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I have data sets in which important information is allocated in the edges, which are also very sensitive to inaccuracies. I would like to find a regression model based on edge recognition that brings my data closer to the expected avoiding overfitting. Here is an example:

Example Please note that although I could simulate the data behavior for this very specific case, in reality, I do not have prior knowledge or known model of the data.

Several edge-detection algorithms are based on derivative computations, however for such scarce (and frequently noisy) data, derivatives are not a very robust solution. So far, the closest I have got with derivatives is performing y-y'' transformation. Therefore, I am looking in the direction of regression models with machine learning methods, however I have very little experience on that.

Is there any regression model which is suitable for edge detection and enhancement?

I also provide a link with the corresponding data. Any idea/suggestion/help would be very appreciated, I am currently working on Matlab and Python.

Thanks in advance! .imgur.com/vfqv0.png

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In working with similar looking data, I have not had luck with regression models. Instead, I am currently using Symbolic Aggregate approXimation (SAX) as a means to cluster and classify edges and have had reasonable success with this approach. It seems to be resistant to noise, amplitude variations and focuses a lot more on shape. It might be worth a look.

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  • $\begingroup$ Thank you Jason, you have opened a new window to explore. I will definitely have a look at it. $\endgroup$
    – Nacu
    Jul 20 '15 at 9:52
  • $\begingroup$ If this does not work for you and you do find any other approaches that work, I would appreciate any updates as it is always good to find alternatives. $\endgroup$
    – Jason K.
    Jul 21 '15 at 2:15
  • $\begingroup$ Sure! Always new ideas are welcome! I will keep you updated and hopefully more people come to the discussion as well... I implemented a simple code to my data and, as you mentioned, the algorithm cares more about edges. Therefore, it is good to model the data itself. However, one of my major issues are also the random shifts of the experimental data respect to the model. So, at the moment, I am trying to put some constraints based on differences to see if the result improves. $\endgroup$
    – Nacu
    Jul 21 '15 at 8:48

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