Module fcmpy.ml.hebbian.nhl_algorithm
For more information and details about the algorithm, please refer to Unsupervised learning techniques for fine-tuning fuzzy cognitive map causal links Elpiniki I. Papageorgioua,, Chrysostomos Styliosb, Peter P. Groumposa
Expand source code
'''
For more information and details about the algorithm, please refer to
Unsupervised learning techniques for fine-tuning fuzzy cognitive
map causal links
Elpiniki I. Papageorgioua,, Chrysostomos Styliosb, Peter P. Groumposa
'''
import numpy as np
import math
import copy
class NHL:
def __init__(self, nConcept, e=None, n=None, gamma=None, h=None, lbd=None, beta=None):
self.n = n if n is not None else 0.1 # learning rate
self.gamma = gamma if gamma is not None else 0.98 # decay coef
self.h = h if h is not None else 0 # tanh coef
self.lbd = lbd if lbd is not None else 1 # steepness of continuous function
self.termination1 = False
self.termination2 = False
self.termination3 = False
self.W = np.zeros([1, nConcept, nConcept]) # initial W matrix
self.A = np.zeros([1, nConcept]) # initial A matrix
self.doc = [] # list of indexes which nodes are doc nodes
self.doc_values = {} # np array with min max value or dictionay with 2 values for each key
self.e = e if e is not None else 0.002 # termination2 coefficient
self.steps = 0
self.nConcept = nConcept
# or create a dictionary with parameters that is being checked each sept (or e.g. 100 steps) if the algorithm
# doesnt finish update the dictionary
def add_node(self, node, val, doc=False, doc_values=None, prt=False):
'''
:param node: node index
:param val: value of the node
:param doc: bool val if it is DOC
:param doc_values: doc value as [t_min,t_max]
:param prt: print the array of the nodes
Adding the nodes to the map, we should add all the nodes before adding edges
make sure you add not more nodes then you define when creating nhl
e.g.
map = nhl(nConcepts = ...,...)
map.add(1,0.8,doc = [0.7,0.86])
'''
# check if it is the beginning of the simulation
if self.steps != 0:
raise Exception('cannot change the node values during the simulation')
# checking if the values are the numbers
try:
float(node)
float(val)
except ValueError:
raise Exception('node and val have to be numbers')
# add the val to the initial activitation values
self.A[0, node] = val
if doc is True:
# check for the if DOC values were added
if doc_values is None or len(doc_values) != 2:
raise Exception('you have to define DOC upper and ')
# check for the if DOC values were added
try:
float(doc_values[0])
float(doc_values[1])
except ValueError:
raise Exception('lower and upper bound have to number in the array')
self.doc.append(node)
self.doc_values[node] = doc_values
# if prt is true, show the values of A
if prt is True:
print(self.A)
def add_edge(self, source, target, value, prt=False):
'''
:param source: index of the source node
:param target: index of target node
:param value: value of the edge (including sign
:param prt: print the weight array
Adding the edge between 2 nodes, we can define whether:
- increament of source will cause increment of target ( value >0)
- increament of source will cause decrement of target ( value <0)
e.g.
map = nhl(nConcepts = ...,...)
map.add_node(1,0.8,doc=True,doc_values = [0.7,0.86])
map.add_node(2,0.5)
map.add_edge(1,2,-.8)
'''
# checking if node exist
try:
self.A[0,source]
self.A[0, target]
except IndexError:
raise Exception('one of the nodes doesnt exist')
try:
float(value)
except ValueError:
raise Exception('value is not a number')
self.W[0, source, target] = value
# show values of W
if prt is True:
print(self.W)
def update_node(self, function=None):
'''
:param i: which concept, i.e. which column in weights
updates node each step, we can indicate which function we want to use as an update function,
most of HB algorithms are using sigmoid function, so it is defined as default. However, since some articles are
proposing use of tanh, we also included this option here
e.g.
map.update_node(1)
'''
edge = 0
if function is None or function == 'sigmoid':
self.A[-1] = 1/(1 + np.exp(-self.lbd*(self.A[-2] + self.A[-2]@self.W[-2]))) # + np.sum((self.W[-2].T*self.A[-2]).T,axis=1)))
elif (function == 'tangens') or (function == 'tanh') or (function == 'tan'):
self.A[self.steps, i] = math.tanh(A)
def update_edge(self):
'''
:param i: index of the target node
:param j: index of the source node
option: 1,2,3
in the literature many different functions were proposed, the function 1 and 2 are basically the same, however
they in the option 2, we function sgn is not used
the option 3 is taken from another articles
e.g.
