Abstract
When analysing three-way arrays, it is a common practice to centre the arrays. Depending on the context, centring is performed over one, two or three modes. In this paper, we outline how centring affects the rank of the array; both in terms of maximum rank and typical rank.
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Notes
- 1.
Technically, this is a matter of assessing the class’ Lebesgue measure, to which we have no clue. To give an example that generally performed transformations may alter ‘randomness’ properties, consider for instance squaring all values, which clearly affects the Lebesgue measure of subclasses of the class of such arrays. However, because [12]’s transformations, as our own, are rank preserving, we expect that the results that are only proven for the maximal rank, also hold for the typical rank of classes of arrays.
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Albers, C.J., Gower, J.C., Kiers, H.A.L. (2018). Rank Properties for Centred Three-Way Arrays. In: Mola, F., Conversano, C., Vichi, M. (eds) Classification, (Big) Data Analysis and Statistical Learning. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55708-3_8
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DOI: https://doi.org/10.1007/978-3-319-55708-3_8
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