ibradje / pfcm

Possiblistic Fuzzy C-Means Algorithm in Python

PFCM

Possiblistic Fuzzy C-Means Algorithm in Python

• Algorithm explanation : https://www.researchgate.net/publication/3336300_A_Possibilistic_Fuzzy_C-Means_Clustering_Algorithm

• Implementation of the algorithm MATLAB : https://www.ijser.org/researchpaper/implementation-of-possibilistic-fuzzy-cmeans-clustering-algorithm-in-matlab.pdf

  Parameters for the main function (pfcm):

  • data: Dataset to be clustered, with size M-by-N, where M is the number of data points and N is the number of coordinates for each data point.
  • c : Number of clusters
  • expo : exponent for the U matrix (default = 2)
  • max_iter : Maximum number of iterations (default = 1000)
  • min_impor : Minimum amount of imporvement (default = 0.005)
  • a : User-defined constant a (default = 1)
  • b : User-defined constant b that should be greater than a (default = 4)
  • nc : User-defined constant nc (default = 2)

  The clustering process stops when the maximum number of iterations is reached, or when objective function improvement or the maximum centers imporvement between two consecutive iterations is less than the minimum amount specified.

  Return values :

  • cntr : The clusters centers
  • U : The C-Partionned Matrix (used in FCM)
  • T : The Typicality Matrix (used in PCM)
  • obj_fcn : The objective function for U and T

  ---

  Parameters of the PFCM Prediction function (pfcm_predict)

  • data: Dataset to be clustered, with size M-by-N, where M is the number of data points and N is the number of coordinates for each data point.
  • cntr : centers of the dataset previoulsy calculated
  • expo : exponent for the U matrix (default = 2)
  • a : User-defined constant a (default = 1)
  • b : User-defined constant b that should be greater than a (default = 4)
  • nc : User-defined constant nc (default = 2)
  The algortihm predicts which clusters the new dataset belongs to
  
  Return values :
  • new_cntr : The new clusters centers
  • U : The C-Partionned Matrix (used in FCM)
  • T : The Typicality Matrix (used in PCM)
  • obj_fcn : The objective function for U and T

pfcm's Issues

Add epsilon to avoid divide by 0

It would be good to add a small number like epsilon = 0.000000001 or something to the pdistfcm function and whenever you have a denominator that could be 0.

def pdistfcm(cntr, data):
    out = np.zeros(shape=(cntr.shape[0], data.shape[0]))
    for k in range(cntr.shape[0]):
        out[k] = np.sqrt(np.sum((np.power(data-cntr[k], 2)).T, axis=0)) + 0.000000000001 #add eps to avoid divide by 0
    return out

Typo in equation for U update

Equation 21 in the PFCM paper has an exponent of 2/(m-1) which SHOULD correspond to 2/(expo-1), but you have 2/(nc-1) in the code. I believe this is a typo in both the predict and pfcm functions.

gpu acceleration

Hello,

First of all, thank you very much for sharing this project. Just one suggestion: could you transform your project to large scale kmeans with GPU capacity? I think it will be quicker when we choose a big number of clusters. What do you think?

Reference:
https://github.com/src-d/kmcuda

Brain MRI Segmentation

Hi, thank you for sharing. What should I change with these codes if I want to segment such a brain MRI (181*217, bmp)which is shown as follow? Looking forward to your reply. Thanks.