Quaternion tools for mathematical prediction
Abstract/Contents
- Abstract
- Existing quaternion neural network structures suffer from two key limitations: first, these structures are computationally expensive to train; and second, they do not perform all mathematical operations in the quaternion domain. Existing quaternion neural networks are limited by using a real-valued, nonlinear activation function independently on each quaternion dimension. The original contributions to knowledge in this work address both limitations. The computational limitations are addressed through the introduction of a version of quaternion Backpropagation that requires significantly fewer training cycles for convergence and is further addressed with the introduction of Direct Quaternion Error, an algorithm that performs equivalently to quaternion Backpropagation under certain conditions and requires considerably less computation per training cycle. As for performing mathematical operations in the quaternion domain, a new multi-valued quaternion neuron and neural network structure are proposed, wherein a discrete-valued activation function that operates simultaneously in all four quaternion dimensions is introduced. Since there are no standard datasets for the evaluation of quaternion neural networks, two applications are used to demonstrate the effectiveness of the proposed techniques. The problems of automated prostate cancer Gleason grading and chaotic time series prediction are investigated. Both of these are difficult prediction problems and are appropriate for benchmarking mathematical classification and prediction techniques. The high-speed quaternion neural network training techniques are shown to be effective in the Gleason grading experiments, and the new multi-valued quaternion neural network is shown to outperform both real-valued and other quaternion-valued neural networks in the chaotic time series prediction.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Greenblatt, Aaron B |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering. |
| Primary advisor | Agaian, S. S |
| Primary advisor | Gill, John T III |
| Thesis advisor | Agaian, S. S |
| Thesis advisor | Gill, John T III |
| Thesis advisor | Smith, Julius O. (Julius Orion) |
| Advisor | Smith, Julius O. (Julius Orion) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Aaron B. Greenblatt. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Aaron Benjamin Greenblatt
Also listed in
Loading usage metrics...