pyclustering: pyclustering.cluster.fcm.fcm Class Reference

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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()

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]**kwargsArbitrary 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()

Returns list of centers of allocated clusters.

Returns: (array_like) Cluster centers.

See also: process()

get_membership()

Definition at line 164 of file fcm.py .

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()

Definition at line 147 of file fcm.py .

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

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.