Hi everyone.
I want to ask about the deffinition of Correlation and Cross- correlation. I recently explored this stuff in the internet and could not concluded the thershold of these two deffinition while their equations are some how different. What I found is like this:
Correlation: is the degree of simmilarity between two time series or signal in the same time or sequence while no lag is considered in the magnitude of (-1 to 1).
Cross-correlation: is the degree of similarity between two time series in different times or space while lag can be considred when time is under investigation. The diffenece between these two time series in different situation like distance, angle, direction etc. can be considered while the space is under investigation respectively.
Auto-correlation: is the cross-correlation of a time series while investitigating the persitance between lagged times of the same time series or signal.
please correct me if I am wrong in any details of the deffinitions.
thankfully yours.
Babak
The term "correlation" has multiple meanings. You describe the statistical correlation coefficient. It describes the linearity of a bunch of values. Another "type" of correlation is defined by:
rho(tau)=K*int(x(t)*m(t+tau), t) with a time series x(t) and a sample function m(t)
The coefficient K has to be adjusted to x(t) (i.e. 1/(2*pi) for periodic signals) as well as the Integration limits. It is related to convolution. Depending on m(t), the correlation becomes another Transformation, i.e.: m(t)=y(t) for cross-correlation, m(t)=x(t) for auto-correlation, m(t)=exp(-i*omega*t) for Fourier transformation.
I hope this helps.
Best Regards
Patrick
Patrick, equations you used are not completely clear for me but I know the classical definitions of them. Here I am interested in the statistic definition of them. I am trying to get the main idea behind them because most of the explanations are in the form of your explanation. It is all about data analysis but what you said is close to the definitions which I have reached before. The transfer function is generally used while signal analysis is under investigation. But in my field we usually prefer not to change the natural structure of the data. Because changes in distribution or
Thanks for your answer.
Correlation defines the degree of similarity between two indicates. If the indicates are alike, then the correlation coefficient will be 1 and if they are entirely different then the correlation coefficient will be 0. When two independent indicates are compared, this procedure will be called as cross-correlation.
That is a good start Atiq, but how much degree of independence is acceptable?
Is it enough to assume that they are independent or it should be physical evidence for it?
If you have any information please let me know. But thanks for your answer
Dear all,
The organization of data matrix is important because the choice of the measure of association is based on that organization (people or variables).
Admit that rows are people and columns are variables. There are a family of correlation coefficients , ex: Person's R and Spearmans's Rho.
With Rho we need to know if the on average the 2 variables have the same order, where with Pearson besides that we need that variables have the same shape (= skewness and Kurtosis).
Now admit that columns are people and rows are variables. Thus the correlation between 2 columns is the correlation or similarities between 2 profiles. thus high correlation means similarity and low measn lack of it (ex Q type of factor analysis). Thus correaltional measures means similarities by the correspodence of patterns across the X variables (characteristics).
Helena
Helena,
correct me if I am wrong. You mean that the correlation measures the similarities of shape of distributions and cross correlation measures the averages?!
It didn’t make sense for me. By the way I am using a Pearson correlation for all of them, i.e. correlation, cross correlation, and auto correlation. All of them are defintion of what you are measuring using the same methodology.
I think correlation is the general term which means the measure for the degree of similarity between two two functions. Cross correlation and auto correlations are two types of correlation.
An answer which may satisfy any one is to match the word description precisely the mathematical operation. The mathematical expression defines completely its function unambiguously. So, You have to stick on the mathematical expression of the process.
Dear Prof Zekry.
Yes you are right. But the question arise when the difinition of the cross-correlation is based on the examining the linear relation between two independent sample. But if they are independent, how can they have correlation?
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