Tucker decomposition on random tensor

[LinjianMa]

As to a random tensor, the relation between decomposition residual and Tucker rank is interesting:
residual drops a lot when rank is 1 and rank is the size of the tensor, while change little in the middle. For example, as to a random tensor with size 4 and F-norm 50, the decomposition residual is as follows:

rank 1 : res = 9.03
rank 2 : res = 8.875
rank 3 : res = 7.965
rank 4 : res = 0.0

Interesting topic to investigate in the future

[LinjianMa]

Decomposition is also affected by the value distribution. For example, random distribution of [0,1] is much easier to decompose than [-1,1]