- (major) I don’t agree with the limitation (ii) of current TN models: “At least one Nth-order factor is required to physically inherit the complex interactions from an Nth-order tensor”. TT and TR can model complex modes interactions if the ranks are large enough. The fact that there is a lack of direct connections from any pair of nodes is not a limitation because any nodes are fully connected through a TR or TT. However, the price to pay with TT or TR to model complex modes interactions is having bigger core tensor (larger number of parameters). The new proposed topology has also a large price to pay in terms of model size because the core tensor C grows exponentially with the number of dimensions, which makes it intractable in practice. The paper lacks from a comparison of TR/TT and TW for a fixed size of both models (see my criticism to experiments below). - The new proposed model can be used only with a small number of dimensions because of the curse of dimensionality imposed by the core tensor C. - (major) I think the proposed TW model is equivalent to TR by noting that, if the core tensor C is represented by a TR (this can be done always), then by fusing this TR with the cores G_n we can reach to TR representation equivalent to the former TW model. I would have liked to see this analysis in the paper and a discussion justifying TW over TR. - (major) Comparison against other models in the experiments are unclear. The value of the used ranks for all the models are omitted which make not possible a fair comparison. To show the superiority of TW over TT and TR, the authors must compare the tensor completion results for all the models but having the same number of model parameters. The number of model parameters can be computed by adding the number of entries of all core tensors for each model (see my question about experiment settings below). - (minor) The title should include the term “tensor completion” because that is the only application of the new model that is presented in the paper. - (minor) The absolute value operation in the definition of the Frobenius norm in line 77 is not needed because tensor entries are real numbers. - (minor) I don’t agree with the statement in line 163: “Apparently, the O(NIR^3+R^N) scales exponentially”. The exponential grow is not apparent, it is a fact.
I updated my scores after rebuttal. See my comments below
Yes, the authors have stated that the main limitation of their proposed model is its exponentionally grow of model parameters with the number of dimensions.
- The new proposed model can be used only with a small number of dimensions because of the curse of dimensionality imposed by the core tensor C.