48. Fuzzy C Means (FCM) using simple example and Python

Опубликовано: 18 Февраль 2026
на канале: The Academician

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Fuzzy c Means (FCM) using simple example and Python
https://github.com/TheAcademcian/fuzz...

#Fuzzy c means clustering algorithm
import numpy as np, numpy.random
from scipy.spatial import distance
k = 2
p = 5

X = np.array([
[1,1,2,1],
[2,1,2,3],
[2,2,4,5],
[50,42,2,83],
[51,43,1,82],
[51,44,3,89],
[53,40,8,80]])

Print the number of data and dimension
n = len(X)
d = len(X[0])
addZeros = np.zeros((n, 1))
X = np.append(X, addZeros, axis=1)
print("The FCM algorithm: \n")
print("The training data: \n", X)
print("\nTotal number of data: ",n)
print("Total number of features: ",d)
print("Total number of Clusters: ",k)

Create an empty array of centers
C = np.zeros((k,d+1))
#print(C)

Randomly initialize the weight matrix
weight = np.random.dirichlet(np.ones(k),size=n)
print("\nThe initial weight: \n", np.round(weight,2))

for it in range(3): # Total number of iterations

Compute centroid
for j in range(k):
denoSum = sum(np.power(weight[:,j],2))

sumMM =0
for i in range(n):
mm = np.multiply(np.power(weight[i,j],p),X[i,:])
sumMM +=mm
cc = sumMM/denoSum
C[j] = np.reshape(cc,d+1)

#print("\nUpdating the fuzzy pseudo partition")
for i in range(n):
denoSumNext = 0
for j in range(k):
denoSumNext += np.power(1/distance.euclidean(C[j,0:d], X[i,0:d]),1/(p-1))
for j in range(k):
w = np.power((1/distance.euclidean(C[j,0:d], X[i,0:d])),1/(p-1))/denoSumNext
weight[i,j] = w

print("\nThe final weights: \n", np.round(weight,2))

for i in range(n):
cNumber = np.where(weight[i] == np.amax(weight[i]))
X[i,d] = cNumber[0]

print("\nThe data with cluster number: \n", X)

SSE = 0
for j in range(k):
for i in range(n):
SSE += np.power(weight[i,j],p)*distance.euclidean(C[j,0:d], X[i,0:d])

print("\nSSE: ",np.round(SSE,4))