Average Time Complexity Of Decision Trees
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Average Time Complexity of Decision Trees
Author: Igor Chikalov
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-08-04
Decision tree is a widely used form of representing algorithms and knowledge. Compact data models and fast algorithms require optimization of tree complexity. This book is a research monograph on average time complexity of decision trees. It generalizes several known results and considers a number of new problems. The book contains exact and approximate algorithms for decision tree optimization, and bounds on minimum average time complexity of decision trees. Methods of combinatorics, probability theory and complexity theory are used in the proofs as well as concepts from various branches of discrete mathematics and computer science. The considered applications include the study of average depth of decision trees for Boolean functions from closed classes, the comparison of results of the performance of greedy heuristics for average depth minimization with optimal decision trees constructed by dynamic programming algorithm, and optimization of decision trees for the corner point recognition problem from computer vision. The book can be interesting for researchers working on time complexity of algorithms and specialists in test theory, rough set theory, logical analysis of data and machine learning.
Combinatorial Machine Learning
Decision trees and decision rule systems are widely used in different applications as algorithms for problem solving, as predictors, and as a way for knowledge representation. Reducts play key role in the problem of attribute (feature) selection. The aims of this book are (i) the consideration of the sets of decision trees, rules and reducts; (ii) study of relationships among these objects; (iii) design of algorithms for construction of trees, rules and reducts; and (iv) obtaining bounds on their complexity. Applications for supervised machine learning, discrete optimization, analysis of acyclic programs, fault diagnosis, and pattern recognition are considered also. This is a mixture of research monograph and lecture notes. It contains many unpublished results. However, proofs are carefully selected to be understandable for students. The results considered in this book can be useful for researchers in machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and logical analysis of data. The book can be used in the creation of courses for graduate students.
Decision Support System
This book presents different tools and techniques used for Decision Support Systems (DSS), including decision tree and table, and their modifications, multi-criteria decision analysis techniques, network tools of decision support, and various case-based reasoning methods supported by examples and case studies. Latest developments for each of the techniques have been discussed separately, and possible future research areas are duly identified as intelligent and spatial DSS. Features: Discusses all the major tools and techniques for Decision Support System supported by examples. Explains techniques considering their deterministic and stochastic aspects. Covers network tools including GERT and Q-GERT. Explains the application of both probability and fuzzy orientation in the pertinent techniques. Includes a number of relevant case studies along with a dedicated chapter on software. This book is aimed at researchers and graduate students in information systems, data analytics, operation research, including management and computer science areas.