Merge pull request #26 from murilocamargos/master

Add subtractive clustering technique as partitioning method

pyFTS/partitioners/SubClust.py

@@ -0,0 +1,96 @@
+"""
+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
+
+
+def imax(vec):
+    i = np.argmax(vec)
+    return (i, vec[i])
+
+
+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
+
+
+class SubClustPartitioner(partitioner.Partitioner):
+    """SubClust 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)
+
+    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