def main():
plot.close('all')
# 0 Read data, selecting digits 3 and 8, dimension reduction
print
print "Read data, selecting digits 3 and 8, dimension reduction"
print
test_path = "test.h5"
training_path = "train.h5"
images_train = vigra.readHDF5(test_path, "images")
labels_train = vigra.readHDF5(test_path, "labels")
images_test = vigra.readHDF5(training_path, "images")
labels_test = vigra.readHDF5(training_path, "labels")
print 'Size of the training set: {}'.format(np.shape(images_train))
print np.shape(labels_train)
print 'Size of the test set: {}'.format(np.shape(images_test))
print np.shape(labels_test)
# Reshape data
n = images_train.shape[0]
d = images_train.shape[1]
images_train = images_train.reshape(n, d * d)
n = images_test.shape[0]
assert d != images_test.shape[
0], 'Test and training sets have different dim'
images_test = images_test.reshape(n, d * d)
# Select 3s and 8s
ind3 = (labels_train == 3)
ind8 = (labels_train == 8)
images_train_38 = images_train[ind3 + ind8]
labels_train_38 = labels_train[ind3 + ind8]
ind3 = (labels_test == 3)
ind8 = (labels_test == 8)
images_test_38 = images_test[ind3 + ind8]
labels_test_38 = labels_test[ind3 + ind8]
# Dimension reduction
rimages_train_38 = dr(images_train_38, labels_train_38, [3, 8])
rimages_test_38 = dr(images_test_38, labels_test_38, [3, 8])
print 'Size of the training set of 3s and 8s: {}'.format(
np.shape(rimages_train_38))
print 'Size of the test set of 3s and 8s: {}'.format(
np.shape(rimages_test_38))
print
print "1 Naive Bayes"
print
print "1.1 Classification"
print
# Training: priors and likelihood for each d=1,2
# for each feature and class individual histograms <=> 4 histogramms
n = rimages_train_38.shape[0]
d = rimages_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(rimages_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 3, L, dx)
p8, pdf8 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 8, L, dx)
rimages_test_38_predict = naiveBayesClassifier(rimages_test_38, \
p3, p8, pdf3, pdf8, L, dx)
ccr_naiveBayes = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(
ccr_naiveBayes)
print 'Error rate on the test set:{}'.format(1 - ccr_naiveBayes)
plot_histogram(pdf3, dx, "Histograms of the class 3", "histograms3.png")
plot_histogram(pdf8, dx, "Histograms of the class 8", "histograms8.png")
plot_likelihood(pdf3, dx, "Likelihoods of the class 3", "likelihoods3.png")
plot_likelihood(pdf8, dx, "Likelihoods of the class 8", "likelihoods8.png")
print
print "1.2 Generate Threes"
print
# use function naiveBayes_train_single_class to compute the likelihood
# for all feature dimension
n = images_train_38.shape[0]
d = images_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(images_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, L, dx)
# generate 3 new threes
new3th = np.zeros((3, d), dtype=np.int32)
for i in range(0, 3):
new3th[i, :] = generate3naiveBayes(pdf3, dx)
img = new3th[i, :].reshape(np.sqrt(d), np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img)
plot.show()
# end for i
print
print "2 Density Tree"
print
print "Naive splitting"
print
tstart = time.time()
# class 3
prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'naive')
DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# class 8
prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'naive')
DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
tstop = time.time()
print "DT learning time (naive splitting) {}".format(tstop - tstart)
tstart = time.time()
rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38, prior3,
prior8, DT3, DT8, [3, 8])
tstop = time.time()
print "DT classification time (naive splitting) {}".format(tstop - tstart)
ccr_DT = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
print 'Error rate on the test set:{}'.format(1 - ccr_DT)
print
print 'Generate new threes: '
d = images_train_38.shape[1]
# new threes
new3th = np.zeros((3, d), dtype=np.int32)
for i in range(0, 3):
new3th[i, :] = generate3DT(images_train_38, labels_train_38, 3)
img = new3th[i, :].reshape(np.sqrt(d), np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img)
plot.show()
# end for i
print
print "Clever splitting"
print
