Now showing 1 - 5 of 27
- ItemImplementation of the Cavalieri Integral(2023-02) van Zyl, Christoff; Grobler, Trienko; Stellenbosch University. Faculty of Science. Dept. of Computer Science.ENGLISH ABSTRACT: Cavalieri Integration in R n presents a novel visualization mechanism for weighted integration and challenges the notion of strictly rectangular integration strips. It does so by concealing the integrator inside the boundary curves of the integral. This paper investigates the Cavalieri integral as a superset of Riemann-integration in R n−1 , whereby the integral is defined by a translational region in R n−1 , which uniquely defines the integrand, integrator and integration region. In R 2 , this refined translational region definition allows for the visualization of Riemann-Stieltjes integrals along with other forms of weighted integration such as the Riemann–Liouville fractional integral and convolution operator. Programmatic implementation of such visualizations and computation of integral values are also investigated and relies on knowledge relating to numeric integration, algorithmic differentiation and numeric root finding. For the R 3 case, such visualizations over polygonal regions requires a mechanism for the triangulation of a set of nested polygons and transformations which allow for the use of repeated integration to solve the integration value over the produced triangular regions using standard 1-dimensional integration routines.
- ItemRule Induction with Swarm Intelligence(Stellenbosch : Stellenbosch University, 2022-03) van Zyl, Jean-Pierre; Engelbrecht, Andries Petrus; Stellenbosch University. Faculty of Science. Dept. of Computer Science.ENGLISH ABSTRACT: Rule induction is the process by which explainable mappings are created between a set of input data instances and a set of labels for the input instances. This process can be seen as an extension of traditional classification algorithms, because rule induction algorithms perform classification b ut h ave t he addedproperty of being transparent when making inferences. Popular algorithms in existing literature tend to use antiquated approaches to induce rule sets. The existing approaches tend to be greedy in nature and do not provide a platform for algorithm expansion or improvement. This thesis investigates a new approach to rule induction using a set-based particle swarm optimisation algorithm. The investigation starts with a comprehensive review of the relevant literature, after which the novel algorithm is proposed and compared with popular rule induction algorithms. After the establishment of the capabilities and validity of the set-based particle swarm optimisation rule induction algorithm, the effect of the objective function on the algorithm is investigated. The objective function is tested with 12 existing performance evaluation metrics in order to understand how the performance of the algorithm can be improved. These 12 existing metrics are then used as inspiration for the proposal of 11 new performance evaluation metrics which are also tested as part of the objective function effect analysis. The effect o f v arying d istributions o f t he v alues o f t he t arget c lass i s also examined. This thesis also investigates the reformulation of the rule induction problem as a multi-objective optimisation problem and applies the newly developed multi-guide set-based particle swarm optimisation algorithm to the multiobjective formulation of rule induction. The performance of rule induction as a multi-objective problem is evaluated by examining how the trade-off between the defined objectives functions affects performance for different datasets. The existing metrics and newly proposed metrics tested in the single objective formulation of the rule induction problem are also tested in the multi-objective formulation.
- ItemApplication of statistical pattern recognition and deep learning for morphological classification in radio astronomy(Stellenbosch : Stellenbosch University, 2022-04) Becker, Adolf Burger; Grobler, Trienko; Stellenbosch University. Faculty of Science. Dept. of Computer Science.ENGLISH ABSTRACT: The morphological classification of radio sources is important to gain a full under standing of galaxy evolution processes and their relation with local environmental properties. Furthermore, the complex nature of the problem, its appeal for citi zen scientists and the large data rates generated by existing and upcoming radio telescopes combine to make the morphological classification of radio sources an ideal test case for the application of machine learning techniques. One approach that has shown great promise recently is Convolutional Neural Networks (CNNs). Literature, however, lacks two major things when it comes to CNNs and radio galaxy morphological classification. Firstly, a proper analysis to identify whether overfitting occurs when training CNNs to perform radio galaxy morphological clas sification is needed. Secondly, a comparative study regarding the practical appli cability of the CNN architectures in literature is required. Both of these short comings are addressed in this thesis. Multiple performance metrics are used for the latter comparative study, such as inference time, model complexity, compu tational complexity and mean per class accuracy. A ranking system based upon recognition and computational performance is proposed. MCRGNet, ATLAS and ConvXpress (novel classifier) are the architectures that best balance computational requirements with recognition performance.
- ItemAn extension of the linear regression model for improved vessel trajectory prediction utilising a priori AIS Information(Stellenbosch : Stellenbosch University, 2022-04) Burger, Christiaan Neil; Grobler, Trienko Lups; Kleynhans, Waldo; Stellenbosch University. Faculty of Science. Dept. of Computer Science.ENGLISH ABSTRACT: As maritime activities increase globally, there is a greater dependency on technology in monitoring, control and surveillance of vessel activity. One of the most prominent systems for monitoring vessel activity is the Automatic Identification System (AIS). An increase in both vessels fitted with AIS transponders, and satellite- and terrestrial receivers has resulted in a significant increase in AIS messages received globally. This resultant rich spatial and temporal data source related to vessel activity provides analysts with the ability to perform enhanced vessel movement analytics, of which a pertinent example is the improvement of vessel location predictions. In this thesis, we propose a novel method for predicting future locations of vessels by making use of historic AIS data. The proposed method extends a Linear Regression Model (LRM), utilising historic AIS movement data in the form of a priori generated spatial maps of the course over ground (LRMAC). The LRMAC has low complexity and is programmatically easy to implement, and attains accurate prediction results. We first compare the LRM with a Discrete Kalman Filter (DKF) on linear trajectories. We then extend the LRM to form the LRMAC. The LRMAC is compared to another method in literature called the Single Point Neighbour Search (SPNS). For the use case of predicting Cargo and Tanker vessel trajectories, with a prediction horizon of up to six hours, the LRMAC has an improved execution time and performance compared to the SPNS.
- ItemThe generation of longest optimal box repetition-free words(Stellenbosch : Stellenbosch University, 2022-04) Habeck, Manfred; Grobler, Trienko; Van Zijl, Lynette; Geldenhuys, Jaco; Stellenbosch University. Faculty of Science. Dept. of Computer Science.ENGLISH ABSTRACT: This thesis focuses on a specific problem within the field of combinatorial generation, namely, the generation of box repetition-free words. A box is a word over a given alphabet, where the first symbol in the word is the same as the last symbol. For example, the word abaca is a box. A box can contain other boxes. The box abaca contains boxes aba and aca. Boxes can overlap, such as aba and aca in abaca. This work investigates the generation of the longest possible sequence of symbols, over a given alphabet, which does not contain any repeating boxes. We show that an exhaustive enumeration based on a brute force approach with backtracking is not feasible. That is, we checked if adding a symbol to a word would create a repeating box; if not, recursively add another symbol. This method will eventually find all valid words, but takes an unreasonable amount of time for larger alphabets. As a non-enumerative attempt to find individual valid words, the Monte Carlo tree search is used. The search is based on the assumption that prefixes with good past results will also give good results in the future. Based on an analysis of the properties of box repetition-free words, a new search is devised. Factors of words are mapped onto a graph, and all non-optimal edges removed. It is then shown that any Hamiltonian path on this graph will result in a longest optimal word. The results of this work show that backtracking fails to generate longest optimal words within a reasonable time for any alphabet with more than three symbols. The Monte Carlo tree search performs better than backtracking, finding optimal words for an alphabet size of four, but failing for larger alphabets. The new method outperforms both, and with a small optimization, is shown to generate longest optimal words up to an alphabet size of six.