In this example of fuzzy c-means, what is the difference between "sigma" and "center" for the clusters?

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.

1 Answer

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.