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| import numpy
import gzip
import struct
import matplotlib
from sklearn import datasets
from copy import copy
class SVM:
def __init__(self, constant, data_set, label_set):
self._N = len(data_set)
if self._N != len(label_set):
raise Exception("Data size and label size don't match.")
self._C = constant
self._epsilon = 0.001
self._tol = 0.001
self._data = [numpy.ndarray.flatten((1/255)*elt) for elt in data_set]
self._dimension = len(self._data[0])
self._label = label_set
self._alphas = numpy.zeros((1, self._N))
self._b = 0
self._errors = numpy.ndarray((2, 0))
def kernel(self, x1, x2):
x1 = x1.reshape(1,self._dimension)
result = numpy.power(numpy.dot(x1, x2), 3)
return result
def evaluate(self, x):
result = 0
i = 0
while i < self._N:
result += self._alphas[0, i]*self._label[i]*self.kernel(x, self._data[i])
i += 1
result += self._b
return result
def update(self, i1, i2, E2):
i1 = int(i1)
i2 = int(i2)
if i1 == i2:
return 0
y1 = self._label[i1]
y2 = self._label[i2]
alpha1 = self._alphas[0, i1]
alpha2 = self._alphas[0, i2]
#If alpha1 is non-bound, its error is in the cache.
#So we check its position to extract its error.
#Else, we compute it.
if alpha1 > 0 and alpha1 < self._C :
position = 0
for i, elt in enumerate(self._errors[0, :]):
if elt == i1:
position = i
E1 = self._errors[1, position]
else:
E1 = self.evaluate(self._data[i1]) - y1
s = y1*y2
H = L = 0
if y1 != y2:
L = max(0, alpha2 - alpha1)
H = min(self._C, self._C + alpha2 - alpha1)
else:
L = max(0, alpha2 + alpha1 - self._C)
H = min(self._C, alpha2 + alpha1)
if H == L:
return 0
K11 = self.kernel(self._data[i1], self._data[i1])
K12 = self.kernel(self._data[i1], self._data[i2])
K22 = self.kernel(self._data[i2], self._data[i2])
eta = K11 + K22 - 2*K12
if eta > 0:
alpha2_new = alpha2 + (y2*(E1 - E2)/eta)
if alpha2_new < L:
alpha2_new = L
elif alpha2_new > H:
alpha2_new = H
else:
f1 = y1*(E1 + self._b) - alpha1*K11 - s*alpha2*K12
f2 = y2*(E2 + self._b) - alpha2*K22 - s*alpha1*K12
L1 = alpha1 + s*(alpha2 - L)
H1 = alpha1 + s*(alpha2 - H)
FuncL = L1*f1 + L*f2 + (1/2)*numpy.square(L1)*K11 + (1/2)*numpy.square(L)*K22 + s*L1*L*K12
FuncH = H1*f1 + H*f2 + (1/2)*numpy.square(H1)*K11 + (1/2)*numpy.square(H)*K22 + s*H1*H*K12
if FuncL < FuncH - self._epsilon:
alpha2_new = L
elif FuncL > FuncH + self._epsilon:
alpha2_new = H
else:
alpha2_new = alpha2
if numpy.abs(alpha2_new - alpha2) < self._epsilon*(alpha2_new+alpha2+ self._epsilon):
return 0
alpha1_new = alpha1 + s*(alpha2 - alpha2_new)
#Update of the threshold.
b1 = E1 + y1*(alpha1_new - alpha1)*K11 + y2*(alpha2_new - alpha2)*K12 + self._b
b2 = E2 + y1*(alpha1_new - alpha1)*K12 + y2*(alpha2_new - alpha2)*K22 + self._b
if L < alpha1_new < H:
b_new = b1
elif L < alpha2_new < H:
b_new = b2
else:
b_new = (b1+b2)/2
#Update the cache error
#If alpha2 was bound and its new value is non-bound, we add its index and its error to the cache.
#If alpha2 was unbound and its new value is bound, we delete it from the cache.
if (alpha2 == 0 or alpha2 == self._C) and (alpha2_new > 0 and alpha2_new < self._C):
vector_alpha2_new = numpy.array([i2, E2])
vector_alpha2_new = vector_alpha2_new.reshape((2, 1))
self._errors = numpy.concatenate((self._errors, vector_alpha2_new), 1)
if (alpha2 > 0 and alpha2 < self._C) and (alpha2_new == 0 or alpha2_new == self._C):
l = 0
position = 0
while l < len(self._errors[0, :]):
if self._errors[0, l] == i2:
position = l
l += 1
self._errors = numpy.delete(self._errors, position, 1)
#We do the exact same thing with alpha1.
if (alpha1 == 0 or alpha1 == self._C) and (alpha1_new > 0 and alpha1_new < self._C):
vector_alpha1_new = numpy.array([i1, E1])
vector_alpha1_new = vector_alpha1_new.reshape((2, 1))
self._errors = numpy.concatenate((self._errors, vector_alpha1_new), 1)
if (alpha1 > 0 and alpha1 < self._C) and (alpha1_new == 0 or alpha1_new == self._C):
l = 0
position = 0
while l < len(self._errors[0, :]):
if self._errors[0, l] == i1:
position = l
l += 1
self._errors = numpy.delete(self._errors, position, 1)
#Then we update the error for each non bound point using the new values for alpha1 and alpha2.
