrybut ≠ wartość". Algorytm opiera się na idei dynamicznego programowania. Dla danej tablicy decyzyjnyej T konstruowany jest skierowany graf acykliczny Λ(T). W wyniku procedury optymalizacji względem długości, na podstawie grafu Λ(T) można opisać cały zbiór nienadmiarowych reguł wzbraniających o minimlanej długości.
7
Content available remote Dynamic Programming Approach for Partial Decision Rule Optimization
51%
Amin T. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2012
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tom Vol. 119, nr 3/4
233-248
EN
This paper is devoted to the study of an extension of dynamic programming approach which allows optimization of partial decision rules relative to the length or coverage. We introduce an uncertainty measure J(T) which is the difference between number of rows in a decision table T and number 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.
8
Content available remote Greedy Algorithms for Construction of Approximate Tests for Decision Tables with Many-Valued Decisions
51%
Azad M. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2012
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tom Vol. 120, nr 3/4
231-242
EN
The paper is devoted to the study of a greedy algorithm for construction of approximate tests (super-reducts). This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions. For a given row, we should find a decision from the set attached to this row. We consider bounds on the precision of this algorithm relative to the cardinality of tests.
9
Content available remote Relationships Between Length and Coverage of Decision Rules
51%
Amin T. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2014
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tom Vol. 129, nr 1/2
1--13
EN
The paper describes a new tool for study relationships between length and coverage of exact decision rules. This tool is based on dynamic programming approach. We also present results of experiments with decision tables from UCI Machine Learning Repository.
10
Content available remote Dynamic Programming Approach for Construction of Association Rule Systems
45%
Alsolami F. , Amin T. , Chikalov I. , Moshkov M. , Zielosko B.
Fundamenta Informaticae
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2016
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tom Vol. 147, nr 2/3
159--171
EN
In the paper, an application of dynamic programming approach for optimization of association rules from the point of view of knowledge representation is considered. The association rule set is optimized in two stages, first for minimum cardinality and then for minimum length of rules. 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.
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