# # class 3
# prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'clever')
# DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# # class 8
# prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'clever')
# DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
#
#
# rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
# prior3, prior8, DT3, DT8, [3,8])
#
# ccr_DT = correctClassRate(rimages_test_38_predict,\
# labels_test_38, [3,8], \
# print_confMatrix = True)
#
# print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
# print 'Error rate on the test set:{}'.format(1-ccr_DT)
#
# print
# print "Generate Threes"
# print
print
print "3 Combine DT and Naive Bayes"
print
n = images_train_38.shape[0]
d = images_train_38.shape[1]
print
print "Learning phase"
print
# train 1D-histogramms for each feature and class
tstart = time.time()
L, dx = chooseBinSize(images_train_38) # number of bins, bins size
# pdf dxL matrices
prior3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, L, dx)
prior8, pdf8 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 8, L, dx)
# compute the cdf of each histogramm
cdf3 = []
cdf8 = []
pdf3sorted = []
pdf8sorted = []
for j in range(0, d):
tmp = np.sort(pdf3[j])
pdf3sorted.append(tmp)
cdf3.append(np.cumsum(tmp))
tmp = np.sort(pdf8[j])
pdf8sorted.append(tmp)
cdf8.append(np.cumsum(tmp))
# end for
tstop = time.time()
print "Learning 1D histograms and computing cdf's took {} sec".\
format(tstop-tstart)
# map data to copula using rank order transformation
u = np.zeros(images_train_38.shape, dtype=np.float32)
for j in range(0, d):
ind = np.argsort(images_train_38[:, j])
u[:, j] = ind[:] / float(n + 1)
# end for j
print
print "Generate threes"
new3th = np.zeros((3, d), dtype=np.int32)
for i in range(0, 3):
u1 = generate3(u, labels_train_38, 3)
for j in range(0, d):
dist = abs(cdf3[j] - u1[j])
binx = np.argsort(dist)
new3th[i, j] = np.floor(dx[j] * binx[0] / 2.)
# end for j
img = new3th[i, :].reshape(np.sqrt(d), np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img)
plot.show()
def main():
plot.close('all')
# 0 Read data, selecting digits 3 and 8, dimension reduction
print
print "Read data, selecting digits 3 and 8, dimension reduction"
print
test_path = "test.h5"
training_path = "train.h5"
images_train = vigra.readHDF5(test_path, "images")
labels_train = vigra.readHDF5(test_path, "labels")
images_test = vigra.readHDF5(training_path, "images")
labels_test = vigra.readHDF5(training_path, "labels")
print 'Size of the training set: {}'.format(np.shape(images_train))
print np.shape(labels_train)
print 'Size of the test set: {}'.format(np.shape(images_test))
print np.shape(labels_test)
# Reshape data
n = images_train.shape[0]
d = images_train.shape[1]
images_train = images_train.reshape(n, d * d)
n = images_test.shape[0]
assert d != images_test.shape[
0], 'Test and training sets have different dim'
images_test = images_test.reshape(n, d * d)
# Select 3s and 8s
ind3 = (labels_train == 3)
ind8 = (labels_train == 8)
images_train_38 = images_train[ind3 + ind8]
labels_train_38 = labels_train[ind3 + ind8]
ind3 = (labels_test == 3)
ind8 = (labels_test == 8)
images_test_38 = images_test[ind3 + ind8]
labels_test_38 = labels_test[ind3 + ind8]
# Dimension reduction
rimages_train_38 = dr(images_train_38, labels_train_38, [3, 8])
rimages_test_38 = dr(images_test_38, labels_test_38, [3, 8])
print 'Size of the training set of 3s and 8s: {}'.format(
np.shape(rimages_train_38))
print 'Size of the test set of 3s and 8s: {}'.format(
np.shape(rimages_test_38))
print
print "1 Naive Bayes"
print
print "1.1 Classification"
print
# Training: priors and likelihood for each d=1,2
# for each feature and class individual histograms <=> 4 histogramms
n = rimages_train_38.shape[0]
d = rimages_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(rimages_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 3, dx, L)
p8, pdf8 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 8, dx, L)
rimages_test_38_predict = naiveBayesClassifier(rimages_test_38, \
p3, p8, pdf3, pdf8, dx)
ccr_naiveBayes = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(
ccr_naiveBayes)
print 'Error rate on the test set:{}'.format(1 - ccr_naiveBayes)
