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Content available Element partition trees for h-refined meshes to optimize direct solver performance. Part I: Dynamic programming
Aboueisha H., Calo V. M., Jopek K., Moshkov M., Paszyńska A., Paszyński M., Skotniczny M.
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 2
351--365
EN
We consider a class of two- and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with 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.
2
Content available remote Dynamic Programming Approach for Construction of Association Rule Systems
Alsolami F., Amin T., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2016
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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.
3
Content available remote Relationships Between Length and Coverage of Decision Rules
Amin T., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2014
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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.
4
Content available remote Relationships between Average Depth and Number of Misclassifications for Decision Trees
Chikalov I., Hussain S., Moshkov M.
Fundamenta Informaticae
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2014
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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 Classifiers Based on Optimal Decision Rules
Amin T., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2013
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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).
6
Content available remote A Greedy Algorithm for Construction of Decision Trees for Tables with Many-Valued Decisions : A Comparative Study
Azad M., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2013
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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.
7
Optimization of inhibitory decision rules relative to length
Alsolami F., Chikalov I., Moshkov M., Zielosko B.
Studia Informatica
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2012
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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.
8
Content available remote Greedy Algorithms for Construction of Approximate Tests for Decision Tables with Many-Valued Decisions
Azad M., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2012
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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 Dynamic Programming Approach for Partial Decision Rule Optimization
Amin T., Chikalov I., Moshkov M., Zielosko B.
Fundamenta Informaticae
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2012
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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.
10
Approximate algorithm for β -decision rule optimization
Zielosko B., Moshkov M.
Studia Informatica
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2011
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Vol. 32, nr 2A
329-335
EN
In the paper greedy algorithm for construction of β decision rules and algorithm for construction of β -complete systems of decision rules are studied. Obtined bounds on accuracy of the considered algorithms are presented.
PL
W artykule został przedstawiony algorytm zachłanny dla konstruowania β -reguł decyzyjnych oraz dla konstruowania β -kompletnych systemów reguł decyzyjnych. Zostały zaprezentowane granice dokładności wyników uzyskiwanych za pomocą rozważanych algorytmów.
11
Content available remote On algorithm for constructing of decision trees with minimal depth
Moshkov M., Chikalov I.
Fundamenta Informaticae
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2000
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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.
12
Content available remote Deterministic and nondeterministic decision trees for rough computing
Moshkov M.
Fundamenta Informaticae
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2000
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Vol. 41, Nr 3
301-311
EN
In the paper, infinite information systems are considered which are used in pattern recognition, discrete optimization, computational geometry. Depth and size of deterministic and nondeterministic decision trees over such information systems are studied. Two classes of infinite information 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.
13
Content available remote Decision trees for regular language word recognition
Moshkov M.
Fundamenta Informaticae
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2000
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Vol. 41, Nr 4
449-461
EN
In this paper the problem of recognition of words with fixed length from a regular language is considered. The word under consideration can be interpreted as a description of certain screen image in the following way: the i-th letter of the word encodes the color of the i-th screen cell. In 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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