Study on Support Vector Machines and its Application
- Alternative Author(s)
- 정나영
- Affiliation
- 부경대학교 대학원
- Department
- 대학원 통계학과
- Advisor
- 윤민
- Table Of Contents
- 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1
2 Support Vector Machine . . . . . . . . . . . . 4
2.1 Concepts of support vector machines . . . . . . . . . . . . . 4
2.2 Hard margin SVM ( Maximal margin SVM ) . . . . . . . . 5
2.3 Soft margin SVM . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 ν - SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 ν -SVM with single class . . . . . . . . . . . . . . . . 13
3 Multi-Objective Optimization 15
3.1 Mathematical Foundations . . . . . . . . . . . . . . . . . . . 17
3.2 Preference Order and Domination Set . . . . . . . . . . . . 20
3.3 Scalarization . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Evolutionary multi-objective optimization 25
4.1 Genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.1 Vector Evaluated Genetic Algorithm (VEGA) . . . . 27
4.1.2 Multi-Objective Genetic Algorithm (MOGA) . . . . 28
4.2 Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) . . . . . . . . 32
4.3 Strength Pareto Evolutionary Algorithm (SPEA2) . . . . . 35
5 Proposed Method . . . . . . . . 39
5.1 Multi-objective optimization algorithm using support vector machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Comparison Results . . . . . . . . . . . . . . . . . . . . . . 42
5.2.1 Benchmark Test Problems . . . . . . . . . . . . . . . 42
5.2.2 Real Engineering Problems . . . . . . . . . . . . . . 45
6 Conclusion . . . . . . . . 51
Bibliography . . . . . . . . 52
- Degree
- Master
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- 대학원 > 통계학과
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