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I have a set of time series data (just like voice sequence data) with the pattern as shown in the first figure (theoretical data). The measured data is given as presented in the second figure. What I want to do is localizing/finding the subsequent pattern as shown in the red squares. Is there any algorithm to solve this problem? It looks like the classification/regression problem in machine learning, but I have no idea how to start it.

enter image description here

enter image description here

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  • $\begingroup$ Did you look into independent component analysis? $\endgroup$
    – Peter
    Oct 16 '20 at 19:20
  • $\begingroup$ Not yet, is there any recommendation of literature? Thanks $\endgroup$
    – Land
    Oct 16 '20 at 19:28
  • $\begingroup$ ESL, Ch. 14.7 web.stanford.edu/~hastie/Papers/ESLII.pdf $\endgroup$
    – Peter
    Oct 16 '20 at 19:39
  • $\begingroup$ But on a second thought it might be a good problem for LSTM neural net: jjallaire.github.io/deep-learning-with-r-notebooks/notebooks/… $\endgroup$
    – Peter
    Oct 16 '20 at 19:40
  • $\begingroup$ Thanks, Peter! I will check them both. I have some basic idea about LSTM for prediction problem. Towards this problem, how do you consider them? Classification or regression? $\endgroup$
    – Land
    Oct 16 '20 at 19:44
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The real state of the art here is the Matrix Profile suite, developed by Eamonn Keogh and his team in University of California at Riverside (UCR). Here are some links to get you started:

You'll find links to implementations in the above stuff.

Apart from the team at UCR, there is another (and possibly more efficient) implementation of the relevant algorithms in the STUMPY Python package:

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