def predict_rfmm_distance(V, W, classId, XhT, patClassIdTest, gama=1):
"""
prediction using the distance in the paper "A refined Fuzzy min-max neural network with new learning procedure for pattern classification"
"""
if len(XhT.shape) == 1:
XhT = XhT.reshape(1, -1)
#initialization
yX = XhT.shape[0]
predicted_class = np.full(yX, None)
misclass = np.zeros(yX)
mem = np.zeros((yX, V.shape[0]))
# classifications
for i in range(yX):
mem[i, :] = simpsonMembership(
XhT[i, :], V, W, gama) # calculate memberships for all hyperboxes
bmax = mem[i, :].max() # get max membership value
maxVind = np.nonzero(mem[i, :] == bmax)[
0] # get indexes of all hyperboxes with max membership
if len(np.unique(classId[maxVind])) > 1:
misclass[i] = True
else:
misclass[i] = ~(np.any(classId[maxVind] == patClassIdTest[i]))
if len(np.unique(classId[maxVind])) > 1:
#print("Using Manhattan function")
XgT_mat = np.ones((len(maxVind), 1)) * XhT[i]
# compute the distance from XgT_mat to all average points of all hyperboxes with the same membership value
dist = rfmm_distance(XgT_mat, V[maxVind], W[maxVind])
id_min_dist = dist.argmin()
predicted_class[i] = classId[maxVind[id_min_dist]]
if classId[maxVind[id_min_dist]] == patClassIdTest[i]:
misclass[i] = False
else:
misclass[i] = True
else:
predicted_class[i] = classId[maxVind[0]]
if classId[maxVind[0]] == patClassIdTest[i]:
misclass[i] = False
else:
misclass[i] = True
# results
summis = np.sum(misclass).astype(np.int64)
result = Bunch(summis=summis,
misclass=misclass,
predicted_class=predicted_class)
return result
def predict(V,
W,
classId,
XhT,
patClassIdTest,
gama=1,
is_using_manhattan=True):
"""
FMNN classifier (test routine)
result = predict(V,W,classId,XhT,patClassIdTest,gama)
INPUT
V Tested model hyperbox lower bounds
W Tested model hyperbox upper bounds
classId Input data (hyperbox) class labels (crisp)
XhT Test input data (rows = objects, columns = features)
patClassIdTest Test data class labels (crisp)
gama Membership function slope (default: 1)
OUTPUT
result A object with Bunch datatype containing all results as follows:
+ summis Number of misclassified objects
+ misclass Binary error map
+ sumamb Number of objects with maximum membership in more than one class
+ out Soft class memberships
+ mem Hyperbox memberships
"""
if len(XhT.shape) == 1:
XhT = XhT.reshape(1, -1)
#initialization
yX = XhT.shape[0]
predicted_class = np.full(yX, None)
misclass = np.zeros(yX)
mem = np.zeros((yX, V.shape[0]))
# classifications
for i in range(yX):
mem[i, :] = simpsonMembership(
XhT[i, :], V, W, gama) # calculate memberships for all hyperboxes
bmax = mem[i, :].max() # get max membership value
maxVind = np.nonzero(mem[i, :] == bmax)[
0] # get indexes of all hyperboxes with max membership
winner_cls = np.unique(classId[maxVind])
if len(winner_cls) > 1:
if is_using_manhattan == True:
#print("Using Manhattan function")
XgT_mat = np.ones((len(maxVind), 1)) * XhT[i]
# Find all average points of all hyperboxes with the same membership value
avg_point_mat = (V[maxVind] + W[maxVind]) / 2
# compute the manhattan distance from XgT_mat to all average points of all hyperboxes with the same membership value
maht_dist = manhattan_distance(avg_point_mat, XgT_mat)
id_min_dist = maht_dist.argmin()
predicted_class[i] = classId[maxVind[id_min_dist]]
else:
