kneed 0.0.4

Knee-point detection in Python

# kneed
## Knee-point detection in Python
[](https://mybinder.org/v2/gh/arvkevi/kneed/master)

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
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, invert=False)

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)
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, 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