I have two curves (data sets exist), which are visually the same. Now, I am going to quantize the comparison results and to show the degree of similarity by a criterion. Is there any solution? If so, how to do that by MATLAB or other statistical softwares.
1- A method is using of r = corr2(A,B) that returns the correlation coefficient (r) between A and B.
2- After some googling I saw that a similar question, in which it said that you can play around with Fourier transforms to get the correlation:
http://stackoverflow.com/questions/7396814/cross-correlation-in-matlab-without-using-the-inbuilt-function
3- or it:
http://dsp.stackexchange.com/questions/14306/percentage-difference-between-two-signals
4- and final:
http://stats.stackexchange.com/questions/13927/fit-between-two-curves
@Monther Alhamdoosh This is not correct. The RMSE between two vectors (curves, time series, etc.) depends (naturally) on the difference between the vectors, whereas correlation does not.
Think of a straight line and start translating a new line above the original one (i.e. both parallel to Ox). The RMSE will increase by the amount of the translation, whereas the correlation will remain zero.
@Valentin Curtef Here, my meaning of similarity is the degree of synchronicity and closeness of two curves to each other.
What do you think about "Kolmogorov–Smirnov test"?
https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
Besides the answers given in the links posted by Omid, you could use also a modified version of the Kullback-Leibler divergence, given your signals are somehow transferable to probability-distribution like forms (e.g. converging towards zero for +/-inf).
For comparison of noisy and clean velocity profiles I recently used the following formula:
- D(Y,X) = mean(N(xi)-log(gi)) for i = 1:length(Y) == length(X)
- N(z) = (z-min(X))/range(X) if xi > min(X), 0 otherwise, e.g. normalization w.r.t. X
- gi = abs(N(yi)/N(xi) - 1) + 1 if xi > min(X), 1 otherwise, approx. of Y/X to assure g >= 1
Which basically weighs the absolute difference between X and Y by the true signal X and diminishes the influence of outliers of the gain by using the log.
Hope that helps,
Greetings, David
Hey Kaveh!
Just saw your answer, if synchronicity and closeness is your goal, then indeed cross-correlation is the way to go (which measures synchronicity and similarity, e.g. lag and correlation).
Greetings, David
@Kaveh Mollazade Do not confuse testing with measure. The KS Test is used to determine if a population is from a theoretical distribution, or if two population describe the same distribution. By any permutation of one or both of the vectors (curves, time series), the test will give you the same result, but Correlation or RMSE will be different.
Hey Kaveh,
just an update: If your signals are paths, there was just a publication BRM.
Greetings, David
Conference Paper A Neurocomputational Approach to Modeling Human Behavior in ...
As David Mack said, the linked paper (which has been out more than a year but was just announced by BRM today) handles that problem for 2D paths, where the exact spatial coordinates are compared, without timing data (which would make it a trajectory), but you do not care about the specific segmentation of the curve (whether it is smooth or bumpy, small or large segments, or different-length segments).
An optimization approach for mapping and measuring the divergence and correspondence between paths
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