'''
self.W[-1] = self.gamma*self.W[-2] + self.n * (np.abs(self.sgn(self.W[0]))*self.A[-2])* ((np.abs(self.sgn(self.W[0])).T*self.A[-2]).T-self.sgn(self.W[0])*self.W[-2]*np.abs(self.sgn(self.W[0]))*self.A[-2])
def termination(self):
'''
:return: if termination conditionas are satifying
checking if simulation is completed
'''
# changing for or
if self.termination1 and self.termination2:
return True
else:
return False
def update_termination(self):
'''
updating termination conditions each step
the values of termination conditions are False as default
after each step the function is checking for 2 termination conditions i.e.
- if the cost function value is decreasing
- if change between doc is smaller than defined threshold (default is 0.002)
:param step: which is the current step
'''
if self.steps < 2:
return
# 1st termination condition
self.termination1 = self.f1()
# checking for either one or second term
# check if there was a change between the DOC values greater than e
# term2
if np.all([abs(self.A[-1][i]-self.A[-2][i]) < self.e for i in self.doc]):
self.termination2 = True
@staticmethod
def sgn(X):
'''
function used to veryfiy if the sig of the weight is the same for output weights as it is for input weights
'''
W = copy.deepcopy(X)
with np.nditer(W, op_flags=['readwrite']) as it:
for x in it:
if x > 0:
x[...] = 1
elif x < 0:
x[...] = -1
elif x == 0:
x[...] = 0
return W
def next_step(self):
'''
next step of the function
increasing the dimension of np array for A and W
'''
# increase step value and dimensions of A and W
self.steps += 1
# add new axis to W and A and assign the value to 0
self.W = np.resize(self.W, [self.steps + 1, self.W.shape[1], self.W.shape[2]])
self.W[self.steps] = np.zeros([self.W.shape[1], self.W.shape[2]])
self.A = np.resize(self.A, [self.steps + 1, self.A.shape[1]])
self.A[self.steps] = np.zeros([1, self.A.shape[1]])
@staticmethod
def sign(x):
if x < 0:
return -1
if x == 0:
return 0
return 1
def f1(self):
# since we are trying to minimizng F1, we should stop when the derivative is small (e.g. less than 0.1)
score = 0
for doc in self.doc_values.keys():
t = sum(self.doc_values[doc])/2
if (math.sqrt((self.A[-1,doc]-t)**2)<math.sqrt((self.A[-2,doc]-t)**2)) and (self.doc_values[doc][0] <= self.A[-1,doc] and self.doc_values[doc][1] >= self.A[-1,doc]):
score +=1
return score == len(self.doc)Classes
class NHL (nConcept, e=None, n=None, gamma=None, h=None, lbd=None, beta=None)-
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class NHL: def __init__(self, nConcept, e=None, n=None, gamma=None, h=None, lbd=None, beta=None): self.n = n if n is not None else 0.1 # learning rate self.gamma = gamma if gamma is not None else 0.98 # decay coef self.h = h if h is not None else 0 # tanh coef self.lbd = lbd if lbd is not None else 1 # steepness of continuous function self.termination1 = False self.termination2 = False self.termination3 = False self.W = np.zeros([1, nConcept, nConcept]) # initial W matrix self.A = np.zeros([1, nConcept]) # initial A matrix self.doc = [] # list of indexes which nodes are doc nodes self.doc_values = {} # np array with min max value or dictionay with 2 values for each key self.e = e if e is not None else 0.002 # termination2 coefficient self.steps = 0 self.nConcept = nConcept # or create a dictionary with parameters that is being checked each sept (or e.g. 100 steps) if the algorithm # doesnt finish update the dictionary def add_node(self, node, val, doc=False, doc_values=None, prt=False): ''' :param node: node index :param val: value of the node :param doc: bool val if it is DOC :param doc_values: doc value as [t_min,t_max] :param prt: print the array of the nodes Adding the nodes to the map, we should add all the nodes before adding edges make sure you add not more nodes then you define when creating nhl e.g. map = nhl(nConcepts = ...,...) map.add(1,0.8,doc = [0.7,0.86]) ''' # check if it is the beginning of the simulation if self.steps != 0: raise Exception('cannot change the node values during the simulation') # checking if the values are the numbers try: float(node) float(val) except ValueError: raise Exception('node and val have to be numbers') # add the val to the initial activitation values self.A[0, node] = val