Tensor Train Random Projection

doi:10.32604/cmes.2022.021636

	Tensor Train Random Projection
	Feng, Yani1 ; Tang, Kejun 2; He, Lianxing 3; Zhou, Pingqiang1 ; Liao, Qifeng1
	2023
发表期刊	CMES - COMPUTER MODELING IN ENGINEERING AND SCIENCES
ISSN	1526-1492
EISSN	1526-1506
卷号	134 期号:2 页码:1197-1218
发表状态	已发表
DOI	10.32604/cmes.2022.021636
摘要	This work proposes a Tensor Train Random Projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a Tensor Train (TT) representation with TT-ranks equal to one. Based on the tensor train format, this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy, compared with existing methods. We provide a theoretical analysis of the bias and the variance of TTRP, which shows that this approach is an expected isometric projection with bounded variance, and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores. Detailed numerical experiments with synthetic datasets and the MNIST dataset are conducted to demonstrate the efficiency of TTRP. © 2023 Tech Science Press. All rights reserved.
关键词	Dimension reduction High-dimensional dataset Isometric projections Pairwise distances Random projection methods Random projections Scalings Speed up Storage costs Tensor trains
URL	查看原文
收录类别	EI ; SCOPUS
语种	英语
出版者	Tech Science Press
EI入藏号	20224012817970
EI主题词	Tensors
EI分类号	921.1 Algebra
原始文献类型	Journal article (JA)
Scopus 记录号	2-s2.0-85138801675
来源库	Scopus
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/235988
专题	信息科学与技术学院_PI研究组_周平强组信息科学与技术学院_PI研究组_廖奇峰组信息科学与技术学院_博士生
通讯作者	Liao, Qifeng
作者单位	1.School of Information Science and Technology,ShanghaiTech University,Shanghai,201210,China 2.Peng Cheng Laboratory,Shenzhen,518055,China 3.Innovation Academy for Microsatellites,Chinese Academy of Sciences,Shanghai,201210,China
第一作者单位	信息科学与技术学院
通讯作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Feng, Yani,Tang, Kejun,He, Lianxing,et al. Tensor Train Random Projection[J]. CMES - COMPUTER MODELING IN ENGINEERING AND SCIENCES,2023,134(2):1197-1218.
APA	Feng, Yani,Tang, Kejun,He, Lianxing,Zhou, Pingqiang,&Liao, Qifeng.(2023).Tensor Train Random Projection.CMES - COMPUTER MODELING IN ENGINEERING AND SCIENCES,134(2),1197-1218.
MLA	Feng, Yani,et al."Tensor Train Random Projection".CMES - COMPUTER MODELING IN ENGINEERING AND SCIENCES 134.2(2023):1197-1218.