MATLAB: How to compute the similarity of two signals and get the correct consistency or coherence metric

Question

I was wondering about the consistency metric. Generally, it allows us to deduce the parity or similarity between two signals, right? If so, if the probability is higher (from 0.5 to 1), does it means that there is a strong similarity of the signals? If the margin is less than (0.1-0.43), can this predict the poor coherence between the signals (or poor similarity, the probability the signals are different)? So, if we got the metric <0, is this approved the signal is totally different? Because I'm getting negative numbers. Is this hypothesis possible?

Can I have a clear understanding of the consistency metric of the signal? Here is my small code. Thanks in advance.

s1 = signal3
s2 = signal4     

if  s1 ~= s2
    [C1] = xcorr(s1);        
    [C2] = xcorr(s2);
    signal_mix = C1.*C2   %mixing vector
    signal_mix1 = signal_mix
else
    s1(1,:) == s2(1,:)
    s3 = s1
    s3= s2
    signal_mix = s2
end

n =2;
   
for i = length(signal_mix1)
    signal_mix1(i) = min(C1(i),C2(i))/ max(C1(i),C2(i)) % consistency score
    signal_mix2 = sum(signal_mix1(i))
end

Answer 1

Correlation provides a metric of the linear dependence between two signals. The normalized correlation coefficient (which is the result of xcorr and then divided by the standard deviation of each of the two waveforms) will provide a result that is between +1 and -1, where +1 means the two waveforms are virtually identical other than perhaps a gain scaling between the two, and -1 means the two waveforms are also identical with the addition of a sign change (one is the inverse of the other) with again the possibility of a gain scaling between the two. 0 means the two waveforms are uncorrelated, and there is no linear relationship between the two. Everything else is between these extremes.

Note the plot below from Wikipedia showing scatter plots of two functions x vs y for different correlation coefficients. Also observe how the waveforms may have a strong non-linear similarity but have 0 correlation, as given by all the results in the lower part of the graphic.