pyclustering.cluster.elbow.elbow Class Reference

Class represents Elbow method that is used to find out appropriate amount of clusters in a dataset. More...

Public Member Functions
def	__init__ (self, data, kmin, kmax, **kwargs)
	Construct Elbow method. More...
def	process (self)
	Performs analysis to find out appropriate amount of clusters. More...
def	get_amount (self)
	Returns appropriate amount of clusters.
def	get_wce (self)
	Returns list of total within cluster errors for each K-value, for example, in case of kstep = 1: (kmin, kmin + 1, ..., kmax).

Detailed Description

Class represents Elbow method that is used to find out appropriate amount of clusters in a dataset.

The elbow is a heuristic method of interpretation and validation of consistency within cluster analysis designed to help find the appropriate number of clusters in a dataset.Elbow method performs clustering using K-Means algorithm for each K and estimate clustering results using sum of square erros. By default K-Means++ algorithm is used to calculate initial centers that are used by K-Means algorithm.

The Elbow is determined by max distance from each point (x, y) to segment from kmin-point (x0, y0) to kmax-point (x1, y1), where 'x' is K (amount of clusters), and 'y' is within-cluster error. Following expression is used to calculate Elbow length:

\[Elbow_{k} = \frac{\left ( y_{0} - y_{1} \right )x_{k} + \left ( x_{1} - x_{0} \right )y_{k} + \left ( x_{0}y_{1} - x_{1}y_{0} \right )}{\sqrt{\left ( x_{1} - x_{0} \right )^{2} + \left ( y_{1} - y_{0} \right )^{2}}}\]

Usage example of Elbow method for cluster analysis:

from pyclustering.cluster.kmeans import kmeans, kmeans_visualizer
from pyclustering.cluster.center_initializer import kmeans_plusplus_initializer
from pyclustering.cluster.elbow import elbow
from pyclustering.utils import read_sample
from pyclustering.samples.definitions import SIMPLE_SAMPLES
 
# read sample 'Simple3' from file (sample contains four clusters)
sample = read_sample(SIMPLE_SAMPLES.SAMPLE_SIMPLE3)
 
# create instance of Elbow method using K value from 1 to 10.
kmin, kmax = 1, 10
elbow_instance = elbow(sample, kmin, kmax)
 
# process input data and obtain results of analysis
elbow_instance.process()
amount_clusters = elbow_instance.get_amount()  # most probable amount of clusters
wce = elbow_instance.get_wce()  # total within-cluster errors for each K
 
# perform cluster analysis using K-Means algorithm
centers = kmeans_plusplus_initializer(sample, amount_clusters,
                                      amount_candidates=kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE).initialize()
kmeans_instance = kmeans(sample, centers)
kmeans_instance.process()
 
# obtain clustering results and visualize them
clusters = kmeans_instance.get_clusters()
centers = kmeans_instance.get_centers()
kmeans_visualizer.show_clusters(sample, clusters, centers)

By default Elbow uses K-Means++ initializer to calculate initial centers for K-Means algorithm, it can be changed using argument 'initializer':

# perform analysis using Elbow method with random center initializer for K-Means algorithm inside of the method.
kmin, kmax = 1, 10
elbow_instance = elbow(sample, kmin, kmax, initializer=random_center_initializer)
elbow_instance.process()

Elbows analysis with further K-Means clustering.

Definition at line 22 of file elbow.py.

Constructor & Destructor Documentation

__init__()

def pyclustering.cluster.elbow.elbow.__init__	(		self,
			data,
			kmin,
			kmax,
		**	kwargs
	)

Construct Elbow method.

Parameters

[in]	data	(array_like): Input data that is presented as array of points (objects), each point should be represented by array_like data structure.
[in]	kmin	(int): Minimum amount of clusters that should be considered.
[in]	kmax	(int): Maximum amount of clusters that should be considered.
[in]	**kwargs	Arbitrary keyword arguments (available arguments: ccore, initializer, random_state, kstep).

Keyword Args:

• ccore (bool): If True then C++ implementation of pyclustering library is used (by default True).
• initializer (callable): Center initializer that is used by K-Means algorithm (by default K-Means++).
• random_state (int): Seed for random state (by default is None, current system time is used).
• kstep (int): Search step in the interval [kmin, kmax] (by default is 1).

Definition at line 80 of file elbow.py.

Member Function Documentation

process()

def pyclustering.cluster.elbow.elbow.process

(

self

)

Performs analysis to find out appropriate amount of clusters.

Returns

(elbow) Returns itself (Elbow instance).

Definition at line 119 of file elbow.py.

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The documentation for this class was generated from the following file:

• pyclustering/cluster/elbow.py