?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Empirical+Evaluation+of+Four+Tensor+Decomposition+Algorithms&rft.creator=Turney%2C+Peter+D.&rft.subject=Language&rft.subject=Statistical+Models&rft.subject=Computational+Linguistics&rft.subject=Machine+Learning&rft.subject=Artificial+Intelligence&rft.description=Higher-order+tensor+decompositions+are+analogous+to+the+familiar+Singular+Value+Decomposition+(SVD)%2C+but+they+transcend+the+limitations+of+matrices+(second-order+tensors).+SVD+is+a+powerful+tool+that+has+achieved+impressive+results+in+information+retrieval%2C+collaborative+filtering%2C+computational+linguistics%2C+computational+vision%2C+and+other+fields.+However%2C+SVD+is+limited+to+two-dimensional+arrays+of+data+(two+modes)%2C+and+many+potential+applications+have+three+or+more+modes%2C+which+require+higher-order+tensor+decompositions.+This+paper+evaluates+four+algorithms+for+higher-order+tensor+decomposition%3A+Higher-Order+Singular+Value+Decomposition+(HO-SVD)%2C+Higher-Order+Orthogonal+Iteration+(HOOI)%2C+Slice+Projection+(SP)%2C+and+Multislice+Projection+(MP).+We+measure+the+time+(elapsed+run+time)%2C+space+(RAM+and+disk+space+requirements)%2C+and+fit+(tensor+reconstruction+accuracy)+of+the+four+algorithms%2C+under+a+variety+of+conditions.+We+find+that+standard+implementations+of+HO-SVD+and+HOOI+do+not+scale+up+to+larger+tensors%2C+due+to+increasing+RAM+requirements.+We+recommend+HOOI+for+tensors+that+are+small+enough+for+the+available+RAM+and+MP+for+larger+tensors.&rft.date=2007-11-12&rft.type=Departmental+Technical+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F5841%2F1%2FNRC-49877.pdf&rft.identifier=++Turney%2C+Peter+D.++(2007)+Empirical+Evaluation+of+Four+Tensor+Decomposition+Algorithms.++%5BDepartmental+Technical+Report%5D++++(Unpublished)++&rft.relation=http%3A%2F%2Fcogprints.org%2F5841%2F