"""
High Order FTS
Severiano, S. A. Jr; Silva, P. C. L.; Sadaei, H. J.; Guimarães, F. G. Very Short-term Solar Forecasting
using Fuzzy Time Series. 2017 IEEE International Conference on Fuzzy Systems. DOI10.1109/FUZZ-IEEE.2017.8015732
"""
import numpy as np
from pyFTS.common import FuzzySet, FLR, fts, flrg
from itertools import product
[docs]class HighOrderFLRG(flrg.FLRG):
"""Conventional High Order Fuzzy Logical Relationship Group"""
def __init__(self, order, **kwargs):
super(HighOrderFLRG, self).__init__(order, **kwargs)
self.LHS = []
self.RHS = {}
self.strlhs = ""
[docs] def append_rhs(self, c, **kwargs):
if c not in self.RHS:
self.RHS[c] = c
[docs] def append_lhs(self, c):
if isinstance(c,(tuple,list)):
for k in c:
self.LHS.append(k)
else:
self.LHS.append(c)
def __str__(self):
tmp = ""
for c in sorted(self.RHS):
if len(tmp) > 0:
tmp = tmp + ","
tmp = tmp + c
return self.get_key() + " -> " + tmp
def __len__(self):
return len(self.RHS)
[docs]class WeightedHighOrderFLRG(flrg.FLRG):
"""Weighted High Order Fuzzy Logical Relationship Group"""
def __init__(self, order, **kwargs):
super(WeightedHighOrderFLRG, self).__init__(order, **kwargs)
self.LHS = []
self.RHS = {}
self.count = 0.0
self.strlhs = ""
self.w = None
[docs] def append_rhs(self, fset, **kwargs):
count = kwargs.get('count',1.0)
if fset not in self.RHS:
self.RHS[fset] = count
else:
self.RHS[fset] += count
self.count += count
[docs] def append_lhs(self, c):
self.LHS.append(c)
[docs] def weights(self):
if self.w is None:
self.w = np.array([self.RHS[c] / self.count for c in self.RHS.keys()])
return self.w
[docs] def get_midpoint(self, sets):
if self.midpoint is None:
mp = np.array([sets[c].centroid for c in self.RHS.keys()])
self.midpoint = mp.dot(self.weights())
return self.midpoint
[docs] def get_lower(self, sets):
if self.lower is None:
lw = np.array([sets[s].lower for s in self.RHS.keys()])
self.lower = lw.dot(self.weights())
return self.lower
[docs] def get_upper(self, sets):
if self.upper is None:
up = np.array([sets[s].upper for s in self.RHS.keys()])
self.upper = up.dot(self.weights())
return self.upper
def __str__(self):
_str = ""
for k in self.RHS.keys():
_str += ", " if len(_str) > 0 else ""
_str += k + " (" + str(round(self.RHS[k] / self.count, 3)) + ")"
return self.get_key() + " -> " + _str
def __len__(self):
return len(self.RHS)
[docs]class HighOrderFTS(fts.FTS):
"""Conventional High Order Fuzzy Time Series"""
def __init__(self, **kwargs):
super(HighOrderFTS, self).__init__(**kwargs)
self.name = "High Order FTS"
self.shortname = "HOFTS"
self.detail = "Severiano, Silva, Sadaei and Guimarães"
self.is_high_order = True
self.min_order = 1
self.order= kwargs.get("order", self.min_order)
self.configure_lags(**kwargs)
[docs] def generate_lhs_flrg(self, sample, explain=False):
nsample = [self.partitioner.fuzzyfy(k, mode="sets", alpha_cut=self.alpha_cut)
for k in sample]
if explain:
self.append_log("Fuzzyfication","{} -> {}".format(sample, nsample))
return self.generate_lhs_flrg_fuzzyfied(nsample, explain)
[docs] def generate_lhs_flrg_fuzzyfied(self, sample, explain=False):
lags = []
flrgs = []
for ct, o in enumerate(self.lags):
lhs = sample[o - 1]
lags.append(lhs)
if explain:
self.append_log("Ordering Lags", "Lag {} Value {}".format(o, lhs))
# Trace the possible paths
for path in product(*lags):
flrg = HighOrderFLRG(self.order)
