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題名 Split-and-combine singular value decomposition for large-scale matrix
作者 曾正男
Tzeng,Jengnan
貢獻者 應數系
日期 2013.04
上傳時間 7-Aug-2014 11:35:22 (UTC+8)
摘要 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.
關聯 Journal of Applied Mathematics,Volume 2013, Article ID 683053
資料來源 http://dx.doi.org/10.1155/2013/683053
資料類型 article
DOI http://dx.doi.org/10.1155/2013/683053
dc.contributor 應數系en_US
dc.creator (作者) 曾正男zh_TW
dc.creator (作者) Tzeng,Jengnanen_US
dc.date (日期) 2013.04en_US
dc.date.accessioned 7-Aug-2014 11:35:22 (UTC+8)-
dc.date.available 7-Aug-2014 11:35:22 (UTC+8)-
dc.date.issued (上傳時間) 7-Aug-2014 11:35:22 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/68417-
dc.description.abstract (摘要) 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.en_US
dc.format.extent 290683 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.relation (關聯) Journal of Applied Mathematics,Volume 2013, Article ID 683053en_US
dc.source.uri (資料來源) http://dx.doi.org/10.1155/2013/683053en_US
dc.title (題名) Split-and-combine singular value decomposition for large-scale matrixen_US
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.1155/2013/683053en_US
dc.doi.uri (DOI) http://dx.doi.org/10.1155/2013/683053en_US