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Fuzzy Clustering

Pengertian Fuzzy Clustering

Fuzzy C-Means (FCM) merupakan teknik meengelompokan data yang keberadaan data dalam suatu kelompok ditentukan oleh nilai atau derajat keanggotaan tertentu.

berikut adalah algoritma dari FCM:

<pre>
  https://docs.google.com/spreadsheets/d/1evBtIV5M6rlFC9bljB9d0laFhv3qqoo4/edit#gid=1325169538
</pre>

berikut contoh code program fuzzy C-Means:

​```python
from __future__ import division, print_function
import numpy as np
import matplotlib.pyplot as plt
import skfuzzy as fuzz

colors = ['b', 'orange', 'g', 'r', 'c', 'm', 'y', 'k', 'Brown', 'ForestGreen']


centers = [[4, 2],
           [1, 7],
           [5, 6]]


sigmas = [[0.8, 0.3],
          [0.3, 0.5],
          [1.1, 0.7]]


np.random.seed(42) 
xpts = np.zeros(1)
ypts = np.zeros(1)
labels = np.zeros(1)
for i, ((xmu, ymu), (xsigma, ysigma)) in enumerate(zip(centers, sigmas)):
    xpts = np.hstack((xpts, np.random.standard_normal(200) * xsigma + xmu))
    ypts = np.hstack((ypts, np.random.standard_normal(200) * ysigma + ymu))
    labels = np.hstack((labels, np.ones(200) * i))

fig0, ax0 = plt.subplots()
for label in range(3):
    ax0.plot(xpts[labels == label], ypts[labels == label], '.',
             color=colors[label])
ax0.set_title('Test data: 200 points x3 clusters.')

fig2, ax2 = plt.subplots()
ax2.plot(np.r_[2:11], fpcs)
ax2.set_xlabel("Number of centers")
ax2.set_ylabel("Fuzzy partition coefficient")

cntr, u_orig, _, _, _, _, _ = fuzz.cluster.cmeans(
    alldata, 3, 2, error=0.005, maxiter=1000)

# Show 3-cluster model
fig2, ax2 = plt.subplots()
ax2.set_title('Trained model')
for j in range(3):
    ax2.plot(alldata[0, u_orig.argmax(axis=0) == j],
             alldata[1, u_orig.argmax(axis=0) == j], 'o',
             label='series ' + str(j))
ax2.legend()

newdata = np.random.uniform(0, 1, (1100, 2)) * 10

u, u0, d, jm, p, fpc = fuzz.cluster.cmeans_predict(
    newdata.T, cntr, 2, error=0.005, maxiter=1000)

cluster_membership = np.argmax(u, axis=0)  

fig3, ax3 = plt.subplots()
ax3.set_title('Random points classifed according to known centers')
for j in range(3):
    ax3.plot(newdata[cluster_membership == j, 0],
             newdata[cluster_membership == j, 1], 'o',
             label='series ' + str(j))
ax3.legend()

plt.show()