SPACES OF FIBONACCI DIFFERENCE IDEAL CONVERGENT SEQUENCES IN RANDOM 2–NORMED SPACE

In this article, by using Fibonacci difference matrix  and the notion of ideal convergence of sequences in random 2–normed space, we introduce some new spaces of Fibonacci difference ideal convergent sequences with respect to random -norm and study some inclusion relations, topological and algebraic properties of these spaces.

Contributions to statistical machine learning algorithm

This thesis's research focus is on computational statistics along with DEAR (abbreviation of differential equation associated regression) model direction, and that in mind, the journal papers are written as contributions to statistical machine learning algorithm literature

Unplanned dilution and ore-loss optimisation in underground mines via cooperative neuro-fuzzy network

The aim of study is to establish a proper unplanned dilution and ore-loss (UB: uneven break) management system. To achieve the goal, UB prediction and consultation systems were established using artificial neural network (ANN) and fuzzy expert system (FES). Attempts have been made to illuminate the UB mechanism by scrutinising the contributions of potential UB influence factors. Ultimately, the proposed UB prediction and consultation systems were unified as a cooperative neuro fuzzy system

Building well-performing classifier ensembles: model and decision level combination.

There is a continuing drive for better, more robust generalisation performance from classification systems, and prediction systems in general. Ensemble methods, or the combining of multiple classifiers, have become an accepted and successful tool for doing this, though the reasons for success are not always entirely understood. In this thesis, we review the multiple classifier literature and consider the properties an ensemble of classifiers - or collection of subsets - should have in order to be combined successfully. We find that the framework of Stochastic Discrimination provides a well-defined account of these properties, which are shown to be strongly encouraged in a number of the most popular/successful methods in the literature via differing algorithmic devices. This uncovers some interesting and basic links between these methods, and aids understanding of their success and operation in terms of a kernel induced on the training data, with form particularly well suited to classification. One property that is desirable in both the SD framework and in a regression context, the ambiguity decomposition of the error, is de-correlation of individuals. This motivates the introduction of the Negative Correlation Learning method, in which neural networks are trained in parallel in a way designed to encourage de-correlation of the individual networks. The training is controlled by a parameter λ governing the extent to which correlations are penalised. Theoretical analysis of the dynamics of training results in an exact expression for the interval in which we can choose λ while ensuring stability of the training, and a value λ∗ for which the training has some interesting optimality properties. These values depend only on the size N of the ensemble. Decision level combination methods often result in a difficult to interpret model, and NCL is no exception. However in some applications, there is a need for understandable decisions and interpretable models. In response to this, we depart from the standard decision level combination paradigm to introduce a number of model level combination methods. As decision trees are one of the most interpretable model structures used in classification, we chose to combine structure from multiple individual trees to build a single combined model. We show that extremely compact, well performing models can be built in this way. In particular, a generalisation of bottom-up pruning to a multiple-tree context produces good results in this regard. Finally, we develop a classification system for a real-world churn prediction problem, illustrating some of the concepts introduced in the thesis, and a number of more practical considerations which are of importance when developing a prediction system for a specific problem

Biomedical applications of belief networks

Biomedicine is an area in which computers have long been expected to play a significant role. Although many of the early claims have proved unrealistic, computers are gradually becoming accepted in the biomedical, clinical and research environment. Within these application areas, expert systems appear to have met with the most resistance, especially when applied to image interpretation.In order to improve the acceptance of computerised decision support systems it is necessary to provide the information needed to make rational judgements concerning the inferences the system has made. This entails an explanation of what inferences were made, how the inferences were made and how the results of the inference are to be interpreted. Furthermore there must be a consistent approach to the combining of information from low level computational processes through to high level expert analyses.nformation from low level computational processes through to high level expert analyses. Until recently ad hoc formalisms were seen as the only tractable approach to reasoning under uncertainty. A review of some of these formalisms suggests that they are less than ideal for the purposes of decision making. Belief networks provide a tractable way of utilising probability theory as an inference formalism by combining the theoretical consistency of probability for inference and decision making, with the ability to use the knowledge of domain experts.nowledge of domain experts. The potential of belief networks in biomedical applications has already been recog¬ nised and there has been substantial research into the use of belief networks for medical diagnosis and methods for handling large, interconnected networks. In this thesis the use of belief networks is extended to include detailed image model matching to show how, in principle, feature measurement can be undertaken in a fully probabilistic way. The belief networks employed are usually cyclic and have strong influences between adjacent nodes, so new techniques for probabilistic updating based on a model of the matching process have been developed.An object-orientated inference shell called FLAPNet has been implemented and used to apply the belief network formalism to two application domains. The first application is model-based matching in fetal ultrasound images. The imaging modality and biological variation in the subject make model matching a highly uncertain process. A dynamic, deformable model, similar to active contour models, is used. A belief network combines constraints derived from local evidence in the image, with global constraints derived from trained models, to control the iterative refinement of an initial model cue.In the second application a belief network is used for the incremental aggregation of evidence occurring during the classification of objects on a cervical smear slide as part of an automated pre-screening system. A belief network provides both an explicit domain model and a mechanism for the incremental aggregation of evidence, two attributes important in pre-screening systems.Overall it is argued that belief networks combine the necessary quantitative features required of a decision support system with desirable qualitative features that will lead to improved acceptability of expert systems in the biomedical domain

Computational Physics: An Introduction to Monte Carlo Simulations of Matrix Field Theory

This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since 2010 to physics students at Annaba University. The second part is much more advanced and deals with the problem of how to set up working Monte Carlo simulations of matrix field theories which involve finite dimensional matrix regularizations of noncommutative and fuzzy field theories, fuzzy spaces and matrix geometry. The study of matrix field theory in its own right has also become very important to the proper understanding of all noncommutative, fuzzy and matrix phenomena. The second part, which consists of 9 simulations, was delivered informally to doctoral students who are working on various problems in matrix field theory. Sample codes as well as sample key solutions are also provided for convenience and completness. An appendix containing an executive arabic summary of the first part is added at the end of the book.Comment: 350 pages, v2: slight change in titl