################################################################################
# Peach - Computational Intelligence for Python
# Jose Alexandre Nalon
#
# This file: tutorial/fuzzy-c-means.py
# Basic example of Fuzzy C-Means
################################################################################
# We import numpy for arrays and peach for the library. Actually, peach also
# imports the numpy module, but we want numpy in a separate namespace:
from numpy import *
import peach as p
# We create the example list (the training set) and the corresponding membership
# values for each example. There are 15 two-dimensional examples, and 15 pairs
# of membership values. This means that each example will be classified in two
# classes, with the corresponding membership values. This means that the vector
# [ 0, 0 ] will be classified with membership values 0.7 in the first class and
# membership values 0.3 in the second class and so on. Notice that, with this
# values, we expect the two centers, after the clustering, to be located at
# [ 1., 1. ] and [ 6., 6. ].
x = array( [
[ 0., 0. ], [ 0., 1. ], [ 0., 2. ], [ 1., 0. ], [ 1., 1. ], [ 1., 2. ],
[ 2., 0. ], [ 2., 1. ], [ 2., 2. ], [ 5., 5. ], [ 5., 6. ], [ 5., 7. ],
[ 6., 5. ], [ 6., 6. ], [ 6., 7. ], [ 7., 5. ], [ 7., 6. ], [ 7., 7. ] ] )
mu = array( [
[ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.7, 0.3 ],
[ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.7, 0.3 ], [ 0.3, 0.7 ],
[ 0.3, 0.7 ], [ 0.3, 0.7 ], [ 0.3, 0.7 ], [ 0.3, 0.7 ], [ 0.3, 0.7 ],
[ 0.3, 0.7 ], [ 0.3, 0.7 ], [ 0.3, 0.7 ] ] )
# Notice that the starting values for the memberships could be randomly choosen,
# at least for simple cases like this. You could try the lines below to
# initialize the membership array:
#
# from numpy.random import random
# mu = random((18, 1))
# mu = hstack((mu, 1.-mu))
# This parameter measures the smoothness of convergence
m = 2.0
# We create the algorithm. We must pass, in this order, the example set, the
# corresponding membership values, and the parameter `m`. This parameter is
# optional, though, and if not given, will default to 2.
fcm = p.FuzzyCMeans(x, mu, m)
# The __call__ interface runs the algorithm till completion. It returns the
# center of the classification. If we want to check the membership values for
# the vectors, the .mu instance variable can be checked. Notice that we pass the
# parameter emax = 0 to the algorithm. This is the maximum error accepted. In
# general, fuzzy c-means will converge very fastly and with little error. A
# imax parameter -- the maximum number of iterations, can also be given. If it
# isn't given, 20 iterations will be assumed.
print "After 20 iterations, the algorithm converged to the centers:"
print fcm(emax=0)
print
print "The membership values for the examples are given below:"
print fcm.mu
print