Class represents Fuzzy C-means (FCM) clustering algorithm. More...

Public Member Functions
def	__init__ (self, data, initial_centers, **kwargs)
	Initialize Fuzzy C-Means algorithm. More...

def	process (self)
	Performs cluster analysis in line with Fuzzy C-Means algorithm. More...

def	get_clusters (self)
	Returns allocated clusters that consists of points that most likely (in line with membership) belong to these clusters. More...

def	get_centers (self)
	Returns list of centers of allocated clusters. More...

def	get_membership (self)
	Returns cluster membership (probability) for each point in data. More...

Detailed Description

Class represents Fuzzy C-means (FCM) clustering algorithm.

Fuzzy clustering is a form of clustering in which each data point can belong to more than one cluster.

Fuzzy C-Means algorithm uses two general formulas for cluster analysis. The first is to updated membership of each point:

\[w_{ij}=\frac{1}{\sum_{k=0}^{c}\left ( \frac{\left \| x_{i}-c_{j} \right \|}{\left \| x_{i}-c_{k} \right \|} \right )^{\frac{2}{m-1}}}\]

The second formula is used to update centers in line with obtained centers:

\[c_{k}=\frac{\sum_{i=0}^{N}w_{k}\left ( x_{i} \right )^{m}x_{i}}{\sum_{i=0}^{N}w_{k}\left ( x_{i} \right )^{m}}\]

Fuzzy C-Means clustering results depend on initial centers. Algorithm K-Means++ can used for center initialization from module 'pyclustering.cluster.center_initializer'.

CCORE implementation of the algorithm uses thread pool to parallelize the clustering process.

Here is an example how to perform cluster analysis using Fuzzy C-Means algorithm:

from pyclustering.samples.definitions import FAMOUS_SAMPLES
from pyclustering.cluster import cluster_visualizer
from pyclustering.cluster.center_initializer import kmeans_plusplus_initializer
from pyclustering.cluster.fcm import fcm
from pyclustering.utils import read_sample
 
# load list of points for cluster analysis
sample = read_sample(FAMOUS_SAMPLES.SAMPLE_OLD_FAITHFUL)
 
# initialize
initial_centers = kmeans_plusplus_initializer(sample, 2, kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE).initialize()
 
# create instance of Fuzzy C-Means algorithm
fcm_instance = fcm(sample, initial_centers)
 
# run cluster analysis and obtain results
fcm_instance.process()
clusters = fcm_instance.get_clusters()
centers = fcm_instance.get_centers()
 
# visualize clustering results
visualizer = cluster_visualizer()
visualizer.append_clusters(clusters, sample)
visualizer.append_cluster(centers, marker='*', markersize=10)
visualizer.show()

The next example shows how to perform image segmentation using Fuzzy C-Means algorithm:

from pyclustering.cluster.center_initializer import kmeans_plusplus_initializer
from pyclustering.cluster.fcm import fcm
from pyclustering.utils import read_image, draw_image_mask_segments
 
# load list of points for cluster analysis
data = read_image("stpetersburg_admiral.jpg")
 
# initialize
initial_centers = kmeans_plusplus_initializer(data, 3, kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE).initialize()
 
# create instance of Fuzzy C-Means algorithm
fcm_instance = fcm(data, initial_centers)
 
# run cluster analysis and obtain results
fcm_instance.process()
clusters = fcm_instance.get_clusters()
 
# visualize segmentation results
draw_image_mask_segments("stpetersburg_admiral.jpg", clusters)

Image segmentation using Fuzzy C-Means algorithm.

Definition at line 20 of file fcm.py.

Constructor & Destructor Documentation

◆ init()

def pyclustering.cluster.fcm.fcm.__init__	(		self,
			data,
			initial_centers,
		**	kwargs
	)

Initialize Fuzzy C-Means algorithm.

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]	initial_centers	(array_like): Initial coordinates of centers of clusters that are represented by array_like data structure: [center1, center2, ...].
[in]	**kwargs	Arbitrary keyword arguments (available arguments: 'tolerance', 'itermax', 'm').

Keyword Args:

ccore (bool): Defines should be CCORE library (C++ pyclustering library) used instead of Python code or not.
tolerance (float): Stop condition: if maximum value of change of centers of clusters is less than tolerance then algorithm stops processing.
itermax (uint): Maximum number of iterations that is used for clustering process (by default: 200).
m (float): Hyper-parameter that controls how fuzzy the cluster will be. The higher it is, the fuzzier the cluster will be in the end. This parameter should be greater than 1 (by default: 2).

Definition at line 93 of file fcm.py.

Member Function Documentation

◆ get_centers()

def pyclustering.cluster.fcm.fcm.get_centers ( self )

Returns list of centers of allocated clusters.

Returns: (array_like) Cluster centers.

See also: process(); get_clusters(); get_membership()

Definition at line 164 of file fcm.py.

◆ get_clusters()

def pyclustering.cluster.fcm.fcm.get_clusters ( self )

Returns allocated clusters that consists of points that most likely (in line with membership) belong to these clusters.

Remarks: Allocated clusters can be returned only after data processing (use method process()). Otherwise empty list is returned.

Returns: (list) List of allocated clusters, each cluster contains indexes from input data.

See also: process(); get_centers(); get_membership()

Definition at line 147 of file fcm.py.

Referenced by pyclustering.samples.answer_reader.get_cluster_lengths(), and pyclustering.cluster.optics.optics.process().

◆ get_membership()

def pyclustering.cluster.fcm.fcm.get_membership ( self )

Returns cluster membership (probability) for each point in data.

Returns: (array_like) Membership for each point in format [[Px1(c1), Px1(c2), ...], [Px2(c1), Px2(c2), ...], ...], where [Px1(c1), Px1(c2), ...] membership for point x1.

See also: process(); get_clusters(); get_centers()

Definition at line 178 of file fcm.py.

◆ process()

def pyclustering.cluster.fcm.fcm.process ( self )

Performs cluster analysis in line with Fuzzy C-Means algorithm.

Returns: (fcm) Returns itself (Fuzzy C-Means instance).

See also: get_clusters(); get_centers(); get_membership()

Definition at line 128 of file fcm.py.

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

pyclustering/cluster/fcm.py

Public Member Functions