*Electronic Theses and Dissertations (Masters)
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Item Estimating skills in discrete pursuit-evasion games(University of the Witwatersrand, Johannesburg, 2023) Gomes, Byron John; Rosman, BenjaminGame Theory is a well-established field in mathematics, economics, and computer science, with a rich history of studying n-person, zero-sum games. Researchers have utilized the best computational power of their time to create computational players that are able to beat the best human players at complex two-player, zero-sum games such as Chess and Go. In the field of Reinforcement Learning and Robotics, these types of games are considered useful environments to conduct experiments about agent behavior and learning. In this research report we explore a subset of discrete skill-dependent pursuit-evasion games upon which we build a framework to estimate player skills. In this game environment a player’s skill determines the actions available to them in each state and the transition dynamics resulting from the chosen action. The game offers a simplified depresentation of more complex games which often have vast state and action spaces, making it difficult to model and analyze player behavior. In this game environment we find that players with incorrect assumptions about an opponent’s skill perform sub-optimally at winning games. Given that knowledge of an opponent’s skill impacts on player performance, we demonstrate that players can use Bayesian inference to estimate their opponent’s skill, based on the action outcomes of an opponent. We also demonstrate that skill estimation is a valuable exercise for players to undertake and show that the performance of players that estimate their opponent’s skill converges to the performance of players given perfect knowledge of their opponent’s skill. This research contributes to our understanding of Bayesian skill estimation in skill-dependent pursuit-evasion games which may be useful in the fields of Multi-agent Reinforcement Learning and Robotics.Item Comparing the effectiveness of LSTM, ARIMA, and GRU algorithms for forecasting customer charging behavior in the electric mobility industry in Europe(University of the Witwatersrand, Johannesburg, 2023) Pelwan, Robyne ChimereForecasting, a powerful technique for unveiling potential future events, relies on historical data and methodological approaches to provide valuable insights. This dissertation delves into the domain of electric mobility, investigating the effectiveness of three distinct algorithms—Long Short-term Memory (LSTM), Autoregressive Integrated Moving Average (ARIMA), and Gated Recurrent Unit (GRU)—for predicting customer charging behavior. Specifically, it focuses on forecasting the number of charges over a 7-day period using time-series data from European electric mobility customers. In this study, we scrutinize the interplay between algorithmic performance and the intricacies of the dataset. Root mean squared error (RMSE) serves as a metric for gauging predictive accuracy. The findings highlight the supremacy of the ARIMA model in single-variable analysis, surpassing the predictive capabilities of both LSTM and GRU models. Even when additional features are introduced to enhance LSTM and GRU predictions, the superiority of ARIMA remains pronounced. Notably, this research underscores that ARIMA is particularly well-suited for time series data of this nature due to its tailored design. It contributes valuable insights for both researchers and practitioners in the electric mobility industry, aiding in the strategic selection of forecasting methodologies.Item A comparative analysis of classic Geometrical methods and sparse regression methods for linearly unmixing hyperspectral image data(2019) Nicolae, AurelThis research report presents an across-the-board comparative analysis on algorithms for linearly unmixing hyperspectral image data cubes. Convex geometry based endmember extraction algorithms (EEAs) such as the pixel purity index (PPI) algorithm and N-FINDR have been commonly used to derive the material spectral signatures called endmembers from the hyperspectral images. The estimation of their corresponding fractional abundances is done by solving the related inverse problem in a least squares sense. Semi-supervised sparse regression algorithms such as orthogonal matching pursuit (OMP) and sparse unmixing algorithm via variable splitting and augmented Lagrangian (SUnSAL) bypass the endmember extraction process by employing widely available spectral libraries a priori, automatically returning the fractional abundances and sparsity estimates. The main contribution of this work is to serve as a rich resource on hyperspectral image unmixing, providing end-to-end evaluation of a wide variety of algorithms using di erent arti cial data sets.