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A alternative notation for the PARAFAC model

Using the tensor products notation (see Chapter 2) an alternative expression of the PARAFAC model is  [Pg.84]

The PARAFAC model can also be written by using the vec-operator and the Kronecker product. This is given by [Pg.84]

A final way of writing the PARAFAC model is given by the Khatri-Rao product. [Pg.85]

It is instructive to have an understanding of why the Khatri-Rao product is useful for multi-linear models. Starting with a bilinear two-way model [Pg.85]

every bilinear component vec(arb7) can be written as a well-defined vector that is a function of ar and br only. This vector is the Kronecker product of br and ar. Define the Khatri-Rao product of two matrices, A and B, with the same number of columns as [Pg.85]


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