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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. [ABSTRACT FROM AUTHOR]

We prove that the minimum average depth of a decision tree for sorting 8 pairwise different elements is equal to 620160 / 8 ! . We show also that each decision tree for sorting 8 elements, which has minimum average depth (the number of such trees is approximately equal to 8.548 × 10 326365 ), has also minimum depth. Both problems were considered by Knuth (1998). To obtain these results, we use tools based on extensions of dynamic programming which allow us to make sequential optimization of decision trees relative to depth and average depth, and to count the number of decision trees with minimum average depth. [ABSTRACT FROM AUTHOR]

Knowledge representation and extraction are very important tasks in data mining. In this work, we proposed a variety of rule-based greedy algorithms that able to obtain knowledge contained in a given dataset as a series of inhibitory rules containing an expression “attribute ≠ value” on the right-hand side. The main goal of this paper is to determine based on rule characteristics, rule length and coverage, whether the proposed rule heuristics are statistically significantly different or not; if so, we aim to identify the best performing rule heuristics for minimization of rule length and maximization of rule coverage. Friedman test with Nemenyi post-hoc are used to compare the greedy algorithms statistically against each other for length and coverage. The experiments are carried out on real datasets from UCI Machine Learning Repository. For leading heuristics, the constructed rules are compared with optimal ones obtained based on dynamic programming approach. The results seem to be promising for the best heuristics: the average relative difference between length (coverage) of constructed and optimal rules is at most 2.27% (7%, respectively). Furthermore, the quality of classifiers based on sets of inhibitory rules constructed by the considered heuristics are compared against each other, and the results show that the three best heuristics from the point of view classification accuracy coincides with the three well-performed heuristics from the point of view of rule length minimization. [ABSTRACT FROM AUTHOR]

This paper is devoted to the consideration of software systemDaggercreated in KAUST. This system is based on extensions of dynamic programming. It allows sequential optimization of decision trees and rules relative to different cost functions, derivation of relationships between two cost functions (in particular, between number of misclassifications and depth of decision trees), and between cost and uncertainty of decision trees. We describe features ofDaggerand consider examples of this system’s work on decision tables from UCI Machine Learning Repository. We also useDaggerto compare 16 different greedy algorithms for decision tree construction. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we consider so-called nonredundant inhibitory rules, containing an expression “attribute:F value” on the right- hand side, for which the number of misclassifications is at most a threshold γ. We study a dynamic programming approach for description of the considered set of rules. This approach allows also the optimization of nonredundant inhibitory rules relative to the length and coverage. The aim of this paper is to investigate an additional possibility of optimization relative to the number of misclassifications. The results of experiments with decision tables from the UCI Machine Learning Repository show this additional optimization achieves a fewer misclassifications. Thus, the proposed optimization procedure is promising. [Copyright &y& Elsevier]

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). [ABSTRACT FROM AUTHOR]

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 γ, 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 Δγ(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 γ. The graph Δγ(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. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the consideration of an algorithm for sequential optimization of paths in directed graphs relative to di_erent cost functions. The considered algorithm is based on an extension of dynamic programming which allows to represent the initial set of paths and the set of optimal paths after each application of optimization procedure in the form of a directed acyclic graph. [Copyright &y& Elsevier]

in the paper algorithms are considered which allow to optimize decision trees consecutively againsts relatively different criterions. For decision tables over an arbitrary infinite restricted information system [4], these algorithms have polynomial time complexity. [ABSTRACT FROM AUTHOR]