for lhs in path:
flrg.append_lhs(lhs)
flrgs.append(flrg)
return flrgs
[docs] def generate_flrg(self, data):
_tmp_steps = self.standard_horizon - 1
l = len(data)
for k in np.arange(self.max_lag, l - _tmp_steps):
if self.dump: print("FLR: " + str(k))
sample = data[k - self.max_lag: k]
rhs = self.partitioner.fuzzyfy(data[k+_tmp_steps], mode="sets", alpha_cut=self.alpha_cut)
flrgs = self.generate_lhs_flrg(sample)
for flrg in flrgs:
if flrg.get_key() not in self.flrgs:
self.flrgs[flrg.get_key()] = flrg;
for st in rhs:
self.flrgs[flrg.get_key()].append_rhs(st)
[docs] def generate_flrg_fuzzyfied(self, data):
_tmp_steps = self.standard_horizon - 1
l = len(data)
for k in np.arange(self.max_lag, l):
if self.dump: print("FLR: " + str(k))
sample = data[k - self.max_lag: k]
rhs = data[k+_tmp_steps]
flrgs = self.generate_lhs_flrg_fuzzyfied(sample)
for flrg in flrgs:
if flrg.get_key() not in self.flrgs:
self.flrgs[flrg.get_key()] = flrg
for st in rhs:
self.flrgs[flrg.get_key()].append_rhs(st)
[docs] def train(self, data, **kwargs):
self.configure_lags(**kwargs)
if not kwargs.get('fuzzyfied',False):
self.generate_flrg(data)
else:
self.generate_flrg_fuzzyfied(data)
[docs] def forecast(self, ndata, **kwargs):
explain = kwargs.get('explain', False)
fuzzyfied = kwargs.get('fuzzyfied', False)
mode = kwargs.get('mode', 'mean')
ret = []
l = len(ndata) if not explain else self.max_lag + 1
if l < self.max_lag:
return ndata
elif l == self.max_lag:
l += 1
for k in np.arange(self.max_lag, l):
sample = ndata[k - self.max_lag: k]
if not fuzzyfied:
flrgs = self.generate_lhs_flrg(sample, explain)
else:
flrgs = self.generate_lhs_flrg_fuzzyfied(sample, explain)
midpoints = []
memberships = []
for flrg in flrgs:
if flrg.get_key() not in self.flrgs:
if len(flrg.LHS) > 0:
mp = self.partitioner.sets[flrg.LHS[-1]].centroid
mv = self.partitioner.sets[flrg.LHS[-1]].membership(sample[-1]) if not fuzzyfied else None
midpoints.append(mp)
memberships.append(mv)
if explain:
self.append_log("Rule Matching", "{} -> {} (Naïve) Midpoint: {}".format(str(flrg.LHS), flrg.LHS[-1],
mp))
else:
flrg = self.flrgs[flrg.get_key()]
mp = flrg.get_midpoint(self.partitioner.sets)
mv = flrg.get_membership(sample, self.partitioner.sets) if not fuzzyfied else None
midpoints.append(mp)
memberships.append(mv)
if explain:
self.append_log("Rule Matching", "{}, Midpoint: {} Membership: {}".format(flrg.get_key(), mp, mv))
if mode == "mean" or fuzzyfied:
final = np.nanmean(midpoints)
if explain: self.append_log("Deffuzyfication", "By Mean: {}".format(final))
else:
final = np.dot(midpoints, memberships)/np.nansum(memberships)
if explain: self.append_log("Deffuzyfication", "By Memberships: {}".format(final))
ret.append(final)
return ret
[docs]class WeightedHighOrderFTS(HighOrderFTS):
"""Weighted High Order Fuzzy Time Series"""
def __init__(self, **kwargs):
super(WeightedHighOrderFTS, self).__init__(**kwargs)
self.name = "Weighted High Order FTS"
self.shortname = "WHOFTS"
[docs] def generate_lhs_flrg_fuzzyfied(self, sample, explain=False):
lags = []
flrgs = []
for ct, o in enumerate(self.lags):
lags.append(sample[o-1])
if explain:
print("\t (Lag {}) {} \n".format(o, sample[o-1]))
# Trace the possible paths
for path in product(*lags):
flrg = WeightedHighOrderFLRG(self.order)
for lhs in path:
flrg.append_lhs(lhs)
flrgs.append(flrg)
return flrgs