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In this example, 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.

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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.

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