How to restore tensor after applied the PARAFAC model?

Hi everyone,

Suppose I have a tensor have the size of (128 x 128 x 3). When I apply the PARAFAC model (to fit one-component) to decomposition tensor. I get many components a1, b1, c1

My question here:

+/ a1 have size of (128 x 1)

+/ b1 have size of (128 x 1)

+/ c1 have size of (3 x 1).

How to get the result of multiplication a1.b1.c1? (restore original tensor?). Because each factor is not the same size?

Thank you for your help.

Answer 1

[Christine Tobler]

The three component vectors represent the 3 different dimensions here. For the one-component case (all are vectors), you can use

a1 .* (b1.') .* (reshape(c1, 1, 1, []))

which will return an array of size length(a1) x length(b1) x length(c1).

[PaulLe]

Dear Tobler,

Thank you for your help.