fcms

 FUZZY C-MEANS: Fuzzy c-means algorithm for unsupervised classification

         c = fcms(x,Nc,epochs,pdfx)

 Inputs
      x: Input data matrix with points by columns (RxQ)
     Nc: Number of clusters (scalar)
 epochs: (Optional) Number of iterations (Default = 100)
   expo: (Optional) Exponent in the original Bezdek algorithm (Default = 2)
   pdfx: (Optional) Probability density function values associated to each
          input data point (1xQ) (Default = uniform)

 Outputs
      c: Matrix with the centers by columns (RxNc)

 Calls
        c = fcms(x,Nc)
        c = fcms(x,Nc,epochs)
        c = fcms(x,Nc,epochs,expo)
        c = fcms(x,Nc,epochs,expo,pdfx)

 This function implements the Bezdek's fuzzy c-means algorithm. Additionally, a 
 probability value can be associated to each data sample to generate a distribution 
 of points with a given probability density function.

 NOTE: The algorithm performs well in all dimensions if data has a cluster
 structure (multimodality). However, when dimension is high, and the number of
 clusters is lower than the number of prototypes the algorithm places all the
 prototypes in the two clusters. The algorithm does not achieve a magnification
 factor proportional to the density of the data. This nice property only occurs
 for low dimensions (below 5). By selecting an exponent closer to 1, this property
 is more closely achieves for high dimensions, but still fails for data dimensions
 above 20D.