Knee Detection Algorithm

The following algorithm has been used to detect knee/elbow in a graph as follows:

Calculate vector ,

Where and  are the first and last points of the curve marked by the green line.

 ,

Where   is the first point and  are the iterated points.

Calculate Orthogonal Projection of vectors on vector

Then, Calculate the distance of projection vector  from vector of first point of curve, i.e.

Store distance values in

 Find maximum of distance_array.

The x value corresponding to the maximum of distance_array is knee value.

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References

· Satopaa, V., Albrecht, J., Irwin, D., & Raghavan, B. (2011). Finding a ‘kneedle’in a haystack: Detecting knee points in system behavior. 166–171. In 31-st International Conference on Distributed Computing Systems.

· Saluja KPS, Jeevithashree Dv,  Arjun S. and Biswas P., Analyzing Eye Gaze Movement of Users with Different Reading Abilities due to Learning Disability, 3rd International Conference on Graphics and Signal Processing (ICGSP 2019)