"""
Chiu, Stephen L. "Fuzzy model identification based on cluster estimation." Journal of Intelligent & fuzzy systems 2.3 (1994): 267-278.
"""
import numpy as np
import math
import random as rnd
import functools, operator
from pyFTS.common import FuzzySet, Membership
from pyFTS.partitioners import partitioner
[docs]def imax(vec):
i = np.argmax(vec)
return (i, vec[i])
[docs]def subclust(data, ra, rb, eps_sup, eps_inf):
if len(data.shape) == 1:
data = np.reshape(data, (data.shape[0], 1))
centers = np.zeros((0, data.shape[1]))
# Initial potentials
alpha = 4/ra**2
beta = 4/rb**2
pot = np.zeros(data.shape[0])
for i in range(data.shape[0]):
pot[i] = np.sum(np.exp(-alpha*np.linalg.norm(data - data[i,:], axis=1)**2))
pot_max_i, pot_max = imax(pot)
current_pot_max = pot_max
while current_pot_max:
x_star = data[pot_max_i,:]
accept = False
if current_pot_max > eps_sup * pot_max:
# Accept xk as a cluster center and continue
accept = True
elif current_pot_max <= eps_inf * pot_max:
# Reject xk and end the clustering process
break
else:
d_min = np.min(np.linalg.norm(x_star - centers))
if d_min/ra + current_pot_max/pot_max >= 1:
accept = True
else:
pot[pot_max_i] = 0
pot_max_i, current_pot_max = imax(pot)
if accept:
centers = np.vstack((centers, x_star))
# Recompute potentials
for i in range(data.shape[0]):
new_pot = pot[i] - current_pot_max*np.exp(-beta*np.linalg.norm(x_star - data[i,:])**2)
new_pot = max(0, new_pot)
pot[i] = new_pot
pot_max_i, current_pot_max = imax(pot)
return centers
[docs]class SubClustPartitioner(partitioner.Partitioner):
"""Subtractive Clustering Partitioner"""
def __init__(self, **kwargs):
self.ra = kwargs.get('ra', 0.8)
self.rb = kwargs.get('rb', self.ra * 1.5)
self.eps_sup = kwargs.get('eps_sup', 0.5)
self.eps_inf = kwargs.get('eps_inf', 0.15)
super(SubClustPartitioner, self).__init__(name="SubClust", **kwargs)
[docs] def build(self, data):
sets = {}
kwargs = {'type': self.type, 'variable': self.variable}
partitions = subclust(data, self.ra, self.rb, self.epssup, self.epsinf)
partitions = list(np.reshape(partitions, partitions.shape[0]))
partitions.append(self.min)
partitions.append(self.max)
partitions = list(set(partitions))
partitions.sort()
self.partitions = len(partitions)
for c in np.arange(1, len(partitions)-1):
_name = self.get_name(c-1)
if self.membership_function == Membership.trimf:
sets[_name] = FuzzySet.FuzzySet(_name, Membership.trimf,
[partitions[c - 1], partitions[c], partitions[c + 1]],partitions[c], **kwargs)
elif self.membership_function == Membership.trapmf:
b1 = (partitions[c] - partitions[c - 1])/2
b2 = (partitions[c + 1] - partitions[c]) / 2
sets[_name] = FuzzySet.FuzzySet(_name, Membership.trapmf,
[partitions[c - 1], partitions[c] - b1,
partitions[c] + b2, partitions[c + 1]],
partitions[c], **kwargs)
return sets
