Essentially unique — up to order and scale

Kruskal’s result, stated in section 11: under mild conditions a CP decomposition is essentially unique — determined except for the order of the R terms and a rescaling that cancels inside each one (αᵣ βᵣ γᵣ = 1). Nothing else is free, which is why a CP component can be named and an NMF factor, which can also be rotated, cannot.

That is a statement about the decomposition, not a promise ALS makes. On the monkey tensor, three seeds give the same error to four decimal places and the same three weights — in a different order. Matched by their time profiles, every component lines up with a correlation of 1.

So factors[1] from one run and factors[1] from another are not the same component. Match components before comparing them — by correlation, by peak position, or by sorting on the weights. When runs truly disagree, the rank is wrong, not the method.