Answers.Body: <p>In the example you link to, the <em>sigma</em> parameter has got nothing to do with the clustering; it is only used to generate sample data for illustration. It defines the spread of cluster elements around the (pre-defined) centroid of each cluster.</p>
  <p>This is done for demonstration only: you generate clusters which you know exist, and then check that the cluster algorithm can detect those clusters correctly. In normal centroid-based clustering the centroid does not have a specified range -- each data point it simply assigned to its nearest centroid, however far away it it.</p>
  
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Body: <p>In this <a href="https://pythonhosted.org/scikit-fuzzy/auto_examples/plot_cmeans.html" rel="nofollow noreferrer">example</a>, what exactly do &quot;Cluster&quot; and &quot;Sigma&quot; mean? (They chose random coordinates for the three centroids of the groups)</p>
  <ul>
  <li><strong>Centers:</strong> Cluster centers, returned as a <code>JxN</code> array, where <code>J</code> is the number of clusters and <code>N</code> is the number of data dimensions.</li>
  <li><strong>Sigma:</strong> Range of influence of cluster centers for each data dimension, returned as an <code>N</code>-element row vector. All cluster centers have the same set of sigma values.</li>
  </ul>
  <p>Please, elaborate on the difference.</p>
  
Tags: <comparison><unsupervised-learning><notation><clustering><fuzzy-logic>
Title: In this example of fuzzy c-means, what is the difference between "sigma" and "center" for the clusters?
UserDisplayName: user5520049
ThreadText: # In this example of fuzzy c-means, what is the difference between "sigma" and "center" for the clusters?
  
  (Asked by: username_0 on 2021-10-24)
  
  In this [example](https://pythonhosted.org/scikit-fuzzy/auto_examples/plot_cmeans.html), what exactly do "Cluster" and "Sigma" mean? (They chose random coordinates for the three centroids of the groups)
  
  * **Centers:** Cluster centers, returned as a `JxN` array, where `J` is the number of clusters and `N` is the number of data dimensions.
  * **Sigma:** Range of influence of cluster centers for each data dimension, returned as an `N`-element row vector. All cluster centers have the same set of sigma values.
  
  Please, elaborate on the difference.
  
  **Tags:** comparison, unsupervised-learning, notation, clustering, fuzzy-logic
  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2021-10-25. Score: 0
  
  In the example you link to, the *sigma* parameter has got nothing to do with the clustering; it is only used to generate sample data for illustration. It defines the spread of cluster elements around the (pre-defined) centroid of each cluster.
  
  This is done for demonstration only: you generate clusters which you know exist, and then check that the cluster algorithm can detect those clusters correctly. In normal centroid-based clustering the centroid does not have a specified range -- each data point it simply assigned to its nearest centroid, however far away it it.
  
  
  ---
  
  