# select random class
predicted_class[i] = rd.choice(winner_cls)
if predicted_class[i] == patClassIdTest[i]:
misclass[i] = False
else:
misclass[i] = True
else:
predicted_class[i] = classId[maxVind[0]]
if predicted_class[i] == patClassIdTest[i]:
misclass[i] = False
else:
misclass[i] = True
# results
summis = np.sum(misclass).astype(np.int64)
result = Bunch(summis=summis,
misclass=misclass,
predicted_class=predicted_class)
return result
def predict(V, W, classId, XhT, patClassIdTest, gama = 1):
"""
FMNN classifier (test routine)
result = predict(V,W,classId,XhT,patClassIdTest,gama)
INPUT
V Tested model hyperbox lower bounds
W Tested model hyperbox upper bounds
classId Input data (hyperbox) class labels (crisp)
XhT Test input data (rows = objects, columns = features)
patClassIdTest Test data class labels (crisp)
gama Membership function slope (default: 1)
OUTPUT
result A object with Bunch datatype containing all results as follows:
+ summis Number of misclassified objects
+ misclass Binary error map
+ sumamb Number of objects with maximum membership in more than one class
+ out Soft class memberships
+ mem Hyperbox memberships
"""
if len(XhT.shape) == 1:
XhT = XhT.reshape(1, -1)
#initialization
yX = XhT.shape[0]
misclass = np.zeros(yX)
classes = np.unique(classId)
noClasses = classes.size
ambiguity = np.zeros(yX)
mem = np.zeros((yX, V.shape[0]))
out = np.zeros((yX, noClasses))
# classifications
for i in range(yX):
mem[i, :] = simpsonMembership(XhT[i, :], V, W, gama) # calculate memberships for all hyperboxes
bmax = mem[i,:].max() # get max membership value
maxVind = np.nonzero(mem[i,:] == bmax)[0] # get indexes of all hyperboxes with max membership
for j in range(noClasses):
out[i, j] = mem[i, classId == classes[j]].max() # get max memberships for each class
ambiguity[i] = np.sum(out[i, :] == bmax) # number of different classes with max membership
if bmax == 0:
print('zero maximum membership value') # this is probably bad...
# misclass[i] = ~(np.any(classId[maxVind] == patClassIdTest[i]))
#
if len(np.unique(classId[maxVind])) > 1:
misclass[i] = True
else:
misclass[i] = ~(np.any(classId[maxVind] == patClassIdTest[i]))
# results
sumamb = np.sum(ambiguity > 1)
summis = np.sum(misclass).astype(np.int64)
result = Bunch(summis = summis, misclass = misclass, sumamb = sumamb, out = out, mem = mem)
return result
def fit(self, Xh, patClassId):
"""
Training the classifier
Xh Input data (rows = objects, columns = features)
patClassId Input data class labels (crisp). patClassId[i] = 0 corresponds to an unlabeled item
"""
print('--Online Learning for Simpson' 's FMNN--')
if self.isNorm == True:
Xh = self.dataPreprocessing(Xh)
time_start = time.perf_counter()
yX, xX = Xh.shape
mark = np.array([
'*', 'o', 'x', '+', '.', ',', 'v', '^', '<', '>', '1', '2', '3',
'4', '8', 's', 'p', 'P', 'h', 'H', 'X', 'D', '|', '_'
])
mark_col = np.array(['r', 'g', 'b', 'y', 'c', 'm', 'k'])
listLines = list()
if self.isDraw:
drawing_canvas = self.initializeCanvasGraph(
"FMNN - Simpson's fuzzy min-max neural network", xX)
if self.V.size > 0:
# draw existed hyperboxes
color_ = np.array(['k'] * len(self.classId), dtype=object)
for c in range(len(self.classId)):
if self.classId[c] < len(mark_col):
color_[c] = mark_col[self.classId[c]]
hyperboxes = drawbox(self.V[:, 0:np.minimum(xX, 3)],
