Singular value decomposition (SVD) is a popular decomposition method for solving least-squares estimation problems. However, for large datasets, SVD is very time consuming and memory demanding in obtaining least squares solutions. In this paper, we propose a least squares estimator based on an iterative divide-and-merge scheme for large-scale estimation problems. The estimator consists of several levels. At each level, the input matrices are subdivided into submatrices. The submatrices are decomposed by SVD respectively and the results are merged into smaller matrices which become the input of the next level. The process is iterated until the resulting matrices are small enough which can then be solved directly and efficiently by the SVD algorithm. However, the iterative divide-and-merge algorithms executed on a single machine is still time demanding on large scale datasets. We propose two distributed algorithms to overcome this shortcoming by permitting several machines to perform the decomposition and merging of the submatrices in each level in parallel. The first one is implemented in MapReduce on the Hadoop distributed platform which can run the tasks in parallel on a collection of computers. The second one is implemented on CUDA which can run the tasks in parallel using the Nvidia GPUs. Experimental results demonstrate that the proposed distributed algorithms can greatly reduce the time required to solve large-squares problems.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0719111-152616 |
| Date | 19 July 2011 |
| Creators | Peng, Yu-Ting |
| Contributors | Chen-Sen Ouyang, Hsien-Liang Tsai, Chih-Hung Wu, Shie-Jue Lee, Chun-Liang Hou |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0719111-152616 |
| Rights | withheld, Copyright information available at source archive |
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