dimensionality problems with holq

[shabbychef]

First, thanks for writing this package. When I tried to use the holq function on my data I got a strange error which I can replicate with toy data here. The problem seems to arise when one dimension of the input tensor is bigger than the product of the other dimensions, which I think causes some issues in the 2-dimensional LQ used (probably you don't get a full LQ or something):

# this runs (but takes a while)
p <- c(11, 3, 4)
set.seed(1234)
X <- array(stats::rnorm(prod(p)), dim = p)
holq(X)

# this errors
p <- c(13, 3, 4)
set.seed(1234)
X <- array(stats::rnorm(prod(p)), dim = p)
holq(X)

I get the error

Error in A[[mat_index]] %*% L_k : non-conformable arguments

It could be that I have misunderstood how the code is supposed to work, and maybe the HOLQ is not defined for such "weirdly" shaped tensors?

[dcgerard]

Hey @shabbychef,

Thanks for the comment!

Yes, I don't think the way we implemented the algorithm allows for one mode's dimension to be greater than the product of every other mode's dimensions. Not sure if there is a solution to the optimization problem we set up to define the HOLQ in that setting. If there were, I don't think it would not be unique. I would need to think about it more.

• David

[shabbychef]

Looking at the code, I agree it is not clear how to generalize to this case. However, the holq function output is used to compute the isvd, which I had hoped to use. It seems like the Incredible SVD should be defined for "oddly" shaped tensors, in analogy to how SVD is defined for non-square matrices.

[dcgerard]

I agree! Not sure what your application is, but in the meantime, you can try out the HOOI (https://doi.org/10.1137/S0895479898346995) (implemented in tensr::hooi()) or the HOSVD (https://doi.org/10.1137/S0895479896305696) (implemented in tensr::hosvd()). Though, there might be better implementations out there.

Best,
David