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A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign
A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign
Faculty Publications
This research paper focuses on quaternion neural networks (QNNs) - a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. Previous studies have shown that QNNs outperform real-valued neural networks in basic tasks and have potential in high-dimensional problem spaces. However, research on QNNs has been fragmented, with contributions from different mathematical and engineering domains leading to unintentional overlap in QNN literature. This work aims to unify existing research by evaluating four distinct QNN backpropagation algorithms, including the novel GHR-calculus backpropagation algorithm, and providing concise, scalable implementations of each algorithm using a …
Probability Of Agreement As A Simulation Validation Methodology, Matthew C. Ledwith
Probability Of Agreement As A Simulation Validation Methodology, Matthew C. Ledwith
Theses and Dissertations
Determining whether a simulation model is operationally valid requires the rigorous assessment of agreement between observed functional responses of the simulation model and the corresponding real world system or process of interest. This research seeks to extend and formulate the probability of agreement approach to the operational validation of simulation models. The first paper provides a methodological approach and an initial demonstration which leverages bootstrapping to overcome situations where one’s ability to collect real-world data is limited. The second paper extends the probability of agreement approach to account for second-order heteroscedastic variability structures and establishes a weighted probability of agreement …