How can I measure similarity between two signals with different lengths (and with different time points)?

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SOPAE YI 2020-3-9

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评论： SOPAE YI 2020-3-16

采纳的回答： Ameer Hamza

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Hi all,

I want to measure similarity between two signals with different lengths.

Following is my code.

 A = [1.2,1.5;
     2.4,0.5;
     3.2,1.5; 
     4.1,1]
 B = [1,1;
      2,0;
      3,1;
      4,0.5;
      5,1.5]
 BB = [1,1;
      2,0;
      3,1;
      4,0.5;
      5,1.5] 
 C = [1.1,1.2;
     2.2,1.3;
     3.3,1.5; 
     4.2,1.7]
%%%%% B and BB are the same signal 
plot(A(:,1), A(:,2)) % first column is the x-values
hold on;
plot(B(:,1), B(:,2))
figure(2)
plot(C(:,1), C(:,2)) % first column is the x-values
hold on;
plot(BB(:,1), BB(:,2))
 
%%% Similarity between B and A
B=imresize(B, size(A))
r_BA = corr2(B,A)  % Correlation between B and A
maxB = max(B)
maxA = max(A)
nor_B = bsxfun(@rdivide,B,max(B))
nor_A = bsxfun(@rdivide,A,max(A))
nor_r_BA = corr2(nor_A, nor_B)   % Normalized Correlation
%%% Similarity between B and C 
BB=imresize(BB, size(C))
r_BBC = corr2(BB,C)   % Correlation between BB and C
maxBB = max(BB)
maxC = max(C)
nor_BB = bsxfun(@rdivide,BB,max(BB))
nor_C = bsxfun(@rdivide,C,max(C))
nor_r_BBC = corr2(nor_A, nor_BB)  % Normalized Correlation

%plot between B and A

Plot between B and C

It looks like B and A have higher similarity than B and C.

However, the correlation (corr2) value between B and C is greater than B and A.

Normalized correlation values are the same for both.

Please let me know how I can measure similarity of the 2 signals above?

I can accommodate R, SPSS or any other tool to solve this problem.

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采纳的回答

Ameer Hamza 2020-3-9

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编辑：Ameer Hamza 2020-3-9

If you plot the signals after applying imresize you will see that A and B are not very similar to each other. It appears from the discussion on different forums, there is no universal way to address the issue of correlation between vectors of unequal length. The most appropriate strategy seems to be getting rid of extra data from signals to make them of equal length.

https://stackoverflow.com/questions/9973432/correlation-between-vectors-of-different-lengths

https://stats.stackexchange.com/questions/3589/correlation-between-two-variables-of-unequal-size

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SOPAE YI 2020-3-12

编辑：SOPAE YI 2020-3-13

Thanks again Mr. Hamza :--)

I have been experimenting with ‘interp1’ function and found out that Matrix B is losing it’s time information after ‘interp1’. However, the time of each point is important in my research. Therefore, to keep the time information of both A and B, maybe I might be able to use maximum value of cross-correlation as a similarity measure.

I have calculated like below:

>> max(max(normxcorr2(A, B)))

ans = 0.9966

>> max(max(normxcorr2(C, B)))

ans = 0.9413

I do not think this is reasonable result because the scores (0.9966 vs 0.9413) are not different enough to show the difference between the signals properly.

I do not have to keep the actual time values, I just want to keep the proportional time interval between points (points within 1st column). (e.g. Z = [1, 1.2; 6, 2.1; 8, 3.4 ] can be rewritten as ZZ = [1, 1.2; 4, 2.1; 5, 3.4 ] . As they still have the same ratio (3 to 1) of time intervals, they have the same time information.

How can I compute correlation while keeping the time information?

SOPAE YI 2020-3-14

编辑：SOPAE YI 2020-3-14

Thanks a million, Mr. Hamza :--)

I think your suggestion is a brilliant idea.

I will try to figure out a rule to automatically generate A_x.

By the way, I am wondering how you got A_x = [1.2 2 2.9 3.9 5] out of A = [1.2 2.4 3.2 4.1]? (extracting 5 elements out of 4 time points).

Suppose,

E = [1.2,1.5; 2.4,0.5; 3.2,1.5]

B = [1,1; 2,0; 3,1; 4,0.5; 5,1.5];

To compute E_x,

The 1st point is ‘1.2’

and…

(2.4-1.2)/(4.1-1.2) x (5-1.2) = 1.57 so, 2nd point is (1.2+1.57)

(3.2-2.4)/(4.1-1.2) x (5-1.2) = 1.04 so, 3rd point is (1.2+1.57+1.04)

How can I compute the 4th point?

(of course the 5th point is 5, the last point.)

Since I have signals with various lengths (of time), each and every size of my matrices should be converted to be matched with the size of the largest matrix I have.

I am thinking of making a function turning matrices into the size of the largest matrix using ‘interp1’. (input: a matrix, output: a new matrix with the same size of the largest matrix) to be used to cluster a bunch of matrices.