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So I currently have a time series signals which I need to classify each point on each signal.

Points are taken as follow:

  1. For a given timestamp. Make a measure
  2. Each meassure can randomly come from a different source (not equiprobable but I ignore the probability) or be an outlier. (See picture for an example).

The data has the following properties:

  • I ignore the amount of sources a priori, just know there is at least one.
  • Sources are only sinusoidal (so the figure is actually more generic with one signal being just a line).
  • Most of the time have same frequency or similar but different offset, phase and amplitude (although amplitude are also close normally).

I need to classify this sources into as many as they are.

Note that the aquired signal is therefore not an addition of sources but random samples.

enter image description here

My question is not necessary what algorithm to use (which can also help) but actually how to even look for it. Which is the field of study for this kind of problem?

Response to questions.

  • Selection process is uncorrelated. Signals itselves are uncorrelated and which one is aquired is also uncorrelated and random with unknown distribution.
  • I want to classify each point. For example, the point at x=today at 13hs is from source A and the one at 14hs is an outlier.
  • Just in case, source A or B, etc have unknown parameters. Just know there are sinus but I don't know anything else.
  • Estimating each sinusoidal parameters like frequency, amplitude, etc is not required.
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  • $\begingroup$ Welcome! It's really not clear what is "special" about the coloring you chose for the points – I could imagine a lot of other classifiers that would make "as much sense" to me. So, you will need to describe what your signal model is here; I bet you can say more about that than "I have a time series": Describe what it describes, how it's captured, what its axes are, and for what purpose you need to classify each value. Thanks! $\endgroup$
    – Marcus Müller
    Commented Mar 6, 2023 at 9:09
  • $\begingroup$ Thanks for the remarks. I have re-phrased my question in the hopes it's clearer. $\endgroup$
    – Agustin Barrachina
    Commented Mar 6, 2023 at 11:55
  • $\begingroup$ Thanks for the edit! Yeah, if everything is sinusoidal, I'd call your figure not "overgeneralizing", but a bit misleading :) Luckily, this makes the problem a lot more tractable. So, you say "each measurement can randomly come from a different source"; is that selection process itself uncorrelated, or correlated? Or is it correlated to one (or multiple) of the signals? And: what is the actual objective: Do you want to estimate each sinusoidal's phase, amplitude and offset, or do you want to know how many different sources there are, or are you trying to reconstruct just the selection? $\endgroup$
    – Marcus Müller
    Commented Mar 6, 2023 at 13:04
  • $\begingroup$ ah cool; this is kind of some hybrid problem between source separation and spectral estimation, and it's pretty cool. $\endgroup$
    – Marcus Müller
    Commented Mar 6, 2023 at 17:15
  • $\begingroup$ But I'd honestly start by just doing good ole-fashined principal component analysis; that might be pretty robust against the source selection $\endgroup$
    – Marcus Müller
    Commented Mar 6, 2023 at 17:16

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