Learning with Uncertainty 1st Edition by Xizhao Wang, Junhai Zhai ISBN 1498724124 978-1498724128

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ISBN 10: 1498724124
ISBN 13: 978-1498724128
Author:  Xizhao Wang, Junhai Zhai

Learning with uncertainty covers a broad range of scenarios in machine learning, this book mainly focuses on: (1) Decision tree learning with uncertainty, (2) Clustering under uncertainty environment, (3) Active learning based on uncertainty criterion, and (4) Ensemble learning in a framework of uncertainty. The book starts with the introduction to uncertainty including randomness, roughness, fuzziness and non-specificity and then comprehensively discusses a number of key issues in learning with uncertainty, such as uncertainty representation in learning, the influence of uncertainty on the performance of learning system, the heuristic design with uncertainty, etc.

Most contents of the book are our research results in recent decades. The purpose of this book is to help the readers to understand the impact of uncertainty on learning processes. It comes with many examples to facilitate understanding. The book can be used as reference book or textbook for researcher fellows, senior undergraduates and postgraduates majored in computer science and technology, applied mathematics, automation, electrical engineering, etc.

Learning with Uncertainty 1st Table of contents:

1 Uncertainty

1.1 Randomness

1.1.1 Entropy

1.1.2 Joint Entropy and Conditional Entropy

1.1.3 Mutual Information

1.2 Fuzziness

1.2.1 Definition and Representation of Fuzzy Sets

1.2.2 Basic Operations and Properties of Fuzzy Sets

1.2.3 Fuzzy Measures

1.3 Roughness

1.4 Nonspecificity

1.5 Relationships among the Uncertainties

1.5.1 Entropy and Fuzziness

1.5.2 Fuzziness and Ambiguity

References

2 Decision Tree with Uncertainty

2.1 Crisp Decision Tree

2.1.1 ID3 Algorithm

2.1.2 Continuous-Valued Attributes Decision Trees

2.2 Fuzzy Decision Tree

2.3 Fuzzy Decision Tree Based on Fuzzy Rough Set Techniques

2.3.1 Fuzzy Rough Sets

2.3.2 Generating Fuzzy Decision Tree with Fuzzy Rough Set Technique

2.4 Improving Generalization of Fuzzy Decision Tree by Maximizing Fuzzy Entropy

2.4.1 Basic Idea of Refinement

2.4.2 Globally Weighted Fuzzy If-Then Rule Reasoning

2.4.3 Refinement Approach to Updating the Parameters

2.4.3.1 Maximum Fuzzy Entropy Principle

References

3 Clustering under Uncertainty Environment

3.1 Introduction

3.2 Clustering Algorithms Based on Hierarchy or Partition

3.2.1 Clustering Algorithms Based on Hierarchy

3.2.2 Clustering Algorithms Based on Partition

3.3 Validation Functions of Clustering

3.4 Feature Weighted Fuzzy Clustering

3.5 Weighted Fuzzy Clustering Based on Differential Evolution

3.5.1 Differential Evolution and Dynamic Differential Evolution

3.5.1.1 Basic Differential Evolution Algorithm

3.5.1.2 Dynamic Differential Evolution Algorithm

3.5.2 Hybrid Differential Evolution Algorithm Based on Coevolution with Multi-Differential Evolution Strategy

3.6 Feature Weight Fuzzy Clustering Learning Model Based on MEHDE

3.6.1 MEHDE-Based Feature Weight Learning: MEHDE-FWL

3.6.2 Experimental Analysis

3.6.2.1 Comparison between MEHDE-FWL and GD-FWL Based on FCM

3.6.2.2 Comparisons Based on SMTC Clustering

3.6.2.3 Efficiency Analysis of GD-, DE-, DDE-, and MEHDE-Based Searching Techniques

3.7 Summary

References

4 Active Learning with Uncertainty

4.1 Introduction to Active Learning

4.2 Uncertainty Sampling and Query-by-Committee Sampling

4.2.1 Uncertainty Sampling

4.2.1.1 Least Confident Rule

4.2.1.2 Minimal Margin Rule

4.2.1.3 Maximal Entropy Rule

4.2.2 Query-by-Committee Sampling

4.3 Maximum Ambiguity–Based Active Learning

4.3.1 Some Concepts of Fuzzy Decision Tree

4.3.2 Analysis on Samples with Maximal Ambiguity

4.3.3 Maximum Ambiguity–Based Sample Selection

4.3.4 Experimental Results

4.4 Active Learning Approach to Support Vector Machine

4.4.1 Support Vector Machine

4.4.2 SVM Active Learning

4.4.3 Semisupervised SVM Batch Mode Active Learning

4.4.4 IALPSVM: An Informative Active Learning Approach to SVM

4.4.5 Experimental Results and Discussions

4.4.5.1 Experiments on an Artificial Data Set by Selecting a Single Query Each Time

4.4.5.2 Experiments on Three UCI Data Sets by Selecting a Single Query Each Time

4.4.5.3 Experiments on Two Image Data Sets by Selecting a Batch of Queries Each Time

References

5 Ensemble Learning with Uncertainty

5.1 Introduction to Ensemble Learning

5.1.1 Majority Voting and Weighted Majority Voting

5.1.2 Approach Based on Dempster–Shafer Theory of Evidence

5.1.3 Fuzzy Integral Ensemble Approach

5.2 Bagging and Boosting

5.2.1 Bagging Algorithm

5.2.2 Boosting Algorithm

5.3 Multiple Fuzzy Decision Tree Algorithm

5.3.1 Induction of Multiple Fuzzy Decision Tree

5.3.2 Experiment on Real Data Set

5.4 Fusion of Classifiers Based on Upper Integral

5.4.1 Extreme Learning Machine

5.4.2 Multiple Classifier Fusion Based on Upper Integrals

5.4.2.1 Upper Integral and Its Properties

5.4.2.2 A Model of Classifier Fusion Based on Upper Integral

5.4.2.3 Experimental Results

5.5 Relationship between Fuzziness and Generalization in Ensemble Learning

5.5.1 Classification Boundary

5.5.1.1 Boundary and Its Estimation Given by a Learned Classifier

5.5.1.2 Two Types of Methods for Training a Classifier

5.5.1.3 Side Effect of Boundary and Experimental Verification

5.5.2 Fuzziness of Classifiers

5.5.2.1 Fuzziness of Classifier

5.5.2.2 Relationship between Fuzziness and Misclassification

5.5.2.3 Relationship between Fuzziness and Classification Boundary

5.5.2.4 Divide and Conquer Strategy

5.5.2.5 Impact of the Weighting Exponent m on the Fuzziness of Fuzzy K-NN Classifier

5.5.3 Relationship between Generalization and Fuzziness

5.5.3.1 Definition of Generalization and Its Elaboration

5.5.3.2 Classifier Selection

5.5.3.3 Explanation Based on Extreme (max/min) Fuzziness

5.5.3.4 Experimental Results

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Tags: Xizhao Wang, Junhai Zhai, Learning with Uncertainty