Parallelization of eigenvalue-based dimensional reductions via homotopy continuation
type: Item
instance of: scholarly article
title: Parallelization of eigenvalue-based dimensional reductions via homotopy continuation
zbMATH Open document ID: 1400.65022
DOI: 10.1155/2016/5815429
author: Size Bi
author: Xiaoyu Han
author: Jing Tian
author: Xiao Liang
author: Yang Wang
author: Tinglei Huang
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 6953366
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5815429
OpenAlex ID: W2300918803
Wikidata QID: Q59131715
cites work: Modern multidimensional scaling. Theory and applications.
cites work: Eigensolver Methods for Progressive Multidimensional Scaling of Large Data
cites work: Q2934137
cites work: Graph Drawing
cites work: Graph Drawing by High-Dimensional Embedding
cites work: Strategies for spectrum slicing based on restarted Lanczos methods
cites work: Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem
cites work: A simple application of the homotopy method to symmetric eigenvalue problems
cites work: A note on the homotopy method for linear algebraic eigenvalue problems
cites work: Homotopy algorithm for symmetric eigenvalue problems
cites work: Homotopy method for the eigenvalues of symmetric tridiagonal matrices
cites work: Q5166883
cites work: A 3(2) pair of Runge-Kutta formulas
cites work: Numerical Computing with <scp>Matlab</scp>
description: scientific article; zbMATH DE number 6953366