plot_histogram(pdf3, dx, "Histograms of the class 3", "histograms3.png")
plot_histogram(pdf8, dx, "Histograms of the class 8", "histograms8.png")
plot_likelihood(pdf3, dx, "Likelihoods of the class 3", "likelihoods3.png")
plot_likelihood(pdf8, dx, "Likelihoods of the class 8", "likelihoods8.png")
print
print "1.2 Generate Threes"
print
# use function naiveBayes_train_single_class to compute the likelihood
# for all feature dimension
n = images_train_38.shape[0]
d = images_train_38.shape[1]
# Choose bin width
# Choose bin width
L, dx = chooseBinSize(images_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, dx, L)
# generate 5 new threes
new3th = np.zeros((5, d), dtype=np.int32)
for i in range(0, 3):
new3th[i, :] = generate3naiveBayes(pdf3, dx)
img = new3th[i, :].reshape(np.sqrt(d), np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img)
plot.show()
# end for i
print
print "2 Density Tree"
print
print "Naive splitting"
print
# class 3
tstart = time.time()
prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'naive')
DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# class 8
prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'naive')
DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
tstop = time.time()
print "DT learning time (naive splitting) {}".format(tstop - tstart)
tstart = time.time()
rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38, prior3,
prior8, DT3, DT8, [3, 8])
tstop = time.time()
print "DT classification time (naive splitting) {}".format(tstop - tstart)
ccr_DT = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
print 'Error rate on the test set:{}'.format(1 - ccr_DT)
print
print 'Generate new threes: '
print
d = images_train_38.shape[1]
prior3, DT3 = DT_learning(images_train_38, labels_train_38, 3, 'naive')
# new threes
new3th = np.zeros((5, d), dtype=np.int32)
for i in range(0, 3):
new3th[i, :] = generate3DT(DT3, images_train_38, labels_train_38, 3)
img = new3th[i, :].reshape(np.sqrt(d), np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img)
plot.show()
# end for i
print
print "Clever splitting"
print
# # class 3
# prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'clever')
## DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# # class 8
# prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'clever')
## DT_visu alize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
#
#
# rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
# prior3, prior8, DT3, DT8, [3,8])
#
# ccr_DT = correctClassRate(rimages_test_38_predict,\
# labels_test_38, [3,8], \
# print_confMatrix = True)
#
# print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
# print 'Error rate on the test set:{}'.format(1-ccr_DT)
print
print "3 Combine DT and Naive Bayes"
print
n = images_train_38.shape[0]
d = images_train_38.shape[1]
print
print "Learning phase"
print
# train 1D-histogramms for each feature and class
tstart = time.time()
L, dx = chooseBinSize(images_train_38) # number of bins, bins size
# pdf dxL matrices
prior3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, dx, L)
prior8, pdf8 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 8, dx, L)
# compute the cdf of each histogramm
cdf3 = np.zeros(pdf3.shape, dtype=np.float32)
cdf8 = np.zeros(pdf8.shape, dtype=np.float32)
for j in range(0, d):
cdf3[j, :] = np.cumsum(pdf3[j, :])
cdf8[j, :] = np.cumsum(pdf8[j, :])
# end for
tstop = time.time()
print "Learning 1D histograms and computing cdf's took {} sec".\
format(tstop-tstart)
# map data to copula using rank order transformation
u = np.zeros(images_train_38.shape, dtype=np.float32)
for j in range(0, d):
ind = np.sort(images_train_38[:, j])
u[:, j] = ind[:] / float(n + 1)
# end for j
# train a DT on u
tstart = time.time()
prior3, DT3 = DT_learning(u, labels_train_38, 3, 'naive')
prior8, DT8 = DT_learning(u, labels_train_38, 8, 'naive')
tstop = time.time()
print "Learning DTs took {} sec".format(tstop - tstart)
print
print "Classification"
print
ntest = images_test.shape[0]
prediction = np.zeros(ntest, dtype=np.int8)
for i in range(0, n):
x = images_test[i, :]
u3 = np.zeros(d, dtype=np.float32)
u8 = np.zeros(d, dtype=np.float32)
naiveBayesDensity3 = 1.
