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

Fuzzy c Means (FCM) using simple example and Python https://github.com/TheAcademcian/fuzzy-c-means/blob/main/fcmeans.py #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))