"""
S. T. Li, Y. C. Cheng, and S. Y. Lin, “A FCM-based deterministic forecasting model for fuzzy time series,”
Comput. Math. Appl., vol. 56, no. 12, pp. 3052–3063, Dec. 2008. DOI: 10.1016/j.camwa.2008.07.033.
"""
import numpy as np
import pandas as pd
import math
import random as rnd
import functools, operator
from pyFTS.common import FuzzySet, Membership
from pyFTS.partitioners import partitioner
[docs]def fuzzy_distance(x, y):
if isinstance(x, (list, tuple, np.ndarray)):
tmp = functools.reduce(operator.add, [(x[k] - y[k]) ** 2 for k in range(0, len(x))])
else:
tmp = (x - y) ** 2
return math.sqrt(tmp)
[docs]def membership(val, vals):
soma = 0
for k in vals:
if k == 0:
k = 1
soma = soma + (val / k) ** 2
return soma
[docs]def fuzzy_cmeans(k, data, size, m, deltadist=0.001):
data_length = len(data)
# Centroid initialization
centroids = [data[rnd.randint(0, data_length - 1)] for kk in range(0, k)]
# Membership table
membership_table = np.zeros((k, data_length)) #[[0 for kk in range(0, k)] for xx in range(0, data_length)]
mean_change = 1000
m_exp = 1 / (m - 1)
iterations = 0
while iterations < 1000 and mean_change > deltadist:
mean_change = 0
inst_count = 0
for instance in data:
dist_groups = np.zeros(k) #[0 for xx in range(0, k)]
for group_count, group in enumerate(centroids):
dist_groups[group_count] = fuzzy_distance(group, instance)
dist_groups_total = functools.reduce(operator.add, [xk for xk in dist_groups])
for grp in range(0, k):
if dist_groups[grp] == 0:
membership_table[inst_count][grp] = 1
else:
membership_table[inst_count][grp] = 1 / membership(dist_groups[grp], dist_groups)
# membership_table[inst_count][grp] = 1/(dist_groups[grp] / dist_grupos_total)
# membership_table[inst_count][grp] = (1/(dist_groups[grp]**2))**m_exp / (1/(dist_grupos_total**2))**m_exp
inst_count = inst_count + 1
for group_count, group in enumerate(centroids):
if size > 1:
oldgrp = [xx for xx in group]
for atr in range(0, size):
soma = functools.reduce(operator.add,
[membership_table[xk][group_count] * data[xk][atr] for xk in range(0, data_length)])
norm = functools.reduce(operator.add, [membership_table[xk][group_count] for xk in range(0, data_length)])
centroids[group_count][atr] = soma / norm
else:
oldgrp = group
soma = functools.reduce(operator.add,
[membership_table[xk][group_count] * data[xk] for xk in range(0, data_length)])
norm = functools.reduce(operator.add, [membership_table[xk][group_count] for xk in range(0, data_length)])
centroids[group_count] = soma / norm
mean_change = mean_change + fuzzy_distance(oldgrp, group)
mean_change = mean_change / k
iterations = iterations + 1
return centroids
[docs]class FCMPartitioner(partitioner.Partitioner):
"""
"""
def __init__(self, **kwargs):
super(FCMPartitioner, self).__init__(name="FCM", **kwargs)
[docs] def build(self, data):
sets = {}
kwargs = {'type': self.type, 'variable': self.variable}
centroids = fuzzy_cmeans(self.partitions, data, 1, 2)
centroids.append(self.max)
centroids.append(self.min)
centroids = list(set(centroids))
centroids.sort()
for c in np.arange(1, len(centroids) - 1):
_name = self.get_name(c)
if self.membership_function == Membership.trimf:
sets[_name] = FuzzySet.FuzzySet(_name, Membership.trimf,
[round(centroids[c - 1], 3), round(centroids[c], 3),
round(centroids[c + 1], 3)],
round(centroids[c], 3), **kwargs)
elif self.membership_function == Membership.trapmf:
q1 = (round(centroids[c], 3) - round(centroids[c - 1], 3)) / 2
q2 = (round(centroids[c + 1], 3) - round(centroids[c], 3)) / 2
sets[_name] = FuzzySet.FuzzySet(_name, Membership.trimf,
[round(centroids[c - 1], 3), round(centroids[c], 3) - q1,
round(centroids[c], 3) + q2, round(centroids[c + 1], 3)],
round(centroids[c], 3), **kwargs)
return sets