乐胖代购免代理版

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$${\\mathcal {X}} \\in {\\mathbb {R}} ^{I_1 \\times \\cdots \\times I_N} $$<\/jats:tex-math>\n \n X<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n \n I<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \u00d7<\/mml:mo>\n \u22ef<\/mml:mo>\n \u00d7<\/mml:mo>\n \n I<\/mml:mi>\n N<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The CANDECOMP\/PARAFAC (CP) decomposition has been extensively studied and applied to approximate X by N loading matrices

$$A(1),\\ldots ,A(N)$$<\/jats:tex-math>\n \n A<\/mml:mi>\n (<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n ,<\/mml:mo>\n A<\/mml:mi>\n (<\/mml:mo>\n N<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> where N<\/jats:italic> represents the order of the tensor. We propose a novel algorithm, FP-CPD, to parallelize the CANDECOMP\/PARAFAC (CP) decomposition of a tensor

$${\\mathcal {X}} \\in {\\mathbb {R}} ^{I_1 \\times \\cdots \\times I_N} $$<\/jats:tex-math>\n \n X<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n \n I<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n \u00d7<\/mml:mo>\n \u22ef<\/mml:mo>\n \u00d7<\/mml:mo>\n \n I<\/mml:mi>\n N<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Our approach is based on stochastic gradient descent (SGD) algorithm which allows us to parallelize the learning process, and it is very useful in online setting since it updates

$${\\mathcal {X}}^{t+1}$$<\/jats:tex-math>\n \n \n X<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in one single step. Our SGD algorithm is augmented with Nesterov\u2019s accelerated gradient and perturbation methods to accelerate and guarantee convergence. The experimental results using laboratory-based and real-life structural datasets indicate fast convergence and good scalability.<\/jats:p>","DOI":"10.1007\/s41060-023-00402-y","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T20:30:50Z","timestamp":1687552250000},"page":"359-371","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A fast parallel tensor decomposition with optimal stochastic gradient descent: an application in structural damage identification"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8864-0314","authenticated-orcid":false,"given":"Ali","family":"Anaissi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2674-0253","authenticated-orcid":false,"given":"Basem","family":"Suleiman","sequence":"additional","affiliation":[]},{"given":"Widad","family":"Alyassine","sequence":"additional","affiliation":[]},{"given":"Seid Miad","family":"Zandavi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"issue":"1","key":"402_CR1","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1109\/TKDE.2008.112","volume":"21","author":"E Acar","year":"2009","unstructured":"Acar, E., Yener, B.: Unsupervised multiway data analysis: A literature survey. 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