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pythonscipystatisticsdata-analysis
Rye
Rye

Reputation: 177

Approximate maximum of an unknown curve

I have a data set that looks like this: data set I used the scipy.signal.find_peaks function to determine the peaks of the data set, and it works out fine enough, but since this function determines the local maxima of the data, it is not neglecting the noise in the data which causes overshoot. Therefore what I'm determining isn't actually the location of the most likely maxima, but rather the location of an 'outlier'.

Is there another, more exact way to approximate the local maxima?

Upvotes: 0

Views: 263

Answers (1)

Ziur Olpa
Ziur Olpa

Reputation: 2133

I'm not sure that you can consider those points to be outliers so easily, as they look to be close to the place I would expect them to be. But if you don't think they are a valid approximation let me tell you three other ways you can use.

First option

I would construct a physical model of these peaks (a mathematical formula) and do a fitting analysis around the peaks. You can for instance, suppose that the shape of the plot is the sum of some background model (maybe constant or maybe more complicated) plus some Gaussian peaks (or Lorentzian).

This is what we usually do in physics. Of course it will be more accurate taking knowledge from the underlying processes, which I don't have.

Having a good model, this way is definitely better as taking the maximum values, as even if they are not outliers, they still have errors which you want to reduce.

Second option

But if you want a easier way, just a rough estimation and you already found the location of the three peaks programmatically, you can make the average of a few points around the maximum. If you do it so, the function np.where or np.argwhere tend to be useful for this kind of things.

Third option

The easiest option is taking the value by hand. It could sound unacceptable for academic proposes and it probably is. Even worst, it is not a programmatic way, and this is SO. But at the end, it depends on why and for what you need those values and on the confidence interval you need for your measurement.

Upvotes: 2

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