from pyFTS.common import FuzzySet, Membership
import numpy as np
from scipy.spatial import KDTree
[docs]class Partitioner(object):
"""
Universe of Discourse partitioner. Split data on several fuzzy sets
"""
def __init__(self, **kwargs):
"""
Universe of Discourse partitioner scheme. Split data on several fuzzy sets
"""
self.name : str = kwargs.get('name',"")
"""partitioner name"""
self.partitions : int = kwargs.get('npart', 10)
"""The number of universe of discourse partitions, i.e., the number of fuzzy sets that will be created"""
self.sets : dict = {}
"""The fuzzy sets dictionary"""
self.membership_function = kwargs.get('func', Membership.trimf)
"""Fuzzy membership function (pyFTS.common.Membership)"""
self.setnames : list = kwargs.get('names', None)
"""list of partitions names. If None is given the partitions will be auto named with prefix"""
self.prefix : str = kwargs.get('prefix', 'A')
"""prefix of auto generated partition names"""
self.transformation = kwargs.get('transformation', None)
"""data transformation to be applied on data"""
self.indexer = kwargs.get('indexer', None)
self.variable = kwargs.get('variable', None)
"""In a multivariate context, the variable that contains this partitioner"""
self.type : str = kwargs.get('type', 'common')
"""The type of fuzzy sets that are generated by this partitioner"""
self.ordered_sets : list = None
"""A ordered list of the fuzzy sets names, sorted by their middle point"""
self.kdtree : KDTree = None
"""A spatial index to help in fuzzyfication"""
self.margin : float = kwargs.get("margin", 0.1)
"""The upper and lower exceeding margins for the known UoD. The default value is .1"""
self.lower_margin : float = kwargs.get("lower_margin", self.margin)
"""Specific lower exceeding margins for the known UoD. The default value is the self.margin parameter"""
self.upper_margin : float = kwargs.get("lower_margin", self.margin)
"""Specific upper exceeding margins for the known UoD. The default value is the self.margin parameter"""
if kwargs.get('preprocess',True):
data = kwargs.get('data',[None])
if self.indexer is not None:
ndata = self.indexer.get_data(data)
else:
ndata = data
if self.transformation is not None:
ndata = self.transformation.apply(ndata)
else:
ndata = data
if self.indexer is not None:
ndata = self.indexer.get_data(ndata)
_min = np.nanmin(ndata)
if _min == -np.inf:
ndata[ndata == -np.inf] = 0
_min = np.nanmin(ndata)
self.min = float(_min * (1 + self.lower_margin) if _min < 0 else _min * (1 - self.lower_margin))
_max = np.nanmax(ndata)
self.max = float(_max * (1 + self.upper_margin) if _max > 0 else _max * (1 - self.upper_margin))
self.sets = self.build(ndata)
self.partitions = len(self.sets)
if self.ordered_sets is None and self.setnames is not None:
self.ordered_sets = self.setnames[:len(self.sets)]
else:
self.ordered_sets = FuzzySet.set_ordered(self.sets)
del(ndata)
[docs] def build(self, data):
"""
Perform the partitioning of the Universe of Discourse
:param data: training data
:return:
"""
pass
[docs] def get_name(self, counter):
"""
Find the name of the fuzzy set given its counter id.
:param counter: The number of the fuzzy set
:return: String
"""
return self.prefix + str(counter) if self.setnames is None else self.setnames[counter]
[docs] def lower_set(self):
"""
Return the fuzzy set on lower bound of the universe of discourse.
:return: Fuzzy Set
"""
return self.sets[self.ordered_sets[0]]
[docs] def upper_set(self):
"""
Return the fuzzy set on upper bound of the universe of discourse.
:return: Fuzzy Set
"""
return self.sets[self.ordered_sets[-1]]
[docs] def build_index(self):
points = []
#self.index = {}
for ct, key in enumerate(self.ordered_sets):
fset = self.sets[key]
points.append([fset.lower, fset.centroid, fset.upper])
#self.index[ct] = fset.name
import sys
sys.setrecursionlimit(100000)
self.kdtree = KDTree(points)
sys.setrecursionlimit(1000)
[docs] def fuzzyfy(self, data, **kwargs):
"""
Fuzzyfy the input data according to this partitioner fuzzy sets.
:param data: input value to be fuzzyfied
:keyword alpha_cut: the minimal membership value to be considered on fuzzyfication (only for mode='sets')
:keyword method: the fuzzyfication method (fuzzy: all fuzzy memberships, maximum: only the maximum membership)
:keyword mode: the fuzzyfication mode (sets: return the fuzzy sets names, vector: return a vector with the membership
values for all fuzzy sets, both: return a list with tuples (fuzzy set, membership value) )
:returns a list with the fuzzyfied values, depending on the mode
"""
if isinstance(data, (tuple, list, np.ndarray)):
ret = []
for inst in data:
mv = self.fuzzyfy(inst, **kwargs)
ret.append(mv)
return ret
alpha_cut = kwargs.get('alpha_cut', 0.)
mode = kwargs.get('mode', 'sets')
method = kwargs.get('method', 'fuzzy')
nearest = self.search(data, type='index')
mv = np.zeros(self.partitions)
for ix in nearest:
tmp = self[ix].membership(data)
mv[ix] = tmp if tmp >= alpha_cut else 0.
