Use este identificador para citar ou linkar para este item: http://www.repositorio.ufc.br/handle/riufc/779
Título: Uniqueness conditions for constrained three-way factor decompositions with linearly dependent loadings
Autor(es): Almeida, André Lima Férrer de
Stegeman, Alwin
Palavras-chave: Tensor
Teleinformática
Data do documento: 2010
Editor: SIAM Journal on Matrix Analysis and Applications
Citação: ALMEIDA, A. L. F. de ; STEGEMAN, A. (2010)
Abstract: In this paper, we derive uniqueness conditions for a constrained version of the Parallel Factor (Parafac) decomposition, also known as Canonical decomposition (Candecomp). Candecomp/Parafac (CP) decomposes a three-way array into a prespeci ed number of outer product arrays. The constraint is that some vectors forming the outer product arrays are linearly dependent according to a prespeci ed pattern. This is known as the PARALIND family of models. An important subclass is where some vectors forming the outer product arrays are repeated according to a prespeci ed pattern. These are known as CONFAC decompositions. We discuss the relation between PARALIND, CONFAC and the three-way decompositions CP, Tucker3, and the decomposition in block terms. We provide both essential uniqueness conditions and partial uniqueness conditions for PARALIND and CONFAC, and discuss the relation with uniqueness of constrained Tucker3 models and the block decomposition in rank-(L; L; 1) terms. Our results are demonstrated by means of examples.
Descrição: ALMEIDA, André Lima Férrer de; STEGEMAN, Alwin. Uniqueness conditions for constrained three-way factor decompositions with linearly dependent loadings. SIAM Journal on Matrix Analysis and Applications, v. 31, n.3, 2010, p. 1469-1490
URI: http://www.repositorio.ufc.br/handle/riufc/779
ISSN: 1469-1490
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