Cramer-Rao lower bounds for low-rank decomposition ofmultidimensional arrays |
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Authors: | Xiangqian Liu Sidiropoulos ND |
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Affiliation: | Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN; |
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Abstract: | Unlike low-rank matrix decomposition, which is generically nonunique for rank greater than one, low-rank three-and higher dimensional array decomposition is unique, provided that the array rank is lower than a certain bound, and the correct number of components (equal to array rank) is sought in the decomposition. Parallel factor (PARAFAC) analysis is a common name for low-rank decomposition of higher dimensional arrays. This paper develops Cramer-Rao bound (CRB) results for low-rank decomposition of three- and four-dimensional (3-D and 4-D) arrays, illustrates the behavior of the resulting bounds, and compares alternating least squares algorithms that are commonly used to compute such decompositions with the respective CRBs. Simple-to-check necessary conditions for a unique low-rank decomposition are also provided |
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