naiveBayesDensity8 = 1.
for j in range(0, d):
l = np.floor(x[j] / dx[j]) + 1 # bin number
if l > L - 1:
l = L - 1
naiveBayesDensity3 *= pdf3[j, l]
naiveBayesDensity8 *= pdf8[j, l]
u3[j] = cdf3[j, l]
u8[j] = cdf8[j, l]
# end for j
copulaDensity3 = 0
for node in DT3:
if point_in_region(u3, node.region):
copulaDensity3 = node.p
break
# end if
# end for node
copulaDensity8 = 0
for node in DT8:
if point_in_region(u8, node.region):
copulaDensity8 = node.p
break
# end if
# end for node
p_y3_x = naiveBayesDensity3 * copulaDensity3 * prior3
p_y8_x = naiveBayesDensity8 * copulaDensity8 * prior8
# argmax (p_y3_x, p_y8_x)
#print p_y3_x
if p_y3_x > p_y8_x:
prediction[i] = 3
else:
prediction[i] = 8
# end if
# end for i
ccr = correctClassRate(prediction, labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr)
print 'Error rate on the test set:{}'.format(1 - ccr)
def main():
plot.close('all')
# 0 Read data, selecting digits 3 and 8, dimension reduction
print
print "Read data, selecting digits 3 and 8, dimension reduction"
print
test_path = "test.h5"
training_path = "train.h5"
images_train = vigra.readHDF5(test_path, "images")
labels_train = vigra.readHDF5(test_path, "labels")
images_test = vigra.readHDF5(training_path, "images")
labels_test = vigra.readHDF5(training_path, "labels")
print 'Size of the training set: {}'. format(np.shape(images_train))
print np.shape(labels_train)
print 'Size of the test set: {}'. format(np.shape(images_test))
print np.shape(labels_test)
# Reshape data
n = images_train.shape[0]
d = images_train.shape[1]
images_train = images_train.reshape(n,d*d)
n = images_test.shape[0]
assert d!=images_test.shape[0], 'Test and training sets have different dim'
images_test = images_test.reshape(n,d*d)
# Select 3s and 8s
ind3 = (labels_train==3)
ind8 = (labels_train==8)
images_train_38 = images_train[ind3+ind8]
labels_train_38 = labels_train[ind3+ind8]
ind3 = (labels_test==3)
ind8 = (labels_test==8)
images_test_38 = images_test[ind3+ind8]
labels_test_38 = labels_test[ind3+ind8]
# Dimension reduction
rimages_train_38 = dr(images_train_38, labels_train_38, [3,8])
rimages_test_38 = dr(images_test_38, labels_test_38, [3,8])
print 'Size of the training set of 3s and 8s: {}'. format(np.shape(rimages_train_38))
print 'Size of the test set of 3s and 8s: {}'. format(np.shape(rimages_test_38))
print
print "1 Naive Bayes"
print
print "1.1 Classification"
print
# Training: priors and likelihood for each d=1,2
# for each feature and class individual histograms <=> 4 histogramms
n = rimages_train_38.shape[0]
d = rimages_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(rimages_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 3, L, dx)
p8, pdf8 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 8, L, dx)
rimages_test_38_predict = naiveBayesClassifier(rimages_test_38, \
p3, p8, pdf3, pdf8, L, dx)
ccr_naiveBayes = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_naiveBayes)
print 'Error rate on the test set:{}'.format(1-ccr_naiveBayes)
plot_histogram(pdf3, dx, "Histograms of the class 3", "histograms3.png")
plot_histogram(pdf8, dx, "Histograms of the class 8", "histograms8.png")
plot_likelihood(pdf3, dx, "Likelihoods of the class 3", "likelihoods3.png")
plot_likelihood(pdf8, dx, "Likelihoods of the class 8", "likelihoods8.png")
print
print "1.2 Generate Threes"
print
# use function naiveBayes_train_single_class to compute the likelihood
# for all feature dimension
n = images_train_38.shape[0]
