I was wondering if the meaning of an elbow applies to graphs like the following. Basically for each curve obtained, I am looking to find out if there is a way to determine a point such as the one marked by
0 in the graph. In layman terms, I want to find out the maximum trade-off point across all the curves. I am not sure about the exact terminology though. In other words, I am trying to find out the point on the curve where the curve undergoes the maximum change. In this graph however, every change looks almost identical but the amount by which the curve falls before changing differs.
I tried looking at the point at which we obtain the maximum second derivative using the second derivative test but am having a hard time to see if it actually applies to curves like this and if there are any references explaining this.
Can someone please suggest related techniques that can be used to find the elbow point on curves like this? I found the following method called the L-Method but wasn't sure if it is applicable in my case.
EDIT: An attempt to describe what I am trying to do:
I am aware that I will be having a hard time explaining what I am doing but I will try my best. I am trying to fix two thresholds: one that is used to obtain the line and the other that I use to filter noise. The '0' on the graph marks the thresholds. In this particular case, I am using
Threshold 3 and filtering my population to contain only those people that have
>= 2 friends. While this is working well for me, I am trying to determine if there is systematic procedure to explain why these thresholds are better than others. For instance,
Threshold 2 is not such a good filter because it behaves like
Threshold 1 in that it is not filtering any information from the population (which is around 1500). Utilizing
Threshold 4 is not so useful because the returns in going from
Threshold 2 to
Threshold 3 is much higher than that going from
Threshold 3 to