Bounds on Average Time Complexity of Decision Trees

Handle URI:
http://hdl.handle.net/10754/561674
Title:
Bounds on Average Time Complexity of Decision Trees
Authors:
Chikalov, Igor
Abstract:
In this chapter, bounds on the average depth and the average weighted depth of decision trees are considered. Similar problems are studied in search theory [1], coding theory [77], design and analysis of algorithms (e.g., sorting) [38]. For any diagnostic problem, the minimum average depth of decision tree is bounded from below by the entropy of probability distribution (with a multiplier 1/log2 k for a problem over a k-valued information system). Among diagnostic problems, the problems with a complete set of attributes have the lowest minimum average depth of decision trees (e.g, the problem of building optimal prefix code [1] and a blood test study in assumption that exactly one patient is ill [23]). For such problems, the minimum average depth of decision tree exceeds the lower bound by at most one. The minimum average depth reaches the maximum on the problems in which each attribute is "indispensable" [44] (e.g., a diagnostic problem with n attributes and kn pairwise different rows in the decision table and the problem of implementing the modulo 2 summation function). These problems have the minimum average depth of decision tree equal to the number of attributes in the problem description. © Springer-Verlag Berlin Heidelberg 2011.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Journal:
Intelligent Systems Reference Library
Issue Date:
2011
DOI:
10.1007/978-3-642-22661-8_2
Type:
Article
ISSN:
18684394
ISBN:
9783642226601
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChikalov, Igoren
dc.date.accessioned2015-08-03T09:02:01Zen
dc.date.available2015-08-03T09:02:01Zen
dc.date.issued2011en
dc.identifier.isbn9783642226601en
dc.identifier.issn18684394en
dc.identifier.doi10.1007/978-3-642-22661-8_2en
dc.identifier.urihttp://hdl.handle.net/10754/561674en
dc.description.abstractIn this chapter, bounds on the average depth and the average weighted depth of decision trees are considered. Similar problems are studied in search theory [1], coding theory [77], design and analysis of algorithms (e.g., sorting) [38]. For any diagnostic problem, the minimum average depth of decision tree is bounded from below by the entropy of probability distribution (with a multiplier 1/log2 k for a problem over a k-valued information system). Among diagnostic problems, the problems with a complete set of attributes have the lowest minimum average depth of decision trees (e.g, the problem of building optimal prefix code [1] and a blood test study in assumption that exactly one patient is ill [23]). For such problems, the minimum average depth of decision tree exceeds the lower bound by at most one. The minimum average depth reaches the maximum on the problems in which each attribute is "indispensable" [44] (e.g., a diagnostic problem with n attributes and kn pairwise different rows in the decision table and the problem of implementing the modulo 2 summation function). These problems have the minimum average depth of decision tree equal to the number of attributes in the problem description. © Springer-Verlag Berlin Heidelberg 2011.en
dc.titleBounds on Average Time Complexity of Decision Treesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalIntelligent Systems Reference Libraryen
kaust.authorChikalov, Igoren
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