d = images_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(images_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, L, dx)
# generate 3 new threes
new3th = np.zeros((3,d), dtype = np.int32)
for i in range(0,3) :
new3th[i,:] = generate3naiveBayes(pdf3, dx)
img = new3th[i,:].reshape(np.sqrt(d),np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img);
plot.show()
# end for i
print
print "2 Density Tree"
print
print "Naive splitting"
print
tstart = time.time()
# class 3
prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'naive')
DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# class 8
prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'naive')
DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
tstop = time.time()
print "DT learning time (naive splitting) {}". format(tstop-tstart)
tstart = time.time()
rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
prior3, prior8, DT3, DT8, [3,8])
tstop = time.time()
print "DT classification time (naive splitting) {}". format(tstop-tstart)
ccr_DT = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
print 'Error rate on the test set:{}'.format(1-ccr_DT)
print
print 'Generate new threes: '
d = images_train_38.shape[1]
# new threes
new3th = np.zeros((3,d), dtype = np.int32)
for i in range(0,3) :
new3th[i,:] = generate3DT(images_train_38, labels_train_38, 3 )
img = new3th[i,:].reshape(np.sqrt(d),np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img);
plot.show()
# end for i
print
print "Clever splitting"
print
# # class 3
# prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'clever')
# DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# # class 8
# prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'clever')
# DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
#
#
# rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
# prior3, prior8, DT3, DT8, [3,8])
#
# ccr_DT = correctClassRate(rimages_test_38_predict,\
# labels_test_38, [3,8], \
# print_confMatrix = True)
#
# print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
# print 'Error rate on the test set:{}'.format(1-ccr_DT)
#
# print
# print "Generate Threes"
# print
print
print "3 Combine DT and Naive Bayes"
print
n = images_train_38.shape[0]
d = images_train_38.shape[1]
print
print "Learning phase"
print
# train 1D-histogramms for each feature and class
tstart = time.time()
L, dx = chooseBinSize(images_train_38) # number of bins, bins size
# pdf dxL matrices
prior3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, L, dx)
prior8, pdf8 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 8, L, dx)
# compute the cdf of each histogramm
cdf3 = []
cdf8 = []
pdf3sorted = []
pdf8sorted = []
for j in range(0, d):
tmp = np.sort(pdf3[j])
pdf3sorted.append(tmp)
cdf3.append(np.cumsum(tmp) )
tmp = np.sort(pdf8[j])
pdf8sorted.append(tmp)
cdf8.append(np.cumsum(tmp) )
# end for
tstop = time.time()
print "Learning 1D histograms and computing cdf's took {} sec".\
format(tstop-tstart)
# map data to copula using rank order transformation
u = np.zeros(images_train_38.shape, dtype = np.float32)
for j in range(0,d):
ind = np.argsort(images_train_38[:,j])
u[:,j] = ind[:]/float(n+1)
# end for j
print
print "Generate threes"
new3th = np.zeros((3,d), dtype = np.int32)
for i in range(0,3) :
u1 = generate3(u, labels_train_38 , 3 )
for j in range(0,d):
dist =abs(cdf3[j] - u1[j])
binx = np.argsort(dist)
new3th[i,j] = np.floor(dx[j]*binx[0]/2.)