if doc is True: # check for the if DOC values were added if doc_values is None or len(doc_values) != 2: raise Exception('you have to define DOC upper and ') # check for the if DOC values were added try: float(doc_values[0]) float(doc_values[1]) except ValueError: raise Exception('lower and upper bound have to number in the array') self.doc.append(node) self.doc_values[node] = doc_values # if prt is true, show the values of A if prt is True: print(self.A) def add_edge(self, source, target, value, prt=False): ''' :param source: index of the source node :param target: index of target node :param value: value of the edge (including sign :param prt: print the weight array Adding the edge between 2 nodes, we can define whether: - increament of source will cause increment of target ( value >0) - increament of source will cause decrement of target ( value <0) e.g. map = nhl(nConcepts = ...,...) map.add_node(1,0.8,doc=True,doc_values = [0.7,0.86]) map.add_node(2,0.5) map.add_edge(1,2,-.8) ''' # checking if node exist try: self.A[0,source] self.A[0, target] except IndexError: raise Exception('one of the nodes doesnt exist') try: float(value) except ValueError: raise Exception('value is not a number') self.W[0, source, target] = value # show values of W if prt is True: print(self.W) def update_node(self, function=None): ''' :param i: which concept, i.e. which column in weights updates node each step, we can indicate which function we want to use as an update function, most of HB algorithms are using sigmoid function, so it is defined as default. However, since some articles are proposing use of tanh, we also included this option here e.g. map.update_node(1) ''' edge = 0 if function is None or function == 'sigmoid': self.A[-1] = 1/(1 + np.exp(-self.lbd*(self.A[-2] + self.A[-2]@self.W[-2]))) # + np.sum((self.W[-2].T*self.A[-2]).T,axis=1))) elif (function == 'tangens') or (function == 'tanh') or (function == 'tan'): self.A[self.steps, i] = math.tanh(A) def update_edge(self): ''' :param i: index of the target node :param j: index of the source node option: 1,2,3 in the literature many different functions were proposed, the function 1 and 2 are basically the same, however they in the option 2, we function sgn is not used the option 3 is taken from another articles e.g. ''' self.W[-1] = self.gamma*self.W[-2] + self.n * (np.abs(self.sgn(self.W[0]))*self.A[-2])* ((np.abs(self.sgn(self.W[0])).T*self.A[-2]).T-self.sgn(self.W[0])*self.W[-2]*np.abs(self.sgn(self.W[0]))*self.A[-2]) def termination(self): ''' :return: if termination conditionas are satifying checking if simulation is completed ''' # changing for or if self.termination1 and self.termination2: return True else: return False def update_termination(self): ''' updating termination conditions each step the values of termination conditions are False as default after each step the function is checking for 2 termination conditions i.e. - if the cost function value is decreasing - if change between doc is smaller than defined threshold (default is 0.002) :param step: which is the current step ''' if self.steps < 2: return # 1st termination condition self.termination1 = self.f1() # checking for either one or second term # check if there was a change between the DOC values greater than e # term2 if np.all([abs(self.A[-1][i]-self.A[-2][i]) < self.e for i in self.doc]): self.termination2 = True @staticmethod def sgn(X): ''' function used to veryfiy if the sig of the weight is the same for output weights as it is for input weights ''' W = copy.deepcopy(X) with np.nditer(W, op_flags=['readwrite']) as it: for x in it: if x > 0: x[...] = 1 elif x < 0: x[...] = -1 elif x == 0: x[...] = 0 return W def next_step(self): ''' next step of the function increasing the dimension of np array for A and W ''' # increase step value and dimensions of A and W self.steps += 1 # add new axis to W and A and assign the value to 0 self.W = np.resize(self.W, [self.steps + 1, self.W.shape[1], self.W.shape[2]]) self.W[self.steps] = np.zeros([self.W.shape[1], self.W.shape[2]]) self.A = np.resize(self.A, [self.steps + 1, self.A.shape[1]]) self.A[self.steps] = np.zeros([1, self.A.shape[1]]) @staticmethod def sign(x): if x < 0: return -1 if x == 0: return 0 return 1 def f1(self): # since we are trying to minimizng F1, we should stop when the derivative is small (e.g. less than 0.1) score = 0 for doc in self.doc_values.keys(): t = sum(self.doc_values[doc])/2 if (math.sqrt((self.A[-1,doc]-t)**2)<math.sqrt((self.A[-2,doc]-t)**2)) and (self.doc_values[doc][0] <= self.A[-1,doc] and self.doc_values[doc][1] >= self.A[-1,doc]): score +=1 return score == len(self.doc)Static methods