self.W[:, 0:np.minimum(xX, 3)],
drawing_canvas, color_)
listLines.extend(hyperboxes)
self.delay()
# for each input sample
for i in range(yX):
classOfX = patClassId[i]
# draw input samples
if self.isDraw:
color_ = 'k'
if classOfX < len(mark_col):
color_ = mark_col[classOfX]
marker_ = 'd'
if classOfX < len(mark):
marker_ = mark[classOfX]
if xX == 2:
drawing_canvas.plot(Xh[i, 0],
Xh[i, 1],
color=color_,
marker=marker_)
else:
drawing_canvas.plot([Xh[i, 0]], [Xh[i, 1]], [Xh[i, 2]],
color=color_,
marker=marker_)
self.delay()
if self.V.size == 0: # no model provided - starting from scratch
self.V = np.array([Xh[0]])
self.W = np.array([Xh[0]])
self.classId = np.array([patClassId[0]])
if self.isDraw == True:
# draw hyperbox
box_color = 'k'
if patClassId[0] < len(mark_col):
box_color = mark_col[patClassId[0]]
hyperbox = drawbox(
np.asmatrix(self.V[0, 0:np.minimum(xX, 3)]),
np.asmatrix(self.W[0, 0:np.minimum(xX, 3)]),
drawing_canvas, box_color)
listLines.append(hyperbox[0])
self.delay()
else:
idSameClassOfX = np.nonzero(self.classId == classOfX)[0]
# Find all hyperboxes same class with indexOfX
V1 = self.V[idSameClassOfX]
if len(V1) > 0:
W1 = self.W[idSameClassOfX]
b = simpsonMembership(Xh[i], V1, W1, self.gamma)
max_mem_id = np.argmax(b)
# store the index of the winner hyperbox in the list of all hyperboxes of all classes
j = idSameClassOfX[max_mem_id]
if b[max_mem_id] != 1:
adjust = False
# test violation of max hyperbox size and class labels
if (np.maximum(self.W[j], Xh[i]) - np.minimum(
self.V[j], Xh[i])).sum() <= self.teta * xX:
# adjust the j-th hyperbox
self.V[j] = np.minimum(self.V[j], Xh[i])
self.W[j] = np.maximum(self.W[j], Xh[i])
indOfWinner = j
adjust = True
if self.isDraw:
# Handle drawing graph
box_color = 'k'
if self.classId[j] < len(mark_col):
box_color = mark_col[self.classId[j]]
try:
listLines[j].remove()
except:
pass
hyperbox = drawbox(
np.asmatrix(self.V[j,
0:np.minimum(xX, 3)]),
np.asmatrix(self.W[j,
0:np.minimum(xX, 3)]),
drawing_canvas, box_color)
listLines[j] = hyperbox[0]
self.delay()
# if i-th sample did not fit into any existing box, create a new one
if not adjust:
self.V = np.vstack((self.V, Xh[i]))
self.W = np.vstack((self.W, Xh[i]))
self.classId = np.append(self.classId, classOfX)
if self.isDraw:
# handle drawing graph
box_color = 'k'
if self.classId[-1] < len(mark_col):
box_color = mark_col[self.classId[-1]]
hyperbox = drawbox(
np.asmatrix(Xh[i, 0:np.minimum(xX, 3)]),
np.asmatrix(Xh[i, 0:np.minimum(xX, 3)]),
drawing_canvas, box_color)
listLines.append(hyperbox[0])
self.delay()
elif self.V.shape[0] > 1:
for ii in range(self.V.shape[0]):
if ii != indOfWinner:
caseDim = hyperboxOverlapTest(
self.V, self.W, indOfWinner,
ii) # overlap test
if caseDim.size > 0 and self.classId[
ii] != self.classId[indOfWinner]:
self.V, self.W = hyperboxContraction(
self.V, self.W, caseDim, ii,
indOfWinner)
if self.isDraw:
# Handle graph drawing
boxii_color = boxwin_color = 'k'
if self.classId[ii] < len(
mark_col):
boxii_color = mark_col[
self.classId[ii]]
if self.classId[indOfWinner] < len(
mark_col):
boxwin_color = mark_col[
self.classId[indOfWinner]]
try:
listLines[ii].remove()
listLines[indOfWinner].remove()
except:
pass
hyperboxes = drawbox(
self.V[[ii, indOfWinner],
0:np.minimum(xX, 3)],
self.W[[ii, indOfWinner],
0:np.minimum(xX, 3)],
drawing_canvas,
