Publicación: Analysis of 2 x 2 x 2 Tensors
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2010-06-01
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
Resumen
The question about how to determine the rank of a tensor has been widely studied in the literature. However the analytical methods to compute the decomposition of tensors have not been so much developed even for low-rank tensors. In this report we present analytical methods for finding real and complex PARAFAC decompositions of 2 x 2 x 2 tensors before computing the actual rank of the tensor. These methods are also implemented in MATLAB. We also consider the question of how best lower-rank approximation gives rise to problems of degeneracy, and give some analytical explanations for these issues.
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Categorías UNESCO
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tensor decomposition, PARAFAC decomposition, Alternating Least Squares, Tensor Rank, typical and generic rank, best lower-rank approximation, Tensor Toolbox for MATLAB, degeneracy, uniqueness, tensor classification
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Facultad de Ciencias
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Estadística, Investigación Operativa y Cálculo Numérico