Titre : | Contribution On the Estimation of the Copulas Parameters |
Auteurs : | karima Femmam, Auteur ; Brahim Brahimi, Directeur de thèse |
Type de document : | Thése doctorat |
Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2023 |
Format : | 1 vol. (71 p.) / couv. ill. en coul / 30cm |
Langues: | Anglais |
Mots-clés: | Copules, Selection des Caractéritiques, Extraction des Caractéristiques, Réduction des Dimensions, Intercorrélation, ACP. |
Résumé : |
the task of modeling high dimensional datasets has become increasingly difficult and challenging due to the large amount of redundancy present in the data. This redundancy often leads to the presence of noise and inaccurate data modeling and analysis results. While numerous statistical methods have been proposed to address this problem, many of them involve multiple operations and have high time complexity, often resulting in poor classification performance. To deal with that, in this thesis, three Dimensionality Reduction based on the inter-correlation between the huge data attributes are proposed, where this correlation is modeled using the theory of Copulas. The first two Dimensionality Reduction techniques aim to reduce redundancy by selecting only relevant attributes. While the third proposed technique is a feature extraction process that combines Principal Component Analysis PCA and the bivariate Copulas. All these techniques are performed using real-world datasets and compared against powerful Dimensionality Reduction methods in term of reduction, information capturing and models accuracy of the obtained reduced data to evaluate the effectiveness of each technique. |
Sommaire : |
List of Tables ix List of Figures xi Acronyms xiii Notion xv General Introduction 1 1 The theory of Copulas 5 1.1 Introduction 5 1.2 Sklar’s theorem . 6 1.3 Measures of dependence 8 1.3.1 Linear correlation . . . . . . . . 8 1.3.2 Measures of concordance . . . 9 1.3.3 Tail dependence .. 12 1.4 Families of Copulas . 13 1.4.1 Elliptical Copulas 13 1.4.2 Archimedean Copulas. . . . 18 1.5 Empirical Copula . 21 1.6 Conclusion 22 2 Dimensionality R 23 2.2 Feature extraction . 24 2.2.1 Linear Dimensionaltiy Reduction techniques . . . . 24 2.2.2 Non-linear Dimensionality Reduction techniques . . . 28 2.3 Feature selection . . . 29 2.4 Copulas based Dimensionality Reduction .30 2.5 Conclusion . 34 viTABLE OF CONTENTS 3 Feature Selection based on Bivariate Copulas 35 3.1 Introduction . 35 3.2 BCFS .35 3.2.1 The method 36 3.3 GBCFS . . 38 3.3.1 The method 38 3.4 Experimental results . 41 3.4.1 Fitting to Copulas 41 3.4.2 Dimensionality Reduction . 43 3.4.3 Classification accuracy . . 44 3.4.4 Discussion . . . 44 3.5 Conclusion . 45 4 Feature Extraction based on Bivariate Copulas 47 4.1 Introduction47 4.2 Methodology. 47 4.3 Experimental results . 48 4.3.1 Small data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Large data 54 4.3.3 Discussion 59 4.4 Conclusion . 62 Appendix 63 General Conclusion 69 Bibliography 71 |
En ligne : | http://thesis.univ-biskra.dz/id/eprint/6254 |
Disponibilité (1)
Cote | Support | Localisation | Statut |
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TM/143 | Théses de doctorat | bibliothèque sciences exactes | Consultable |