Tucker compression and local optima

We observed that the values of the cost function at different local minima can be very close to each other. Thus, for memory savings based on Tucker compression, the choice between these local minima does not really matter. On the other hand, we found that the subspaces on which the original tensor is projected can be very different. If the subspaces are of importance, different local minima may yield very different results. We provide numerical examples and indicate a relation between the number of local minima that are found and the distribution of the higher-order singular values of the tensor.