Split-and-Combine Singular Value Decomposition for Large-Scale Matrix
The singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essen...
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/683053 |
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| author | Jengnan Tzeng |
| author_facet | Jengnan Tzeng |
| author_sort | Jengnan Tzeng |
| collection | DOAJ |
| description | The singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable. |
| format | Article |
| id | doaj-art-489b7fba7a48441a9c0bd57c089a9849 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-489b7fba7a48441a9c0bd57c089a98492025-02-03T06:01:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/683053683053Split-and-Combine Singular Value Decomposition for Large-Scale MatrixJengnan Tzeng0Department of Mathematical Sciences, National Chengchi University, No. 64, Section 2, ZhiNan Road, Wenshan District, Taipei City 11605, TaiwanThe singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.http://dx.doi.org/10.1155/2013/683053 |
| spellingShingle | Jengnan Tzeng Split-and-Combine Singular Value Decomposition for Large-Scale Matrix Journal of Applied Mathematics |
| title | Split-and-Combine Singular Value Decomposition for Large-Scale Matrix |
| title_full | Split-and-Combine Singular Value Decomposition for Large-Scale Matrix |
| title_fullStr | Split-and-Combine Singular Value Decomposition for Large-Scale Matrix |
| title_full_unstemmed | Split-and-Combine Singular Value Decomposition for Large-Scale Matrix |
| title_short | Split-and-Combine Singular Value Decomposition for Large-Scale Matrix |
| title_sort | split and combine singular value decomposition for large scale matrix |
| url | http://dx.doi.org/10.1155/2013/683053 |
| work_keys_str_mv | AT jengnantzeng splitandcombinesingularvaluedecompositionforlargescalematrix |