def sgn(X)-
function used to veryfiy if the sig of the weight is the same for output weights as it is for input weights
Expand source code
@staticmethod def sgn(X): ''' function used to veryfiy if the sig of the weight is the same for output weights as it is for input weights ''' W = copy.deepcopy(X) with np.nditer(W, op_flags=['readwrite']) as it: for x in it: if x > 0: x[...] = 1 elif x < 0: x[...] = -1 elif x == 0: x[...] = 0 return W def sign(x)-
Expand source code
@staticmethod def sign(x): if x < 0: return -1 if x == 0: return 0 return 1
Methods
def add_edge(self, source, target, value, prt=False)-
:param source: index of the source node :param target: index of target node :param value: value of the edge (including sign :param prt: print the weight array
Adding the edge between 2 nodes, we can define whether: - increament of source will cause increment of target ( value >0) - increament of source will cause decrement of target ( value <0) e.g. map = nhl(nConcepts = …,…) map.add_node(1,0.8,doc=True,doc_values = [0.7,0.86]) map.add_node(2,0.5) map.add_edge(1,2,-.8)
Expand source code
def add_edge(self, source, target, value, prt=False): ''' :param source: index of the source node :param target: index of target node :param value: value of the edge (including sign :param prt: print the weight array Adding the edge between 2 nodes, we can define whether: - increament of source will cause increment of target ( value >0) - increament of source will cause decrement of target ( value <0) e.g. map = nhl(nConcepts = ...,...) map.add_node(1,0.8,doc=True,doc_values = [0.7,0.86]) map.add_node(2,0.5) map.add_edge(1,2,-.8) ''' # checking if node exist try: self.A[0,source] self.A[0, target] except IndexError: raise Exception('one of the nodes doesnt exist') try: float(value) except ValueError: raise Exception('value is not a number') self.W[0, source, target] = value # show values of W if prt is True: print(self.W) def add_node(self, node, val, doc=False, doc_values=None, prt=False)-
:param node: node index :param val: value of the node :param doc: bool val if it is DOC :param doc_values: doc value as [t_min,t_max] :param prt: print the array of the nodes
Adding the nodes to the map, we should add all the nodes before adding edges make sure you add not more nodes then you define when creating nhl e.g. map = nhl(nConcepts = …,…) map.add(1,0.8,doc = [0.7,0.86])
Expand source code
def add_node(self, node, val, doc=False, doc_values=None, prt=False): ''' :param node: node index :param val: value of the node :param doc: bool val if it is DOC :param doc_values: doc value as [t_min,t_max] :param prt: print the array of the nodes Adding the nodes to the map, we should add all the nodes before adding edges make sure you add not more nodes then you define when creating nhl e.g. map = nhl(nConcepts = ...,...) map.add(1,0.8,doc = [0.7,0.86]) ''' # check if it is the beginning of the simulation if self.steps != 0: raise Exception('cannot change the node values during the simulation') # checking if the values are the numbers try: float(node) float(val) except ValueError: raise Exception('node and val have to be numbers') # add the val to the initial activitation values self.A[0, node] = val if doc is True: # check for the if DOC values were added if doc_values is None or len(doc_values) != 2: raise Exception('you have to define DOC upper and ') # check for the if DOC values were added try: float(doc_values[0]) float(doc_values[1]) except ValueError: raise Exception('lower and upper bound have to number in the array') self.doc.append(node) self.doc_values[node] = doc_values # if prt is true, show the values of A if prt is True: print(self.A) def f1(self)-
Expand source code
