How to compute for the distance between two tensors using matlab?

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Josephine Benjamin 2020-8-27

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回答： Dana 2020-8-27

Consider two tensors X={(0 2;1 3), (1 4; 5 6)} and Y={(4 3; 2 1), (2 5; 6 2)}. I want to compute the distance between these two tensors in matlab. Can anyone help me make the matlab code of it. I am not that too familiar with matlab thanks

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Answer 1

Dana 2020-8-27

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It depends on how you define "distance". There are many different ways you could do that in principle. One way would be to use the element-wise p-norm: for a 3-D tensor A, this is given by

and can be computed in MATLAB by norm(A(:),p). For example, for the 2-norm:

>> X=zeros(2,2,2);
>> X(:,:,1) = [0 2;1 3];
>> X(:,:,2) = [1 4; 5 6];
>> Y=zeros(2,2,2);
>> Y(:,:,1)= [4 3; 2 1];
>> Y(:,:,2) = [2 5; 6 2];
>> A = X-Y;
>> p = 2;
>> distance = norm(A(:),p)
distance =
       6.4031