Kneedpunt

Kneedpunt, or knee point, is a term used in data analysis to denote a point on a curve where the rate of change of the slope shifts distinctly, indicating a transition between regimes or a threshold beyond which gains decrease rapidly. In practice, a knee point is often sought to determine an appropriate level of model complexity, components, or clusters. The concept is closely related to the knee or elbow methods used in statistics and machine learning.

In clustering, the elbow method relies on plotting a metric such as within-cluster sum of squares against the number of clusters; the knee point indicates a point after which adding more clusters yields diminishing improvements. In dimensionality reduction, the knee point on the explained variance plot helps select the number of principal components. In dose–response or sigmoidal fitting, the knee marks a threshold where response begins to saturate.

Detection methods range from visual inspection to automated algorithms. The Kneedle algorithm explicitly searches for a knee by analyzing curvature, while other approaches fit piecewise models and identify the intersection, or use maximum curvature criteria.

Limitations include subjectivity, sensitivity to noise and scaling, and non-uniqueness: different methods or data pre-processing can yield different knee points. Practitioners often compare several criteria and assess stability across transformations.

See also: elbow method, knee point detection, Kneedle algorithm, curvature-based methods, model selection. Etymology: the term is used in Dutch-language contexts to refer to the curvature knee of a curve, analogous to the English 'knee point'.