Learning with uncertainty

Content: Machine generated contents note: 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 --
References.