What is the relation between correlation and time-series signal complexity? For example, I was reading a paper that is talking about the Multi scale entropy (MSE) and its advantages over the Shannon entropy. They present two signals, the first one is white noise signals and the second is long-range correlated white noise, they called it 1/f. They said that

MSE results are consistent with the fact that, unlike white noise, 1/f noise contains correlations across multiple time scales and is, therefore, more complex than white noise.

According to my understanding, complexity means that there are many parties have involved in producing this signals. How can we compare it with correlation or other statistical concepts?

If we have a signal and we analyse this signal to its independent components using ICA, then do we decompose the signal complexity? Does the complex signal can produce more independent components?

Is the solution for a signal complexity is to get the contribution of each part separately? So can I say the Blind Source Separation techniques are one of solutions to "kill" the complexity of a signal and make it simple?

  • $\begingroup$ Are you asking what's the definition in the context of the paper or in general? $\endgroup$ – Aksakal Feb 15 '17 at 21:53
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    $\begingroup$ Just a note that there are many kinds of complexity: computational complexity, systems complexity, biological complexity, Santa Fe complexity, information complexity, and so on. I suggest you do a little research and better define what it is you're looking for. In doing so, you will probably answer your own question. $\endgroup$ – Mike Hunter Feb 15 '17 at 22:48

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