Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation
Joint Authors
Bi, Size
Liang, Xiao
Huang, Ting-lei
Han, Xiaoyu
Tian, Jing
Wang, Yang
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-16
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
This paper investigates a homotopy-based method for embedding with hundreds of thousands of data items that yields a parallel algorithm suitable for running on a distributed system.
Current eigenvalue-based embedding algorithms attempt to use a sparsification of the distance matrix to approximate a low-dimensional representation when handling large-scale data sets.
The main reason of taking approximation is that it is still hindered by the eigendecomposition bottleneck for high-dimensional matrices in the embedding process.
In this study, a homotopy continuation algorithm is applied for improving this embedding model by parallelizing the corresponding eigendecomposition.
The eigenvalue solution is converted to the operation of ordinary differential equations with initialized values, and all isolated positive eigenvalues and corresponding eigenvectors can be obtained in parallel according to predicting eigenpaths.
Experiments on the real data sets show that the homotopy-based approach is potential to be implemented for millions of data sets.
American Psychological Association (APA)
Bi, Size& Han, Xiaoyu& Tian, Jing& Liang, Xiao& Wang, Yang& Huang, Ting-lei. 2016. Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1112363
Modern Language Association (MLA)
Bi, Size…[et al.]. Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation. Mathematical Problems in Engineering No. 2016 (2016), pp.1-9.
https://search.emarefa.net/detail/BIM-1112363
American Medical Association (AMA)
Bi, Size& Han, Xiaoyu& Tian, Jing& Liang, Xiao& Wang, Yang& Huang, Ting-lei. Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1112363
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112363