Convert unfolded tensor back to higher dimensional tensor?

I use below function to convert tensor into unfolded matrix

 function X = unfold(A,n)
    d = size(A)
    X = reshape(shiftdim(a,n-1), d(n), []);
 end

But I am unable to understand how to convert a matrix back to tensor Sample code

function X = fold(A,n,d)
  % d is array containing dimension
        % n is order of folding
        % A is unfolded matrix
end

[mona ismail]

hello,

I tried the first code (unfolding one) and it is working only for 1- and 3-mode but not for 2-mode matricization.

do you have any idea how can I get the 2-mode also?

[Kenneth Benicio]

A bit late but could help someone in the future. I had the same problem with the 2-mode unfold and after some research I figure out that it's possible to write the unfolding of a tensor with this function

dim = size(tensor);
order = 1:numel(dim);
order(mode) = [];
order = [mode order];
mtx = reshape(permute(tensor,order), dim(mode), prod(dim)/dim(mode));

Answer 1

[Aakash Deep]

Hey Rohit,

Let's first see how we can unfold a tensor to matrix then you might get some insight how to unfold it back. Let's suppose you have a tensor A with dimensions x*y*z (assume, x=4, y=3, z=2).

A(:,:,1) = [1 2 3; 4 5 6; 7 8 9; 10 11 12]

and

A(:,:,2) = [21 22 23; 24 25 26; 27 28 29; 30 31 32]

Now, you can unfold it in 3 ways that means you can unfold it any of the three dimension. So when you unfold it you will get one of the below possible combination.

A1 (x * yz) = [1 2 3 21 22 23; 4 5 6 24 25 26; 7 8 9 27 28 29; 10 11 12 30 31 32]

In this, all the slices gets placed side by side horizontally.

A2 (y * xz) = [1 4 7 10 21 24 27 30; 2 5 8 11 22 25 28 31; 3 6 9 12 23 26 29 32]

In this, transpose of all the slices concatenates side by side horizontally.

A3(z * xy) = [1 2 3 4 5 6 7 8 9 10 11 12; 21 22 23 24 25 26 27 28 29 30 31 32]

In this, all the slices gets converting into a vector and then these vectors concatenates vertically.

Now, you have to figure it out in which way you can unfold your matrix such that it gets converted into a tensor.

Hope this helps :)

[Rohit Gupta]

Thanks for answer. Actually thats what the issue is. I don't know how to convert matrix back to tensor.

[Aakash Deep]

Can you mention the dimensions of given matrix and the desired tensor?

[Rohit Gupta]

Tensor: 12 x 50 x 40

Unfolded tensor: 50 x 480 (Mode-2 Unfolding)

But i want to know if there is a method for any given dimension tensor given that matrix is a proper Mode-n Unfolded.

[Aakash Deep]

From the given dimension I can clearly see that this is similar to the case as of A2 in the above given example. For this case, the below code will work. Assume A2 is your matrix and B is your tensor.

x = 12;
y = 50;
z = 40;
slice = size(A2,2)/x;
part = size(A2,2)/z;
start=1;
for i=1:slice
   B(:,:,i)=A2(:,start:start+part-1)';
   start=start+part;
end

Hope this helps :)

[snowflake]

Hello,

I'm trying to implement the case 1 for this matrix:

B =
     1    10   100     2    20   200
     3    30   300     4    40   400

and it works, it shows me this tensor:

A(:,:,1) =
     1     2
     3     4
A(:,:,2) =
    10    20
    30    40
A(:,:,3) =
   100   200
   300   400

the code I adapted from you:

x=2; y=2; z=3;
    slice = size(B,2)/y; 
    part = size(B,2)/z; 
    start=1;
    A=zeros(x,y,z);
    for i=1:slice
     A(:,:,i)=B(:,[start start+part+1]); 
       start=start+1;
    end

The problem is it only works for a 2x6 matrix. If I transform B into a 2x9, I'd have to modify one line of code like this so that I tell the program which columns I want:

    A(:,:,i)=B(:,[start start+part start+part+3]);

and it would produce the desired outcome:

A(:,:,1) =
     1     2     3
     4     5     6
A(:,:,2) =
    10    20    30
    40    50    60
A(:,:,3) =
   100   200   300
   400   500   600

for

B =
     1    10   100     2    20   200     3    30   300
     4    40   400     5    50   500     6    60   600

Any idea how I could code it so that it would work for any kind of matrix?