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Knee-point detection in Python

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This repository is an attempt to implement the kneedle algorithm, published here. Given a set of x and y values, kneed will return the knee point of the function. The knee point is the point of maximum curvature.

Table of contents


kneed has been tested with Python 3.7, 3.8, 3.9, and 3.10.


$ conda install -c conda-forge kneed


$ pip install kneed # To install only knee-detection algorithm
$ pip install kneed[plot] # To also install plotting functions for quick visualizations

Clone from GitHub

$ git clone && cd kneed
$ pip install -e .


These steps introduce how to use kneed by reproducing Figure 2 from the manuscript.

Input Data

The DataGenerator class is only included as a utility to generate sample datasets.

Note: x and y must be equal length arrays.

from kneed import DataGenerator, KneeLocator

x, y = DataGenerator.figure2()

print([round(i, 3) for i in x])
print([round(i, 3) for i in y])

[0.0, 0.111, 0.222, 0.333, 0.444, 0.556, 0.667, 0.778, 0.889, 1.0]
[-5.0, 0.263, 1.897, 2.692, 3.163, 3.475, 3.696, 3.861, 3.989, 4.091]

Find Knee

The knee (or elbow) point is calculated simply by instantiating the KneeLocator class with x, y and the appropriate curve and direction.
Here, kneedle.knee and/or kneedle.elbow store the point of maximum curvature.

kneedle = KneeLocator(x, y, S=1.0, curve="concave", direction="increasing")

print(round(kneedle.knee, 3))

print(round(kneedle.elbow, 3))

The knee point returned is a value along the x axis. The y value at the knee can be identified:

print(round(kneedle.knee_y, 3))


The KneeLocator class also has two plotting functions for quick visualizations. Note that all (x, y) are transformed for the normalized plots

# Normalized data, normalized knee, and normalized distance curve.

# Raw data and knee.


Documentation of the parameters and a full API reference can be found here.


An interactive streamlit app was developed to help users explore the effect of tuning the parameters. There are two sites where you can test out kneed by copy-pasting your own data:


You can also run your own version -- head over to the source code for ikneed.



Contributions are welcome, please refer to CONTRIBUTING to learn more about how to contribute.


Finding a “Kneedle” in a Haystack: Detecting Knee Points in System Behavior Ville Satopa † , Jeannie Albrecht† , David Irwin‡ , and Barath Raghavan§ †Williams College, Williamstown, MA ‡University of Massachusetts Amherst, Amherst, MA § International Computer Science Institute, Berkeley, CA