Tensor decomposition: Difference between revisions

Revision as of 02:38, 19 March 2023

Revision as of 08:45, 19 March 2023

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! Symbols!! Definition

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| <math>{\mathbfa, {A\bf a},{\bf a}^T,\mathbf{aA},a{\mathcal A}}</math> ||Matrixscalar, Column vector, Scalarrow, matrix, tensor

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| <math>{\mathbbbf a}={R}vec(.)}</math> || Setvectorizing either a matrix ofor Reala Numberstensor

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| <math>{vec()\bf A}_{[m]}</math> || Vectorizationmatrixized operatortensor <math>\mathcal A</math>

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| <math>\times_m</math> || mode-m product

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==Introduction==

A multi-way graph with K perspectives is a collection of K matrices <math>{X_1,X_2.....X_K}</math> with dimensions I × J (where I, J are the number of nodes). This collection of matrices is naturally represented as a tensor X of size I × J × K. In order to avoid overloading the term “dimension”, we call an I × J × K tensor a three “mode” tensor, where “modes” are the numbers of indices used to index the tensor.