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    Minimization of Decision Tree Average Depth for Decision Tables with Many-valued Decisions

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    Type
    Conference Paper
    Authors
    Azad, Mohammad cc
    Moshkov, Mikhail cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extensions of Dynamic Programming, Machine Learning and Discrete Optimization Research Group
    Date
    2014-09-13
    Online Publication Date
    2014-09-13
    Print Publication Date
    2014
    Permanent link to this record
    http://hdl.handle.net/10754/550702
    
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    Abstract
    The paper is devoted to the analysis of greedy algorithms for the minimization of average depth of decision trees for decision tables such that each row is labeled with a set of decisions. The goal is to find one decision from the set of decisions. When we compare with the optimal result obtained from dynamic programming algorithm, we found some greedy algorithms produces results which are close to the optimal result for the minimization of average depth of decision trees.
    Citation
    Minimization of Decision Tree Average Depth for Decision Tables with Many-valued Decisions 2014, 35:368 Procedia Computer Science
    Publisher
    Elsevier BV
    Journal
    Procedia Computer Science
    Conference/Event name
    International Conference on Knowledge-Based and Intelligent Information and Engineering Systems, KES 2014
    DOI
    10.1016/j.procs.2014.08.117
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S1877050914010825
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.procs.2014.08.117
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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      Decision and Inhibitory Trees for Decision Tables with Many-Valued Decisions

      Azad, Mohammad (2018-06-06) [Dissertation]
      Advisor: Moshkov, Mikhail
      Committee members: Bajic, Vladimir B.; Zhang, Xiangliang; Boros, Endre
      Decision trees are one of the most commonly used tools in decision analysis, knowledge representation, machine learning, etc., for its simplicity and interpretability. We consider an extension of dynamic programming approach to process the whole set of decision trees for the given decision table which was previously only attainable by brute-force algorithms. We study decision tables with many-valued decisions (each row may contain multiple decisions) because they are more reasonable models of data in many cases. To address this problem in a broad sense, we consider not only decision trees but also inhibitory trees where terminal nodes are labeled with “̸= decision”. Inhibitory trees can sometimes describe more knowledge from datasets than decision trees. As for cost functions, we consider depth or average depth to minimize time complexity of trees, and the number of nodes or the number of the terminal, or nonterminal nodes to minimize the space complexity of trees. We investigate the multi-stage optimization of trees relative to some cost functions, and also the possibility to describe the whole set of strictly optimal trees. Furthermore, we study the bi-criteria optimization cost vs. cost and cost vs. uncertainty for decision trees, and cost vs. cost and cost vs. completeness for inhibitory trees. The most interesting application of the developed technique is the creation of multi-pruning and restricted multi-pruning approaches which are useful for knowledge representation and prediction. The experimental results show that decision trees constructed by these approaches can often outperform the decision trees constructed by the CART algorithm. Another application includes the comparison of 12 greedy heuristics for single- and bi-criteria optimization (cost vs. cost) of trees. We also study the three approaches (decision tables with many-valued decisions, decision tables with most common decisions, and decision tables with generalized decisions) to handle inconsistency of decision tables. We also analyze the time complexity of decision and inhibitory trees over arbitrary sets of attributes represented by information systems in the frameworks of local (when we can use in trees only attributes from problem description) and global (when we can use in trees arbitrary attributes from the information system) approaches.
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      Decision rules for decision tables with many-valued decisions

      Chikalov, Igor; Zielosko, Beata (Rough Sets and Knowledge Technology, Springer Nature, 2011) [Conference Paper]
      In the paper, authors presents a greedy algorithm for construction of exact and partial decision rules for decision tables with many-valued decisions. Exact decision rules can be 'over-fitted', so instead of exact decision rules with many attributes, it is more appropriate to work with partial decision rules with smaller number of attributes. Based on results for set cover problem authors study bounds on accuracy of greedy algorithm for exact and partial decision rule construction, and complexity of the problem of minimization of decision rule length. © 2011 Springer-Verlag.
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      Optimization of decision rule complexity for decision tables with many-valued decisions

      Azad, Mohammad; Chikalov, Igor; Moshkov, Mikhail (2013 IEEE International Conference on Systems, Man, and Cybernetics, Institute of Electrical and Electronics Engineers (IEEE), 2013-10) [Conference Paper]
      We describe new heuristics to construct decision rules for decision tables with many-valued decisions from the point of view of length and coverage which are enough good. We use statistical test to find leaders among the heuristics. After that, we compare our results with optimal result obtained by dynamic programming algorithms. The average percentage of relative difference between length (coverage) of constructed and optimal rules is at most 6.89% (15.89%, respectively) for leaders which seems to be a promising result. © 2013 IEEE.
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