Finding The Elbow Point Of A Curve In A Stable Way?

I am aware of the existence of this, and this on this topic. However, I would like to finalize on an actual implementation in Python this time. My only problem is that the elbow p

Solution 1:

Its sounds like your actual concern is how to smooth your data as it contains noise? in which case perhaps you should fit a curve to the data first, then find the elbow of the fitted curve?

Whether this will work would depend on the source of the noise, and if the noise is important for your application? by the way you may want to see how sensitive your fit is to your data by seeing how it changes (or hopefully doesn't) when a point is omitted from the fit (obviously with a high enough polynomial you will always get a good fit to a specific set of data, but you are presumably interested in the general case)

I have no idea if this approach is acceptable, intuitively though i'd think that sensitivity to small errors is bad. ultimately by fitting a curve you are saying that the underlying process is, in the ideal case, modelled by the curve, and any deviation from the curve is an error/noise