Olutayo O. Oladunni

Knowledge-Based multiclass support vector machines applied to vertical two-phase flow

We present a knowledge-based linear multi-classification model for vertical two-phase flow regimes in pipes with the transition equations of McQuillan & Whalley [1] used as prior knowledge. Using published experimental data for gas-liquid vertical two-phase flows, and expert domain knowledge of the two-phase flow regime transitions, the goal of the model is to identify the transition region between different flow regimes. The prior knowledge is in the form of polyhedral sets belonging to one or more classes. The resulting formulation leads to a Tikhonov regularization problem that can be solved using matrix or iterative methods.

A regularized pairwise multi-classification knowledge-based machine and applications

This paper presents a novel knowledge-based linear classification model for multi-category discrimination of sets or objects with prior knowledge. The prior knowledge is in the form of multiple polyhedral sets belonging to one or more categories or classes and it is introduced as additional constraints into the formulation of the Tikhonov linear least squares multi-class support vector machine model. The resulting formulation leads to a least squares problem that can be solved using matrix methods or iterative methods. Investigations include the development of a linear knowledge-based classification model extended to the case of multi-categorical discrimination and expressed as a single unconstrained optimization problem. Advantages of this formulation include explicit expressions for the classification weights of the classifier(s) and its ability to incorporate and handle prior knowledge directly to the classifiers. In addition it can provide fast solutions to the optimal classification weights for multi-categorical separation without the use of specialized solver-software. To evaluate the model, data and prior knowledge from the Wisconsin breast cancer prognosis and two-phase flow regimes in pipes were used to train and test the proposed formulation.

A Pairwise Reduced Kernel-based Multi-classification Tikhonov Regularization Machine

This paper presents a reduced kernel-based classification model for multi-category discrimination of sets or objects. The proposed model is based on the Tikhonov regularization scheme. This approach extends Mangasarian reduced support vector machine (RSVM) model in a least square framework for the case of multi-categorical discrimination. The dimension reduction of the kernel matrix is achieved by selecting random subsets of the training set. Advantages of this formulation include explicit expressions for the classification weights of the classifier(s), its ability to incorporate several classes in a single optimization problem, and computational tractability in providing the optimal classification weights for multi-categorical separation. Computational results are also provided for two-phase flow data.

A nonlinear multi-classification knowledge-based kernel machine

This paper presents a knowledge-based nonlinear kernel classification model for multi-category discrimination of sets or objects with prior knowledge. A kernel function is employed to find a nonlinear classifier capable of discriminating future points into an appropriate class. The prior knowledge is in the form of multiple polyhedral sets belonging to one or more categories or classes, and it is introduced as additional constraints into the formulation of the regularized nonlinear kernel least squares multi-class support vector machine model. The resulting formulation leads to a linear system of equations that can be solved using matrix methods or iterative methods. This work extends previous work (Oladunni et al. in ICCS 2006, Lecture notes in Computer Science, Part I, LNCS, vol 3991. Springer, Berlin, pp 188–195, 2006) that incorporated similar prior knowledge into a regularized linear least squares multi-class model. To evaluate the model, data and prior knowledge from the two-phase flow regimes in pipes were used to train and test the proposed formulation.

Support Vector Machines and Applications

Support Vector Machines (SVMs) methods have become a popular tool for predictive data mining problems and novelty detection. They show good generalization performance on many real-life datasets and they are motivated theoretically through convex programming formulations. There are relatively few free parameters to adjust using cross validation and the architecture of the SVM learning machine does not need to be found by experimentation as in the case of Artificial Neural Networks (ANNs). We discuss the fundamentals of SVMs with emphasis to multiclass classification problems and applications in science, business and engineering.

Regularization Based Classification Models

This paper presents Tikhonov regularization based classification models for binary discrimination of sets or objects. The proposed models include a linear classification, nonlinear kernel classification and a reduced kernel classification model in the case of large scale problems. For the reduced kernel formulation, the dimension reduction of the kernel matrix is achieved by selecting random subsets of the training set. Advantages of the regularized classification formulations include explicit expressions for the classification weights of the classifier as well as its computational tractability in providing the optimal classification weights for two-class separation problems. Computational results are also provided for validation of the classification models.

Regularized Knowledge-Based Kernel Machine

This paper presents a knowledge-based kernel classification model for binary classification of sets or objects with prior knowledge. The prior knowledge is in the form of multiple polyhedral sets belonging to one or two classes, and it is introduced as additional constraints into a regularized knowledge-based optimization problem. The resulting formulation leads to a least squares problem that can be solved using matrix or iterative methods. To evaluate the model, the experimental laminar & turbulent flow data and the Reynolds number equation used as prior knowledge were used to train and test the proposed model.