How to reliable find the distance between matrices?

Question

Serbring 2020-12-1

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https://ww2.mathworks.cn/matlabcentral/answers/671958-how-to-reliable-find-the-distance-between-matrices

回答： Pratyush Roy 2021-4-1

Dear all,

I need to compute the distance among matrices. These matrices describe the usage of vehicle and they report the joint probability distribution between two variables. The variables are binned.The matrix contains positive numbers. The distance metric would provide an information about the dissimilarity between the usage of two vehicles. I have tried as the following:

m=zeros(3,15,16);
m(1,13,12)=1;
m(2,12,13)=1;
m(3,1,1)=1;
norm(squeeze(m(1,:,:))-squeeze(m(2,:,:)))
norm(squeeze(m(1,:,:))-squeeze(m(3,:,:)))
norm(squeeze(m(1,:,:))-squeeze(m(2,:,:)))

The three matrices contains the same number but it is positioned in a different position. For matrix 1 (m(1,:,:)) and 2 (m(2,:,:)), the number 1 is located in a similar position, but in a very different position than matrix 3 (m(3,:,:)). The matrix 3 is the consequence of a very different vehicle usage than the others. lThis made me think that is necessary a different distance metric . Is there any other which you may reccomend for my purpose?

thank you.

best regards.