# end for j
img = new3th[i,:].reshape(np.sqrt(d),np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img);
plot.show()
def main():
plot.close('all')
# 0 Read data, selecting digits 3 and 8, dimension reduction
print
print "Read data, selecting digits 3 and 8, dimension reduction"
print
test_path = "test.h5"
training_path = "train.h5"
images_train = vigra.readHDF5(test_path, "images")
labels_train = vigra.readHDF5(test_path, "labels")
images_test = vigra.readHDF5(training_path, "images")
labels_test = vigra.readHDF5(training_path, "labels")
print 'Size of the training set: {}'. format(np.shape(images_train))
print np.shape(labels_train)
print 'Size of the test set: {}'. format(np.shape(images_test))
print np.shape(labels_test)
# Reshape data
n = images_train.shape[0]
d = images_train.shape[1]
images_train = images_train.reshape(n,d*d)
n = images_test.shape[0]
assert d!=images_test.shape[0], 'Test and training sets have different dim'
images_test = images_test.reshape(n,d*d)
# Select 3s and 8s
ind3 = (labels_train==3)
ind8 = (labels_train==8)
images_train_38 = images_train[ind3+ind8]
labels_train_38 = labels_train[ind3+ind8]
ind3 = (labels_test==3)
ind8 = (labels_test==8)
images_test_38 = images_test[ind3+ind8]
labels_test_38 = labels_test[ind3+ind8]
# Dimension reduction
rimages_train_38 = dr(images_train_38, labels_train_38, [3,8])
rimages_test_38 = dr(images_test_38, labels_test_38, [3,8])
print 'Size of the training set of 3s and 8s: {}'. format(np.shape(rimages_train_38))
print 'Size of the test set of 3s and 8s: {}'. format(np.shape(rimages_test_38))
print
print "1 Naive Bayes"
print
print "1.1 Classification"
print
# Training: priors and likelihood for each d=1,2
# for each feature and class individual histograms <=> 4 histogramms
n = rimages_train_38.shape[0]
d = rimages_train_38.shape[1]
# Choose bin width
L, dx = chooseBinSize(rimages_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 3, dx, L)
p8, pdf8 = naiveBayes_train_single_class(rimages_train_38, \
labels_train_38, 8, dx, L)
rimages_test_38_predict = naiveBayesClassifier(rimages_test_38, \
p3, p8, pdf3, pdf8, dx)
ccr_naiveBayes = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_naiveBayes)
print 'Error rate on the test set:{}'.format(1-ccr_naiveBayes)
plot_histogram(pdf3, dx, "Histograms of the class 3", "histograms3.png")
plot_histogram(pdf8, dx, "Histograms of the class 8", "histograms8.png")
plot_likelihood(pdf3, dx, "Likelihoods of the class 3", "likelihoods3.png")
plot_likelihood(pdf8, dx, "Likelihoods of the class 8", "likelihoods8.png")
print
print "1.2 Generate Threes"
print
# use function naiveBayes_train_single_class to compute the likelihood
# for all feature dimension
n = images_train_38.shape[0]
d = images_train_38.shape[1]
# Choose bin width
# Choose bin width
L, dx = chooseBinSize(images_train_38)
# train classifier for each class separatly
p3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, dx, L)
# generate 5 new threes
new3th = np.zeros((5,d), dtype = np.int32)
for i in range(0,3) :
new3th[i,:] = generate3naiveBayes(pdf3, dx)
img = new3th[i,:].reshape(np.sqrt(d),np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img);
plot.show()
# end for i
print
print "2 Density Tree"
print
print "Naive splitting"
print
# class 3
tstart = time.time()
prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'naive')
DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# class 8
prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'naive')
DT_visualize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
tstop = time.time()
print "DT learning time (naive splitting) {}". format(tstop-tstart)
tstart = time.time()
rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
prior3, prior8, DT3, DT8, [3,8])
