Direction Set Based Methods For Adaptive Least Squares Problems: Improvements And Innovations
| dc.contributor.author | Ahmad, Noor Atinah | |
| dc.date.accessioned | 2023-01-16T08:07:09Z | |
| dc.date.available | 2023-01-16T08:07:09Z | |
| dc.date.issued | 2008-06-01 | |
| dc.description.abstract | The main objective of this research is to provide a mathematically tractable solutions to the adaptive filtering problem by formulating the problem as an adaptive least squares problem. This approach follows the work of Chen (1998) in his study of direction-set based CDS) adaptive filtering algorithm. Through the said formulation, we relate the DS algorithm to a class of projection method. In particular, the simplified version of the algorithm, which is the Euclidean direction search (EDS) algorithm is shown to be related to a class of iterative methods called relaxation methods. This findings enable us to improve the EDS algorithm to the accelerated EDS where an acceleration parameter is introduced to optimize the step size during each line search. Our formulation also allows us to consider other types of search method, in particular the conjugate direction based methods. Global convergence of existing conjugate gradient (CG) based method are proved by viewing the methods as a form of conjugate gradient method without line search. Another globally convergent descent algorithm is developed based on pair-wise conjugation of gradient. In stochastic setting, this new algorithm proved to be comparable to existing CG based method. Furthermore, due to the absence of explicit computation of the stochastically recursive conjugate search directions, the algorithm provides a much lower computational complexity, which makes it more favorable for high speed computing. We also extend our formulation to the preconditioned adaptive least squares problem which is shown to be an appropriate formulation for transform-domain adaptive filtering. Although analyses of alternative pre conditioners are still at an early stage of research, we are able to provide a new preconditioner for the problem derived directly from the mathematical formulation of the problem. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/17236 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.title | Direction Set Based Methods For Adaptive Least Squares Problems: Improvements And Innovations | en_US |
| dc.type | Technical Report | en_US |
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