for i,error in enumerate(self._errors[1, :]):
self._errors[1, i] = error + (alpha2_new - alpha2)*y2*self.kernel(self._data[i2], self._data[int(self._errors[0, i])]) + (alpha1_new - alpha1)*y1*self.kernel(self._data[i1], self._data[int(self._errors[0, i])]) - self._b + b_new
#Storing the new values of alpha1 and alpha2:
self._alphas[0, i1] = alpha1_new
self._alphas[0, i2] = alpha2_new
self._b = b_new
print(self._errors)
return 1
def examineExample(self, i2):
i2 = int(i2)
y2 = self._label[i2]
alpha2 = self._alphas[0, i2]
if alpha2 > 0 and alpha2 < self._C:
position = 0
for i, elt in enumerate(self._errors[0, :]):
if elt == i2:
position = i
E2 = self._errors[1, position]
else:
E2 = self.evaluate(self._data[i2]) - y2
r2 = E2*y2
if (r2< -self._tol and alpha2 < self._C) or (r2 > self._tol and alpha2 > 0):
n = numpy.shape(self._errors)[1]
if n > 1:
i1 = 0
if E2 > 0:
min = self._errors[1, 0]
position = 0
for l, elt in enumerate(self._errors[1, :]):
if elt < min:
min = elt
position = l
i1 = self._errors[0, position]
else:
max = self._errors[1, 0]
position = 0
for l, elt in enumerate(self._errors[1, :]):
if elt > max:
max = elt
position = l
i1 = self._errors[0, position]
if self.update(i1, i2, E2):
return 1
#loop over all non bound examples starting at a random point.
list_index = [i for i in range(n)]
numpy.random.shuffle(list_index)
for i in list_index:
i1 = self._errors[0, i]
if self.update(i1, i2, E2):
return 1
#Loop over all the training examples, starting at a random point.
list_bound = [i for i in range(self._N) if not numpy.any(self._errors[0, :] == i)]
numpy.random.shuffle(list_bound)
for i in list_bound:
i1 = i
if self.update(i1, i2, E2):
return 1
return 0
def SMO(self):
numChanged = 0
examineAll = 1
cpt = 1
while(numChanged > 0 or examineAll):
numChanged = 0
if examineAll == 1:
for i in range(self._N):
numChanged += self.examineExample(i)
else:
for i in self._errors[0, :]:
numChanged += self.examineExample(i)
if examineAll == 1:
examineAll = 0
elif numChanged == 0:
examineAll = 1
cpt += 1
def load_training_data(a, b):
train = gzip.open("train-images-idx3-ubyte.gz", "rb")
labels = gzip.open("train-labels-idx1-ubyte.gz", "rb")
train.read(4)
labels.read(4)
number_images = train.read(4)
number_images = struct.unpack(">I", number_images)[0]
rows = train.read(4)
rows = struct.unpack(">I", rows)[0]
cols = train.read(4)
cols = struct.unpack(">I", cols)[0]
number_labels = labels.read(4)
number_labels = struct.unpack(">I", number_labels)[0]
image_list = []
label_list = []
if number_images != number_labels:
raise Exception("The number of labels doesn't match with the number of images")
else:
for l in range(number_labels):
if l % 1000 == 0:
print("l:{}".format(l))
mat = numpy.zeros((rows, cols), dtype = numpy.uint8)
for i in range(rows):
for j in range(cols):
pixel = train.read(1)
pixel = struct.unpack(">B", pixel)[0]
mat[i][j] = pixel
image_list += [mat]
lab = labels.read(1)
lab = struct.unpack(">B", lab)[0]
label_list += [lab]
train.close()
labels.close()
i = 0
index_a = []
index_b = []
while i < number_labels:
if label_list[i] == a:
index_a += [i]
elif label_list[i] == b:
index_b += [i]
i += 1
image_list = [m for i,m in enumerate(image_list) if (i in index_a) | (i in index_b)]
mean = (a+b)/2
label_list = [ numpy.sign(m - mean) for l,m in enumerate(label_list) if l in index_a+index_b]
return ([image_list, label_list])
def load_test_data():
test = gzip.open("t10k-images-idx3-ubyte.gz", "rb")
labels = gzip.open("t10k-labels-idx1-ubyte.gz", "rb")
test.read(4)
labels.read(4)
number_images = test.read(4)
number_images = struct.unpack(">I", number_images)[0]
rows = test.read(4)
rows = struct.unpack(">I", rows)[0]
cols = test.read(4)
cols = struct.unpack(">I", cols)[0]
number_labels = labels.read(4)
number_labels = struct.unpack(">I", number_labels)[0]
image_list = []
label_list = []
if number_images != number_labels:
raise Exception("The number of labels doesn't match with the number of images")
else:
for l in range(number_labels):
if l % 1000 == 0:
print("l:{}".format(l))
mat = numpy.zeros((rows, cols), dtype = numpy.uint8)
for i in range(rows):
for j in range(cols):
pixel = test.read(1)
pixel = struct.unpack(">B", pixel)[0]
mat[i][j] = pixel
image_list += [mat]
lab = labels.read(1)
lab = struct.unpack(">B", lab)[0]
label_list += [lab]
test.close()
labels.close()
return ([image_list, label_list])
data = load_training_data(0, 7)
images_training = data[0]
labels_training = data[1]
svm = SVM(0.1, images_training[0:200], labels_training[0:200])
svm.SMO()
def view(image, label=""):
print("Number : {}".format(label))
pylab.imshow(image, cmap = pylab.cm.gray)
pylab.show() |
