Highly Scalable Parallelism of Integrated Randomized Singular Value Decomposition with Big Data Applications

• Main Authors: Mu Yang, 楊慕
• Other Authors: Weichung Wang
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/bvks4s

碩士 === 國立臺灣大學 === 應用數學科學研究所 === 105 === Low-rank approximation plays an important role in big data analysis. Integrated Singular Value Decomposition (iSVD) is an algorithm for computing low-rank approximate singular value decomposition of large size matrices. The iSVD integrates different low-rank SVDs obtained by multiple random subspace sketches and achieve higher accuracy and better stability. While iSVD takes higher computational costs due to multiple random sketches and the integration process, these operations can be parallelized to save computational time. We parallelize iSVD for multicore clusters, and modify the algorithms and data structures to increase the scalability and reduce communication. With parallelization, iSVD can find the approximate SVD of matrices with huge size, and achieve near-linear scalability with respect to the matrix size and the number of machines, and gained further 4X faster timing performance on sketching by using GPU. We implement the algorithms in C++, with several techniques for high maintainability, extensibility, and usability. The iSVD is applied on some huge size application using hybrid CPU-GPU supercomputer systems.