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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 8-Nov-2013 11:59:23 (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, Vol.0, No.0 資料類型 article dc.contributor 應數系 en_US dc.creator (作者) 曾正男 zh_TW dc.creator (作者) Tzeng,Jengnan - dc.date (日期) 2013.04 en_US dc.date.accessioned 8-Nov-2013 11:59:23 (UTC+8) - dc.date.available 8-Nov-2013 11:59:23 (UTC+8) - dc.date.issued (上傳時間) 8-Nov-2013 11:59:23 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/61536 - 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. - dc.format.extent 1408896 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.relation (關聯) Journal of Applied Mathematics, Vol.0, No.0 en_US dc.title (題名) Split-and-combine singular value decomposition for large-scale matrix - dc.type (資料類型) article en
