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

15 次查看（过去 30 天）

显示更早的评论

SOPAE YI 2020-3-9

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/509877-how-can-i-measure-similarity-between-two-signals-with-different-lengths-and-with-different-time-poi

评论： SOPAE YI 2020-3-16

采纳的回答： Ameer Hamza

在 MATLAB Online 中打开

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.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Ameer Hamza 2020-3-9

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/509877-how-can-i-measure-similarity-between-two-signals-with-different-lengths-and-with-different-time-poi#answer_419265

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

15 个评论
显示 13更早的评论隐藏 13更早的评论

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.

Ameer Hamza 2020-3-14

Glad to be of help. Best of luck with your work.

SOPAE YI 2020-3-16

Mr. Hamza,

You've been such a great help!!

I am very much appreciative of your sharing your expertise, sir.

Stay healthy and happy!!!

请先登录，再进行评论。

类别

Signal Processing Signal Processing Toolbox Transforms, Correlation, and Modeling Correlation and Convolution

在 Help Center 和 File Exchange 中查找有关 Correlation and Convolution 的更多信息

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by

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

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

15 个评论
显示 13更早的评论隐藏 13更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

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

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

15 个评论 显示 13更早的评论隐藏 13更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

15 个评论
显示 13更早的评论隐藏 13更早的评论