tstop = time.time()
print "DT classification time (naive splitting) {}". format(tstop-tstart)
ccr_DT = correctClassRate(rimages_test_38_predict,\
labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
print 'Error rate on the test set:{}'.format(1-ccr_DT)
print
print 'Generate new threes: '
print
d = images_train_38.shape[1]
prior3, DT3 = DT_learning(images_train_38, labels_train_38, 3, 'naive')
# new threes
new3th = np.zeros((5,d), dtype = np.int32)
for i in range(0,3) :
new3th[i,:] = generate3DT(DT3, images_train_38, labels_train_38, 3 )
img = new3th[i,:].reshape(np.sqrt(d),np.sqrt(d))
plot.figure()
plot.gray()
plot.imshow(img);
plot.show()
# end for i
print
print "Clever splitting"
print
# # class 3
# prior3, DT3 = DT_learning(rimages_train_38, labels_train_38, 3, 'clever')
## DT_visualize2D(DT3, rimages_train_38, labels_train_38, 3, "naiveDT3.png")
# # class 8
# prior8, DT8 = DT_learning(rimages_train_38, labels_train_38, 8, 'clever')
## DT_visu alize2D(DT8, rimages_train_38, labels_train_38, 8, "naiveDT8.png")
#
#
# rimages_test_38_predict = DT_Classifier_2classes(rimages_test_38,
# prior3, prior8, DT3, DT8, [3,8])
#
# ccr_DT = correctClassRate(rimages_test_38_predict,\
# labels_test_38, [3,8], \
# print_confMatrix = True)
#
# print 'Correct Classification rate on the test set:{}'.format(ccr_DT)
# print 'Error rate on the test set:{}'.format(1-ccr_DT)
print
print "3 Combine DT and Naive Bayes"
print
n = images_train_38.shape[0]
d = images_train_38.shape[1]
print
print "Learning phase"
print
# train 1D-histogramms for each feature and class
tstart = time.time()
L, dx = chooseBinSize(images_train_38) # number of bins, bins size
# pdf dxL matrices
prior3, pdf3 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 3, dx, L)
prior8, pdf8 = naiveBayes_train_single_class(images_train_38, \
labels_train_38, 8, dx, L)
# compute the cdf of each histogramm
cdf3 = np.zeros(pdf3.shape, dtype = np.float32)
cdf8 = np.zeros(pdf8.shape, dtype = np.float32)
for j in range(0, d):
cdf3[j,:] = np.cumsum(pdf3[j,:])
cdf8[j,:] = np.cumsum(pdf8[j,:])
# end for
tstop = time.time()
print "Learning 1D histograms and computing cdf's took {} sec".\
format(tstop-tstart)
# map data to copula using rank order transformation
u = np.zeros(images_train_38.shape, dtype = np.float32)
for j in range(0,d):
ind = np.sort(images_train_38[:,j])
u[:,j] = ind[:]/float(n+1)
# end for j
# train a DT on u
tstart = time.time()
prior3, DT3 = DT_learning(u, labels_train_38, 3, 'naive')
prior8, DT8 = DT_learning(u, labels_train_38, 8, 'naive')
tstop = time.time()
print "Learning DTs took {} sec". format(tstop-tstart)
print
print "Classification"
print
ntest = images_test.shape[0]
prediction = np.zeros(ntest, dtype = np.int8)
for i in range(0,n):
x = images_test[i,:]
u3 = np.zeros(d, dtype = np.float32)
u8 = np.zeros(d, dtype = np.float32)
naiveBayesDensity3 = 1.
naiveBayesDensity8 = 1.
for j in range(0, d):
l= np.floor(x[j]/dx[j])+1 # bin number
if l>L-1:
l=L-1
naiveBayesDensity3 *= pdf3[j,l]
naiveBayesDensity8 *= pdf8[j,l]
u3[j]= cdf3[j,l]
u8[j]= cdf8[j,l]
# end for j
copulaDensity3 = 0
for node in DT3:
if point_in_region(u3, node.region):
copulaDensity3 = node.p
break
# end if
# end for node
copulaDensity8 = 0
for node in DT8:
if point_in_region(u8, node.region):
copulaDensity8 = node.p
break
# end if
# end for node
p_y3_x = naiveBayesDensity3*copulaDensity3*prior3
p_y8_x = naiveBayesDensity8*copulaDensity8*prior8
# argmax (p_y3_x, p_y8_x)
#print p_y3_x
if p_y3_x>p_y8_x :
prediction[i] = 3
else:
prediction[i] = 8
# end if
# end for i
ccr = correctClassRate(prediction, labels_test_38, [3,8], \
print_confMatrix = True)
print 'Correct Classification rate on the test set:{}'.format(ccr)
print 'Error rate on the test set:{}'.format(1-ccr)