1994
DOI: 10.1007/bf02296130
|View full text |Cite
|
Sign up to set email alerts
|

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Abstract: INDSCAL, CANDECOMP, PARAFAC, three-way rank, tensor rank,

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
6
0

Year Published

2000
2000
2011
2011

Publication Types

Select...
6

Relationship

2
4

Authors

Journals

citations
Cited by 7 publications
(6 citation statements)
references
References 4 publications
0
6
0
Order By: Relevance
“…Table 2 summarizes what is known about the typical rank of arrays holding I symmetric slices of order J × J . As in Table 1, the uncolored numbers refer to trivial cases, where the number of slices I equals or exceeds the number of rank-one matrices needed to span the space of symmetric J × J matrices (Rocci & Ten Berge, 1994). The green cells refer to cases treated by Ten Berge, Sidiropoulos and Rocci (2004).…”
Section: An Overview Of Typical Rank Resultsmentioning
confidence: 99%
“…Table 2 summarizes what is known about the typical rank of arrays holding I symmetric slices of order J × J . As in Table 1, the uncolored numbers refer to trivial cases, where the number of slices I equals or exceeds the number of rank-one matrices needed to span the space of symmetric J × J matrices (Rocci & Ten Berge, 1994). The green cells refer to cases treated by Ten Berge, Sidiropoulos and Rocci (2004).…”
Section: An Overview Of Typical Rank Resultsmentioning
confidence: 99%
“…For instance, when seven symmetric 3 x 3 matrices are strung out as row vectors in a 7 x 9 matrix X, we can verify that the array is tall. Nevertheless, both the number of dimensions needed for perfect INDSCAL fit and the typical rank are 6 rather than 7, see Rocci & ten Berge (1994). This discrepancy can be explained by the fact that symmetry does not arise with random sampling.…”
Section: The Typical Rank When I = Jk -Jmentioning
confidence: 87%
“…The following theoretical results are known for generic INDSCAL data X ∈ R I×J×J : a) By Zellini (1979), see also Rocci and Ten Berge (1994), if I ≥ J(J + 1)/2, then rank(X) = J(J + 1)/2. b) I × 2 × 2 and I × 3 × 3 arrays are studied by Ten Berge, Sidiropoulos and Rocci (2004).…”
Section: Indscal Arraysmentioning
confidence: 99%