def f1(self): # since we are trying to minimizng F1, we should stop when the derivative is small (e.g. less than 0.1) score = 0 for doc in self.doc_values.keys(): t = sum(self.doc_values[doc])/2 if (math.sqrt((self.A[-1,doc]-t)**2)<math.sqrt((self.A[-2,doc]-t)**2)) and (self.doc_values[doc][0] <= self.A[-1,doc] and self.doc_values[doc][1] >= self.A[-1,doc]): score +=1 return score == len(self.doc) def next_step(self)-
next step of the function increasing the dimension of np array for A and W
Expand source code
def next_step(self): ''' next step of the function increasing the dimension of np array for A and W ''' # increase step value and dimensions of A and W self.steps += 1 # add new axis to W and A and assign the value to 0 self.W = np.resize(self.W, [self.steps + 1, self.W.shape[1], self.W.shape[2]]) self.W[self.steps] = np.zeros([self.W.shape[1], self.W.shape[2]]) self.A = np.resize(self.A, [self.steps + 1, self.A.shape[1]]) self.A[self.steps] = np.zeros([1, self.A.shape[1]]) def termination(self)-
:return: if termination conditionas are satifying
checking if simulation is completed
Expand source code
def termination(self): ''' :return: if termination conditionas are satifying checking if simulation is completed ''' # changing for or if self.termination1 and self.termination2: return True else: return False def update_edge(self)-
:param i: index of the target node :param j: index of the source node option: 1,2,3
in the literature many different functions were proposed, the function 1 and 2 are basically the same, however they in the option 2, we function sgn is not used the option 3 is taken from another articles e.g.
Expand source code
def update_edge(self): ''' :param i: index of the target node :param j: index of the source node option: 1,2,3 in the literature many different functions were proposed, the function 1 and 2 are basically the same, however they in the option 2, we function sgn is not used the option 3 is taken from another articles e.g. ''' self.W[-1] = self.gamma*self.W[-2] + self.n * (np.abs(self.sgn(self.W[0]))*self.A[-2])* ((np.abs(self.sgn(self.W[0])).T*self.A[-2]).T-self.sgn(self.W[0])*self.W[-2]*np.abs(self.sgn(self.W[0]))*self.A[-2]) def update_node(self, function=None)-
:param i: which concept, i.e. which column in weights
updates node each step, we can indicate which function we want to use as an update function, most of HB algorithms are using sigmoid function, so it is defined as default. However, since some articles are proposing use of tanh, we also included this option here e.g. map.update_node(1)
Expand source code
def update_node(self, function=None): ''' :param i: which concept, i.e. which column in weights updates node each step, we can indicate which function we want to use as an update function, most of HB algorithms are using sigmoid function, so it is defined as default. However, since some articles are proposing use of tanh, we also included this option here e.g. map.update_node(1) ''' edge = 0 if function is None or function == 'sigmoid': self.A[-1] = 1/(1 + np.exp(-self.lbd*(self.A[-2] + self.A[-2]@self.W[-2]))) # + np.sum((self.W[-2].T*self.A[-2]).T,axis=1))) elif (function == 'tangens') or (function == 'tanh') or (function == 'tan'): self.A[self.steps, i] = math.tanh(A) def update_termination(self)-
updating termination conditions each step the values of termination conditions are False as default after each step the function is checking for 2 termination conditions i.e. - if the cost function value is decreasing - if change between doc is smaller than defined threshold (default is 0.002) :param step: which is the current step
Expand source code
def update_termination(self): ''' updating termination conditions each step the values of termination conditions are False as default after each step the function is checking for 2 termination conditions i.e. - if the cost function value is decreasing - if change between doc is smaller than defined threshold (default is 0.002) :param step: which is the current step ''' if self.steps < 2: return # 1st termination condition self.termination1 = self.f1() # checking for either one or second term # check if there was a change between the DOC values greater than e # term2 if np.all([abs(self.A[-1][i]-self.A[-2][i]) < self.e for i in self.doc]): self.termination2 = True