Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators

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학위논문 (석사)-- 서울대학교 대학원 공과대학 산업공학과, 2017. 8. 이경식.One-class classification (OCC) is a supervised learning technique for classification, where the classifier is constructed only by training the objects in the target class and determines whether new ones belong to the class or not. There have been attempts to solve OCC problem such as Support Vector Machines (SVM), Parzen Density Estimation (PDE) and other methods commonly used in multi-class classification. In this paper, a new approach to OCC was proposed. The classifier consists of norm balls covering the objects in the target class: an object is classified in the target class if at least one of the norm balls covers it, otherwise it is rejected. We presented an algorithm of generating finite norm ball candidates. Then, by applying two conditions for 'good' norm ball the final candidates were chosen out of the candidates. An integer programming model for the selection of the optimal norm balls was solved so that the norm balls with the minimum number effectively detect the target objects with the good predictive power. The experiments were carried out to test the overall performance of our classifier using some artificial and real data from UCI Repository. The results showed that proposed model was comparable to OCC methods in the comparison group. Also, it had high sparsity leading to low testing burden compared to the other classifiers. In the noise experiment, maximum norm ball classifier was robust to noises.Abstract i Contents iv List of Tables vii List of Figures x Chapter 1 Introduction 1 1.1 Backgrounds 1 1.2 Literature Review 3 1.3 Motivations 6 Chapter 2 Norm Ball Classifier 11 2.1 Definition of Norm Ball Classifier 11 2.2 Construction of Norm Ball Classifier 13 2.2.1 Generation of Norm Ball Candidates 13 2.2.2 Selection of Norm Balls 16 Chapter 3 Experiments 21 3.1 Experiment Design 21 3.1.1 Data 21 3.1.2 NBCs and Comparison One-Class Classifier Group 22 3.1.3 Experimental Settings 23 3.1.4 Performance Measure 25 3.2 Computational Results 26 3.2.1 Artificial Data 26 3.2.2 Real Data 31 3.2.3 Noise Experiment 37 Chapter 4 Conclusions 51 4.1 Discussions 51 4.2 Further Research 54 Chapter 5 Appendix 57 Bibliography 75 국문초록 81Maste