[boxii_color, boxwin_color])
listLines[ii] = hyperboxes[0]
listLines[
indOfWinner] = hyperboxes[1]
self.delay()
else:
# create a new hyperbox
self.V = np.vstack((self.V, Xh[i]))
self.W = np.vstack((self.W, Xh[i]))
self.classId = np.append(self.classId, classOfX)
if self.isDraw:
# handle drawing graph
box_color = 'k'
if self.classId[-1] < len(mark_col):
box_color = mark_col[self.classId[-1]]
hyperbox = drawbox(
np.asmatrix(Xh[i, 0:np.minimum(xX, 3)]),
np.asmatrix(Xh[i, 0:np.minimum(xX, 3)]),
drawing_canvas, box_color)
listLines.append(hyperbox[0])
self.delay()
time_end = time.perf_counter()
self.elapsed_training_time = time_end - time_start
return self
def pruning_val(self, XTest, patClassIdTest, accuracy_threshold=0.5):
"""
pruning handling based on validation (validation routine) with hyperboxes stored in self. V, W, classId
result = pruning_val(XlT,XuT,patClassIdTest)
INPUT
XlT Test data lower bounds (rows = objects, columns = features)
XuT Test data upper bounds (rows = objects, columns = features)
patClassIdTest Test data class labels (crisp)
accuracy_threshold The minimum accuracy for each hyperbox
"""
#initialization
yX = XTest.shape[0]
mem = np.zeros((yX, self.V.shape[0]))
no_predicted_samples_hyperboxes = np.zeros((len(self.classId), 2))
# classifications
for i in range(yX):
mem[i, :] = simpsonMembership(
XTest[i, :], self.V, self.W,
self.gamma) # calculate memberships for all hyperboxes
bmax = mem[i, :].max() # get max membership value
maxVind = np.nonzero(mem[i, :] == bmax)[
0] # get indexes of all hyperboxes with max membership
if len(maxVind) == 1:
# Only one hyperbox with the highest membership function
if self.classId[maxVind[0]] == patClassIdTest[i]:
no_predicted_samples_hyperboxes[
maxVind[0],
0] = no_predicted_samples_hyperboxes[maxVind[0], 0] + 1
else:
no_predicted_samples_hyperboxes[
maxVind[0],
1] = no_predicted_samples_hyperboxes[maxVind[0], 1] + 1
else:
# More than one hyperbox with highest membership => random choosing
id_min = maxVind[np.random.randint(len(maxVind))]
if self.classId[id_min] != patClassIdTest[
i] and patClassIdTest[i] != 0:
no_predicted_samples_hyperboxes[
id_min,
1] = no_predicted_samples_hyperboxes[id_min, 1] + 1
else:
no_predicted_samples_hyperboxes[
id_min,
0] = no_predicted_samples_hyperboxes[id_min, 0] + 1
# pruning handling based on the validation results
tmp_no_box = no_predicted_samples_hyperboxes.shape[0]
accuracy_larger_half = np.zeros(tmp_no_box).astype(np.bool)
accuracy_larger_half_keep_nojoin = np.zeros(tmp_no_box).astype(np.bool)
for i in range(tmp_no_box):
if (no_predicted_samples_hyperboxes[i, 0] +
no_predicted_samples_hyperboxes[i, 1] !=
0) and no_predicted_samples_hyperboxes[i, 0] / (
no_predicted_samples_hyperboxes[i, 0] +
no_predicted_samples_hyperboxes[i, 1]
) >= accuracy_threshold:
accuracy_larger_half[i] = True
accuracy_larger_half_keep_nojoin[i] = True
if (no_predicted_samples_hyperboxes[i, 0] +
no_predicted_samples_hyperboxes[i, 1] == 0):
accuracy_larger_half_keep_nojoin[i] = True
# keep one hyperbox for class prunned all
current_classes = np.unique(self.classId)
class_tmp = self.classId[accuracy_larger_half]
for c in current_classes:
if c not in class_tmp:
pos = np.nonzero(self.classId == c)
id_kept = np.random.randint(len(pos))
# keep pos[id_kept]
accuracy_larger_half[pos[id_kept]] = True
