Unable to detect knee and elbow about kneed

[d-kleine]

@dpapadop I have just looked into your bug report. As far as I understand, you want to locate both knee and elbow for the given plot. Why do you use df_test['y'] when plotting y_cum? y and y_cum are completely different:
plt.plot(df_test['x'], df_test['y'])

How I would solve this issue:

1. I would first go looking up the knee point:

kneedle = KneeLocator(x=df_test['x'], y=df_test['y_cum'], curve='concave', direction='increasing', online=True, S=1)
knee_point = kneedle.knee
knee_point

This gives me a knee point at x=9

2. Then I would reduce the sensibility down to zero for finding the elbow, see here:

S is a measure of how many “flat” points we expect to see in the unmodified data curve before declaring a knee.

(for further information, see original paper Finding a “Kneedle” in a Haystack: Detecting Knee Points in System Behavior by Ville Satopää et al. as well)

kneedle = KneeLocator(x=df_test['x'], y=df_test['y_cum'], curve='convex', direction='increasing', online=True, S=0)
elbow_point = kneedle.elbow
elbow_point

Then I get an elbow point at x=4.

Kind regards
DK