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PL
Artykuł stanowi kontynuację badań dotyczących zmodyfikowanego algorytmu dynamicznego programowania dla optymalizacji reguł decyzyjnych względem pokrycia. Praca przedstawia wyniki eksperymentalne dotyczące regułowego klasyfikatora, dla zbiorów danych umieszczonych w Repozytorium Uczenia Maszynowego.
EN
The article is a continuation of research connected with a modified dy-namic programming algorithm for optimization of decision rules relative to coverage. The paper contains experimental results for rule based classifier using data sets from UCI Machine Learning Repository.
PL
Artykuł przedstawia optymalizację częściowych reguł asocjacyjnych generowanych przez algorytm zachłanny względem liczby pomyłek (błędnych zaklasyfikowań). Zaproponowana optymalizacja ma na celu: (i) uzyskanie reguł o stosunkowo dobrej jakości, które w kolejnych etapach badań zostaną wykorzystane do budowy klasyfikatorów, (ii) zmniejszenie liczby konstruowanych reguł, co ma znaczenie z punktu widzenia reprezentacji wiedzy. Praca przedstawia wyniki eksperymentalne dla zbiorów danych umieszczonych w Repozytorium Uczenia Maszynowego.
EN
In the paper, an optimization of partial association rules relative to number of misclassifications is presented. The aims of proposed optimization are: (i) construction of rules with small number of misclassifications, what is important from the point of view of construction of classifiers, (ii) decreasing the number of rules, what is important from the point of view of knowledge representation. The paper contains experimental results for data sets from UCI Machine Learning Repository.
3
Content available remote Dynamic Programming Approach for Construction of Association Rule Systems
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.
EN
In the paper, an application of dynamic programming approach to global optimization of approximate association rules relative to coverage and length is presented. It is an extension of the dynamic programming approach to optimization of decision rules to inconsistent tables. Experimental results with data sets from UCI Machine Learning Repository are included.
5
Content available remote Relationships Between Length and Coverage of Decision Rules
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.
PL
W artykule zaproponowano heurystykę na podstawie algorytmu dynamicznego programowania dla optymalizacji dokładnych reguł decyzyjnych odnośnie do pokrycia. Celem przeprowadzonych badań jest: (i) zbadanie pokrycia reguł konstruowanych za pomocą proponowanego algorytmu oraz porównanie z pokryciem reguł konstruowanych za pomocą algorytmu dynamicznego programowania, (ii) zbadanie rozmiaru grafu (liczba węzłów i krawędzi w skierowanym grafie acyklicznym) skonstruowanego za pomocą proponowanego algorytmu oraz porównanie go z rozmiarem grafu skonstruowanego za pomocą algorytmu dynamicznego programowania.
EN
In the paper, author proposes a heuristics based on dynamic programming algorithm for optimization of exact decision rules relative to coverage. There are two aims for the proposed algorithm: (i) study of coverage of rules and comparison with coverage of rules constructed by the dynamic programming algorithm, (ii) study of size of directed acyclic graph (the number of nodes and edges) and comparison with size of the graph constructed by the dynamic programming algorithm.
7
Content available remote Classifiers Based on Optimal Decision Rules
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).
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.
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.
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.
11
Content available remote Dynamic Programming Approach for Partial Decision Rule Optimization
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.
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.
PL
W artykule przedstawiono sposób konstruowania częściowych reguł asocjacyjnych z wykorzystaniem algorytmu zachłannego. Podejście to jest odmienne od znanego algorytmu A priori i jego modyfikacji, wykorzystujących zbiory częste. Przedstawione wyniki badań oraz rezultaty z przeprowadzonych eksperymentów pokazują, że algorytm zachłanny pozwala konstruować stosunkowo małą liczbę krótkich, częściowych reguł asocjacyjnych o dobrej jakości, które pokrywają wszystkie obiekty danego systemu informacyjnego.
EN
The paper presents greedy algorithm for partial association rule construction. This approach is different from the known algorithm Apriori and its modifications based on frequent itemsets. Theoretical and experimental results show, that the greedy algorithm constructs relatively small number of short partial association rules which have good accuracy and cover all objects from given information system.
14
Content available remote Greedy Algorithms with Weights for Construction of Partial Association Rules
EN
This paper is devoted to the study of approximate algorithms for minimization of the total weight of attributes occurring in partial association rules. We consider mainly greedy algorithms with weights for construction of rules. The paper contains bounds on precision of these algorithms and bounds on the minimal weight of partial association rules based on an information obtained during the greedy algorithm run.
15
Content available remote Greedy Algorithm for Attribute Reduction
EN
In the paper the accuracy of greedy algorithm for construction of partial tests (superreducts) and partial decision rules is considered. Results of experiments with greedy algorithm are described.
16
Content available remote On Construction of Partial Reducts and Irreducible Partial Decision Rules
EN
In the paper for the most part of binary decision tables upper and lower bounds on the cardinality of partial reducts and length of irreducible partial decision rules are obtained. The number of partial reducts and the number of irreducible partial decision rules are evaluated. Complexity of algorithms for construction of all partial reducts and all irreducible partial decision rules is studied on the basis of obtained bounds.
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