for j in xrange(old_svm.get_num_support_vectors()):
sv_id = int(old_svm.get_support_vectors()[j])
alpha = old_svm.get_alpha(j)
inner_sum = inner_sum + alpha * kv.kernel(sv_id, idx)
inner.append(inner_sum)
#general case
linterm_manual[idx] = B * tmp_lab[idx] * inner_sum - 1.0
################
# compare pre-svms
assert (presvm_liblinear.get_bias() == 0.0)
assert (presvm_libsvm.get_bias() == 0.0)
tmp_out = presvm_liblinear.classify(feat).get_labels()
tmp_out2 = presvm_libsvm.classify(feat).get_labels()
# compare outputs
for i in xrange(N):
try:
assert (abs(inner[i] - tmp_out[i]) <= 0.001)
assert (abs(inner[i] - tmp_out2[i]) <= 0.001)
except Exception, message:
print "difference in outputs: (%.4f, %.4f, %.4f)" % (tmp_out[i],
tmp_out2[i])
sv_id = int(old_svm.get_support_vectors()[j])
alpha = old_svm.get_alpha(j)
inner_sum = inner_sum + alpha * kv.kernel(sv_id, idx)
inner.append(inner_sum)
#general case
linterm_manual[idx] = B *tmp_lab[idx] * inner_sum - 1.0
################
# compare pre-svms
assert(presvm_liblinear.get_bias() == 0.0)
assert(presvm_libsvm.get_bias() == 0.0)
tmp_out = presvm_liblinear.classify(feat).get_labels()
tmp_out2 = presvm_libsvm.classify(feat).get_labels()
# compare outputs
for i in xrange(N):
try:
assert(abs(inner[i]-tmp_out[i])<= 0.001)
assert(abs(inner[i]-tmp_out2[i])<= 0.001)
except Exception, message:
print "difference in outputs: (%.4f, %.4f, %.4f)" % (tmp_out[i], tmp_out2[i])
def classifier_perceptron_graphical(n=100, distance=5, learn_rate=1., max_iter=1000, num_threads=1, seed=None, nperceptrons=5):
from shogun.Features import RealFeatures, BinaryLabels
from shogun.Classifier import Perceptron, LibLinear, L2R_L2LOSS_SVC
from modshogun import MSG_INFO
# 2D data
_DIM = 2
# To get the nice message that the perceptron has converged
dummy = BinaryLabels()
# dummy.io.set_loglevel(MSG_INFO)
np.random.seed(seed)
# Produce some (probably) linearly separable training data by hand
# Two Gaussians at a far enough distance
X = np.array(np.random.randn(_DIM,n))+distance
Y = np.array(np.random.randn(_DIM,n))
label_train_twoclass = np.hstack((np.ones(n), -np.ones(n)))
fm_train_real = np.hstack((X,Y))
feats_train = RealFeatures(fm_train_real)
labels = BinaryLabels(label_train_twoclass)
perceptron = Perceptron(feats_train, labels)
perceptron.set_learn_rate(learn_rate)
perceptron.set_max_iter(max_iter)
perceptron.set_initialize_hyperplane(False)
# Find limits for visualization
x_min = min(np.min(X[0,:]), np.min(Y[0,:]))
x_max = max(np.max(X[0,:]), np.max(Y[0,:]))
y_min = min(np.min(X[1,:]), np.min(Y[1,:]))
y_max = max(np.max(X[1,:]), np.max(Y[1,:]))
fig1, axes1 = plt.subplots(1,1)
fig2, axes2 = plt.subplots(1,1)
for i in xrange(nperceptrons):
# Initialize randomly weight vector and bias
perceptron.set_w(np.random.random(2))
perceptron.set_bias(np.random.random())
# Run the perceptron algorithm
perceptron.train()
# Construct the hyperplane for visualization
# Equation of the decision boundary is w^T x + b = 0
b = perceptron.get_bias()
w = perceptron.get_w()
hx = np.linspace(x_min-1,x_max+1)
hy = -w[1]/w[0] * hx
axes1.plot(hx, -1/w[1]*(w[0]*hx+b))
axes2.plot(hx, -1/w[1]*(w[0]*hx+b), alpha=0.5)