ix = np.ravel(np.argwhere(mv > 0.))
if ix.size == 0:
mv[self.check_bounds(data)] = 1.
if method == 'fuzzy' and mode == 'vector':
return mv
elif method == 'fuzzy' and mode == 'sets':
try:
ix = np.ravel(np.argwhere(mv > 0.))
sets = [self.ordered_sets[i] for i in ix if i < self.partitions]
return sets
except Exception as ex:
return None
elif method == 'maximum' and mode == 'sets':
mx = max(mv)
ix = np.ravel(np.argwhere(mv == mx))
return self.ordered_sets[ix[0]]
elif mode == 'both':
ix = np.ravel(np.argwhere(mv > 0.))
sets = [(self.ordered_sets[i], mv[i]) for i in ix]
return sets
[docs] def defuzzyfy(self, values, mode='both'):
if not isinstance(values, list):
values = [values]
num = []
den = []
for val in values:
fset = val[0]
mv = val[1]
if mode == 'both':
num.append( self.sets[fset].centroid * mv )
den.append(mv)
elif mode == 'sets':
num.append(self.sets[fset].centroid)
elif mode == 'vector':
num.append(self.sets[self.ordered_sets[fset]].centroid * mv)
den.append(mv)
else:
raise Exception('Unknown deffuzyfication mode')
if mode in ('both','vector'):
return np.nansum(num) / np.nansum(den)
else:
return np.nanmean(num)
[docs] def check_bounds(self, data):
"""
Check if the input data is outside the known Universe of Discourse and, if it is, round it to the closest
fuzzy set.
:param data: input data to be verified
:return: the index of the closest fuzzy set when data is outside de universe of discourse or None if
the data is inside the UoD.
"""
if data < self.min:
return 0
elif data > self.max:
return self.partitions-1
[docs] def search(self, data, **kwargs):
"""
Perform a search for the nearest fuzzy sets of the point 'data'. This function were designed to work with several
overlapped fuzzy sets.
:param data: the value to search for the nearest fuzzy sets
:param type: the return type: 'index' for the fuzzy set indexes or 'name' for fuzzy set names.
:param results: the number of nearest fuzzy sets to return
:return: a list with the nearest fuzzy sets
"""
if self.kdtree is None:
self.build_index()
type = kwargs.get('type','index')
results = kwargs.get('results', 3)
_, ix = self.kdtree.query([data, data, data], results)
if type == 'name':
return [self.ordered_sets[k] for k in sorted(ix)]
else:
return sorted(ix)
[docs] def plot(self, ax, rounding=0):
"""
Plot the partitioning using the Matplotlib axis ax
:param ax: Matplotlib axis
"""
ax.set_title(self.name)
ax.set_ylim([0, 1.1])
ax.set_xlim([self.min, self.max])
ticks = []
x = []
for key in self.sets.keys():
s = self.sets[key]
if s.type == 'common':
self.plot_set(ax, s)
elif s.type == 'composite':
for ss in s.sets:
self.plot_set(ax, ss)
ticks.append(str(round(s.centroid,rounding))+'\n'+s.name)
x.append(s.centroid)
ax.xaxis.set_ticklabels(ticks)
ax.xaxis.set_ticks(x)
[docs] def plot_set(self, ax, s):
"""
Plot an isolate fuzzy set on Matplotlib axis
:param ax: Matplotlib axis
:param s: Fuzzy Set
"""
if s.mf == Membership.trimf:
ax.plot([s.parameters[0], s.parameters[1], s.parameters[2]], [0, s.alpha, 0])
elif s.mf in (Membership.gaussmf, Membership.bellmf, Membership.sigmf):
tmpx = np.linspace(s.lower, s.upper, 100)
tmpy = [s.membership(kk) for kk in tmpx]
ax.plot(tmpx, tmpy)
elif s.mf == Membership.trapmf:
ax.plot(s.parameters, [0, s.alpha, s.alpha, 0])
elif s.mf == Membership.singleton:
ax.plot([s.parameters[0],s.parameters[0]], [0, s.alpha])
def __str__(self):
"""
Return a string representation of the partitioner, the list of fuzzy sets and their parameters
:return:
"""
tmp = self.name + ":\n"
for key in self.sets.keys():
tmp += str(self.sets[key])+ "\n"
return tmp
def __len__(self):
"""
Return the number of partitions
:return: number of partitions
"""
return self.partitions
def __getitem__(self, item):
"""
Return a fuzzy set by its order or its name.
:param item: If item is an integer then it represents the fuzzy set index (order), if it was a string then
it represents the fuzzy set name.
:return: the fuzzy set
"""
if isinstance(item, (int, np.int, np.int8, np.int16, np.int32, np.int64)):
if item < 0 or item >= self.partitions:
raise ValueError("The fuzzy set index must be between 0 and {}.".format(self.partitions))
return self.sets[self.ordered_sets[item]]
elif isinstance(item, str):
if item not in self.sets:
raise ValueError("The fuzzy set with name {} does not exist.".format(item))
return self.sets[item]
else:
raise ValueError("The parameter 'item' must be an integer or a string and the value informed was {} of type {}!".format(item, type(item)))
def __iter__(self):
"""
Iterate over the fuzzy sets, ordered by its midpoints.
:return: An iterator over the fuzzy sets.
"""
for key in self.ordered_sets:
yield self.sets[key]