kneed 0.1.1

# kneed

## Knee-point detection in Python

[](https://mybinder.org/v2/gh/arvkevi/kneed/master) [](https://travis-ci.com/arvkevi/kneed) [](https://www.codacy.com/app/arvkevi/kneed?utm_source=github.com&utm_medium=referral&utm_content=arvkevi/kneed&utm_campaign=Badge_Grade)

This repository is an attempt to implement the kneedle algorithm, published [here](https://www1.icsi.berkeley.edu/~barath/papers/kneedle-simplex11.pdf). 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.



## Installation

To install use pip:

$ pip install kneed

Or clone the repo:

$ git clone https://github.com/arvkevi/kneed.git
$ python setup.py install
**Tested with Python 3.5 and 3.6**

## Usage

### Reproduce Figure 2 from the paper.

```python
from kneed import DataGenerator, KneeLocator

DG = DataGenerator()
x,y = DG.figure2()

print(x,y)
(array([ 0. , 0.11111111, 0.22222222, 0.33333333, 0.44444444,
0.55555556, 0.66666667, 0.77777778, 0.88888889, 1. ]),
array([-5. , 0.26315789, 1.89655172, 2.69230769, 3.16326531,
3.47457627, 3.69565217, 3.86075949, 3.98876404, 4.09090909]))

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

kneedle.knee
0.22222222222222221

kneedle.plot_knee_normalized()
```


#### Average Knee from 5000 NoisyGaussians when mu=50 and sigma=10

```python
import numpy as np

knees = []
for i in range(5000):
x,y = DG.noisy_gaussian(mu=50, sigma=10, N=1000)
kneedle = KneeLocator(x, y, curve='concave', direction='increasing')
knees.append(kneedle.knee)

np.mean(knees)
60.921051806064931
```

## Application

## Find the optimal number of clusters (k) to use in k-means clustering

See the tutorial in the notebooks folder, this can be achieved with the `direction` keyword argument:

```python
KneeLocator(x, y, curve='convex', direction='decreasing')
```


Contributing

* * *

I welcome contibutions, if you have suggestions or would like to make improvements please submit an issue or pull request.

## Citation

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