Yu.N. Minaev, O.Yu. Filimonova, J.I. Minaeva

Èlektron. model. 2017, 39(1):51-74


The questions of representation of multidimensional (multicomponent) time series (TS) as a 3D tensor model; its following tensor decomposition with the use of procedures of PARAFAC-decomposition and higher-order singular decomposition (HOSVD) allows us to represent the entire TS (or its components — window, a fragment, a segment) in the form of a certain granule — a subset of ordered triples with properties similar to those of the second type FS called the second type psevdoFS.
The analogy is shown between the properties of the existing traces, singular values and F-norm of standard singular decomposition (2D matrix) and HOSVD used for 2D matrix. Examples showing the representation of multidimensional TS by granules — subsets of ordered triples.


singular decomposition, fuzzy multiple granule, higher-order singular decomposition, trace of a matrix, F-norm, time series.


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