Knee/Elbow Point Estimation through Thresholding

Estimating the knee/elbow point in curves is a challenging task. However, most of the time these points represent ideal compromises for parameters, methods and algorithms. Nowadays several IoT and M2M scenarios require autonomous systems that optimize themselves with minimal human intervention. Thus, knee/elbow estimation has become an important research area. Our focus is determining the ideal number of clusters autonomously. In this paper, we formalize the notion of knee/elbow point based on continuous curvature function and propose two theoretical methods based on the same function. We analyse and discuss well-known knee/elbow estimators and propose our own method. Contrary to most methods, ours is resilient to long tails in the curve. We also propose an iterative refinement method to increase the resilience to long heads. All the previously mentioned methods were implemented (and are publicly available) and evaluated against eight datasets. The proposed method is a viable stable solution for knee/elbow estimation.