Split‐and‐Combine Singular Value Decomposition for Large‐Scale Matrix

Jengnan Tzeng

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/683053

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:683053

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().