Twin hyper-ellipsoidal support vector classifier

ตัวจำแนกแบบทวินไฮเปอร์อีลิปซอยดอลซัพพอร์ตเวกเตอร์

Name: Kasemsit Teeyapan

ThaSH: Support vector machines

Classification :.DDC: 006.31

ThaSH: Supervised learning (Machine learning)

Abstract: Designing pattern classifiers is an important step toward creating an intelligent machine which can learn and recognize hidden statistical patterns inside the data. It is also one basic task in the field of machine learning. Generally, learning machines search for the best decision rule from its known set of functions. In the literature, such a predefined function is linear; for example, support vector machine (SVM) has hyperplanes as its underlying form of decision functions. This is because hyperplane is the simplest form of functions and using overly-complicated functions does not always guarantee the best decision boundary. Nevertheless, since hypersurfaces possess one more degree of geometrical sophistication than hyperplanes, research communities also have shown some interests in introducing hypersurfaces as a predefined set of function for learning machines. For instance, support vector data description (SVDD) searches for the best hypersphere from a given set of hyperspheres to form a descriptive boundary around the data. As a result, since hyperellipsoid is also the next complex geometrical shape to hyperspheres, it is tempting to also create learning machines which possess hyperellipsoids as a predefined set of functions. This thesis focuses primarily on designing non-parametric learning machines whose predefined set of function is filled with hyperellipsoids. We propose two novel classifiers based on the formulation of minimum volume covering ellipsoid (MVCE), one for solving one-class classification problems and the other for binary classification problems. For one-class classification, the proposed method called “ellipsoidal support vector data description (eSVDD) with negative examples” aims at constructing a descriptive boundary using the MVCE with soft margins around the target data while also trying to exclude outliers. For binary classification, a novel MVCE-based binary classifier which tries to find two best fitting hyperellipsoids is proposed. The proposed method is named “twin hyper-ellipsoidal support vector machine (TESVM)”. Its concept, as inspired by “twin support vector machine (TWSVM)” and “twin-hypersphere support vector machine (THSVM)”, is to create a soft-margin MVCE around each class of data with an additional objective such that each hyperellipsoid must also be located as far as possible from the other class. The learning machines like SVM and SVDD create more complex decision boundary through kernel tricks; however, the same kernel approach is not directly applicable for the proposed MVCE-based classifiers. In fact, applying kernel tricks to even the MVCE problem itself is not so straightforward since the formulation of MVCE comes in the form of outer products instead of inner products. As a result, we also propose that any MVCE-based classifiers can also be further equipped with kernel methods by using the so-called “empirical feature map” or “kernel principal component analysis map” (kernel PCA map). By projecting the images of the given examples into an approximate kernel-defined space, it is possible to construct a hyperellipsoids in that space, resulting in more complex descriptive boundary in the input space or the original space. All the proposed methods are evaluated against state-of-the-art techniques in several experiments on both artificial and publicly-available standard real-world datasets. For one-class classification, we compare the proposed eSVDD with negative examples against SVDD, SVDD with negative example, as well as eSVDD. For two-class classification, the proposed TESVM is also tested with THSVM, TWSVM, and SVM. The experimental results show that the uses of hyperellipsoids in both eSVDD with negative examples and TESVM are superior to their hyper-spherical counterparts. The inclusion of negative examples into the formulations also helps improve the overall performance of the MVCE-based classifiers. Furthermore, TESVM also provides better results than SVM and TWSVM in term of average accuracy on the standard datasets

Chiang Mai University Library

Address: Chiang Mai

Email: cmulibref@cmu.ac.th

Name: Prabhas Chongstitvatana

Role: Chairman

Name: Nipon Theera-Umpon

Role: Member

Name: Sermsak Uatrongjit

Role: Member

Name: Sansanee Auephanwiriyakul

Role: Member

Name: Ukrit Mankong

Role: Member

Created: 2017

Modified: 2020-01-07

Issued: 2020-01-07

วิทยานิพนธ์/Thesis

application/pdf

CallNumber: Th 006.31 K19T 2017

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Electrical Engineering

Grantor: Chiang Mai University

©copyrights Chiang Mai University

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