print('minimum distance with perceptron is %f' % min_distance(w, b, feats_train))
C = 1
epsilon = 1e-3
svm = LibLinear(C, feats_train, labels)
svm.set_liblinear_solver_type(L2R_L2LOSS_SVC)
svm.set_epsilon(epsilon)
svm.set_bias_enabled(True)
svm.train()
b = svm.get_bias()
w = svm.get_w()
print('minimum distance with svm is %f' % min_distance(w, b, feats_train))
hx = np.linspace(x_min-1,x_max+1)
hy = -w[1]/w[0] * hx
axes2.plot(hx, -1/w[1]*(w[0]*hx+b), 'k', linewidth=2.0)
# Plot the two-class data
axes1.scatter(X[0,:], X[1,:], s=40, marker='o', facecolors='none', edgecolors='b')
axes1.scatter(Y[0,:], Y[1,:], s=40, marker='s', facecolors='none', edgecolors='r')
axes2.scatter(X[0,:], X[1,:], s=40, marker='o', facecolors='none', edgecolors='b')
axes2.scatter(Y[0,:], Y[1,:], s=40, marker='s', facecolors='none', edgecolors='r')
# Customize the plot
axes1.axis([x_min-1, x_max+1, y_min-1, y_max+1])
axes1.set_title('Rosenblatt\'s Perceptron Algorithm')
axes1.set_xlabel('x')
axes1.set_ylabel('y')
axes2.axis([x_min-1, x_max+1, y_min-1, y_max+1])
axes2.set_title('Support Vector Machine')
axes2.set_xlabel('x')
axes2.set_ylabel('y')
plt.show()
return perceptron
def classifier_non_separable_svm(n=100, m=10, distance=5, seed=None):
'''
n is the number of examples per class and m is the number of examples per class that gets its
label swapped to force non-linear separability
'''
from shogun.Features import RealFeatures, BinaryLabels
from shogun.Classifier import LibLinear, L2R_L2LOSS_SVC
# 2D data
_DIM = 2
# To get the nice message that the perceptron has converged
dummy = BinaryLabels()
np.random.seed(seed)
# Produce some (probably) linearly separable training data by hand
# Two Gaussians at a far enough distance
X = np.array(np.random.randn(_DIM, n)) + distance
Y = np.array(np.random.randn(_DIM, n))
# The last five points of each class are swapped to force non-linear separable data
label_train_twoclass = np.hstack(
(np.ones(n - m), -np.ones(m), -np.ones(n - m), np.ones(m)))
fm_train_real = np.hstack((X, Y))
feats_train = RealFeatures(fm_train_real)
labels = BinaryLabels(label_train_twoclass)
# Train linear SVM
C = 1
epsilon = 1e-3
svm = LibLinear(C, feats_train, labels)
svm.set_liblinear_solver_type(L2R_L2LOSS_SVC)
svm.set_epsilon(epsilon)
svm.set_bias_enabled(True)
svm.train()
# Get hyperplane parameters
b = svm.get_bias()
w = svm.get_w()
# Find limits for visualization
x_min = min(np.min(X[0, :]), np.min(Y[0, :]))
x_max = max(np.max(X[0, :]), np.max(Y[0, :]))
y_min = min(np.min(X[1, :]), np.min(Y[1, :]))
y_max = max(np.max(X[1, :]), np.max(Y[1, :]))
hx = np.linspace(x_min - 1, x_max + 1)
hy = -w[1] / w[0] * hx
plt.plot(hx, -1 / w[1] * (w[0] * hx + b), 'k', linewidth=2.0)
# Plot the two-class data
pos_idxs = label_train_twoclass == +1
plt.scatter(fm_train_real[0, pos_idxs],
fm_train_real[1, pos_idxs],
s=40,
marker='o',
facecolors='none',
edgecolors='b')
neg_idxs = label_train_twoclass == -1
plt.scatter(fm_train_real[0, neg_idxs],
fm_train_real[1, neg_idxs],
s=40,
marker='s',
facecolors='none',
edgecolors='r')
# Customize the plot
plt.axis([x_min - 1, x_max + 1, y_min - 1, y_max + 1])
plt.title('SVM with non-linearly separable data')
plt.xlabel('x')
plt.ylabel('y')
plt.show()
return svm