# Pruning
V_prun_remove = self.V[accuracy_larger_half]
W_prun_remove = self.W[accuracy_larger_half]
classId_prun_remove = self.classId[accuracy_larger_half]
W_prun_keep = self.W[accuracy_larger_half_keep_nojoin]
V_prun_keep = self.V[accuracy_larger_half_keep_nojoin]
classId_prun_keep = self.classId[accuracy_larger_half_keep_nojoin]
result_prun_remove = predict(V_prun_remove, W_prun_remove,
classId_prun_remove, XTest,
patClassIdTest, self.gamma)
result_prun_keep_nojoin = predict(V_prun_keep, W_prun_keep,
classId_prun_keep, XTest,
patClassIdTest, self.gamma)
if (result_prun_remove.summis <= result_prun_keep_nojoin.summis):
self.V = V_prun_remove
self.W = W_prun_remove
self.classId = classId_prun_remove
else:
self.V = V_prun_keep
self.W = W_prun_keep
self.classId = classId_prun_keep
def fit(self, Xh, patClassId):
"""
Training the classifier
Xh Input data (rows = objects, columns = features)
patClassId Input data class labels (crisp). patClassId[i] = 0 corresponds to an unlabeled item
"""
if self.isNorm == True:
Xh = self.dataPreprocessing(Xh)
time_start = time.clock()
yX, xX = Xh.shape
# for each input sample
for i in range(yX):
classOfX = patClassId[i]
if self.V.size == 0: # no model provided - starting from scratch
self.V = np.array([Xh[0]])
self.W = np.array([Xh[0]])
self.classId = np.array([patClassId[0]])
else:
idSameClassOfX = np.nonzero(self.classId == classOfX)[0]
idDifClassOfX = np.nonzero(self.classId != classOfX)[0]
# Find all hyperboxes same class with indexOfX
V_same = self.V[idSameClassOfX]
V_dif = self.V[idDifClassOfX]
W_dif = self.W[idDifClassOfX]
isCreateNewBox = False
if len(V_same) > 0:
W_same = self.W[idSameClassOfX]
b = simpsonMembership(Xh[i], V_same, W_same, self.gamma)
max_mem_id = np.argmax(b)
# store the index of the winner hyperbox in the list of all hyperboxes of all classes
j = idSameClassOfX[max_mem_id]
if b[max_mem_id] != 1:
adjust = False
# test violation of max hyperbox size and class labels
V_cmp = np.minimum(self.V[j], Xh[i])
W_cmp = np.maximum(self.W[j], Xh[i])
if ((W_cmp - V_cmp) <= self.teta).all() == True:
if is_overlap_general_formulas(
V_dif, W_dif, V_cmp, W_cmp,
False) == False:
# adjust the j-th hyperbox
self.V[j] = V_cmp
self.W[j] = W_cmp
adjust = True
# if i-th sample did not fit into any existing box, create a new one
if not adjust:
self.V = np.vstack((self.V, Xh[i]))
self.W = np.vstack((self.W, Xh[i]))
self.classId = np.append(self.classId, classOfX)
isCreateNewBox = True
else:
# create a new hyperbox
self.V = np.vstack((self.V, Xh[i]))
self.W = np.vstack((self.W, Xh[i]))
self.classId = np.append(self.classId, classOfX)
isCreateNewBox = True
if isCreateNewBox == True and len(V_dif) > 0:
is_ovl, hyperbox_ids_overlap, min_overlap_dimensions = is_overlap_general_formulas(
V_dif, W_dif, self.V[-1], self.W[-1], True)
if is_ovl == True:
# convert hyperbox_ids_overlap of hyperboxes with other classes to ids of all existing hyperboxes
hyperbox_ids_overlap = idDifClassOfX[
hyperbox_ids_overlap]
# do contraction for parent hyperboxes with indices contained in hyperbox_ids_overlap
self.V, self.W, self.classId = hyperbox_contraction_rfmm(
self.V, self.W, self.classId, hyperbox_ids_overlap,
-1, min_overlap_dimensions)
time_end = time.clock()
self.elapsed_training_time = time_end - time_start
return self
