def output(partId):
# Random Test Cases
x1 = np.sin(np.arange(1, 11))
x2 = np.cos(np.arange(1, 11))
ec = 'the quick brown fox jumped over the lazy dog'
wi = np.abs(np.round(x1 * 1863)).astype(int)
wi = np.concatenate([wi, wi])
if partId == '1':
sim = gaussianKernel(x1, x2, 2)
out = formatter('%0.5f ', sim)
elif partId == '2':
mat = scipy.io.loadmat('ex6data3.mat')
X = mat['X']
y = mat['y'].ravel()
Xval = mat['Xval']
yval = mat['yval'].ravel()
C, sigma = dataset3Params(X, y, Xval, yval)
out = formatter('%0.5f ', C)
out += formatter('%0.5f ', sigma)
elif partId == '3':
word_indices = processEmail(ec) + 1
out = formatter('%d ', word_indices)
elif partId == '4':
x = emailFeatures(wi)
out = formatter('%d ', x)
return out
def plotBoundary(X, y, svm):
#Plot Boundary
u = linspace(min(X[:, 0]), max(X[:, 0]), 200)
v = linspace(min(X[:, 1]), max(X[:, 1]), 200)
z = zeros(shape=(len(u), len(v)))
for i in range(len(u)):
for j in range(len(v)):
z[i, j] = svm.predict(gaussianKernel(array([[u[i], v[j]]]), X))
plot(X[:, 0][y == 1], X[:, 1][y == 1], 'ro', label="c1")
plot(X[:, 0][y == 0], X[:, 1][y == 0], 'b+', label="c2")
contour(u, v, z.T, [0])
xlabel('Microchip Test 1')
ylabel('Microchip Test 2')
legend(['y = 1', 'y = 0', 'Decision boundary'], numpoints=1)
show()
def dataset3Params(X, y, Xval, yval):
choice = np.array([0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30]).reshape(-1, 1)
minError = np.inf
curC = np.inf
cur_sigma = np.inf
for i in range(choice.shape[0]):
for j in range(choice.shape[0]):
func = lambda a, b: gaussianKernel(a, b, choice[j])
func.__name__ = 'gaussianKernel'
model = svmTrain(X, y, choice[i], func)
predictions = svmPredict(model, Xval)
error = np.mean(np.double(np.not_equal(predictions, yval)))
if error < minError:
minError = error
curC = choice[i]
cur_sigma = choice[j]
C = curC
sigma = cur_sigma
return C, sigma
def dataset3Params(X, y, Xval, yval):
choice = np.array([0.01,0.03,0.1,0.3,1,3,10,30]).reshape(-1,1)
minError = np.inf
curC = np.inf
cur_sigma = np.inf
for i in range(choice.shape[0]):
for j in range(choice.shape[0]):
func = lambda a, b: gaussianKernel(a, b, choice[j])
func.__name__ = 'gaussianKernel'
model = svmTrain(X, y, choice[i], func)
predictions = svmPredict(model, Xval)
error = np.mean(np.double(np.not_equal(predictions,yval)))
if error < minError:
minError = error
curC = choice[i]
cur_sigma = choice[j]
C = curC
sigma = cur_sigma
return C, sigma
# # The first two columns contains the exam scores and the third column
# # contains the label.
data = loadtxt('data2.txt', delimiter=',')
X = data[:, 0:2]
y = data[:, 2]
# # Plot data
plt.plot(X[:, 0][y == 1], X[:, 1][y == 1], 'r+', label="c1")
plt.plot(X[:, 0][y == 0], X[:, 1][y == 0], 'bo', label="c2")
plt.legend(['y = 1', 'y = 0'], numpoints=1)
plt.show()
sigma = 0.2 # Gaussian kernel variance
# We calculate the Gaussian kernel between the instances/samples
K = gaussianKernel(X, X, sigma)
C = 5.0 # SVM regularization parameter
# We create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
svc = SVC(C=C, kernel="precomputed")
svc.fit(K, y)
# Plot the decision boundary
u = linspace(min(X[:, 0]), max(X[:, 0]), 200)
v = linspace(min(X[:, 1]), max(X[:, 1]), 200)
z = zeros(shape=(len(u), len(v)))
for i in range(len(u)):
for j in range(len(v)):
z[i, j] = svc.predict(gaussianKernel(array([[u[i], v[j]]]), X, sigma))
clf = svm.SVC(C=C, kernel='linear', tol=1e-3, max_iter=200)
model = clf.fit(X, y)
visualizeBoundaryLinear(X, y, model)
raw_input("Program paused. Press Enter to continue...")
## =============== Part 3: Implementing Gaussian Kernel ===============
# You will now implement the Gaussian kernel to use
# with the SVM. You should complete the code in gaussianKernel.m
#
print 'Evaluating the Gaussian Kernel ...'
x1 = np.array([1, 2, 1])
x2 = np.array([0, 4, -1])
sigma = 2
sim = gaussianKernel(x1, x2, sigma)
print 'Gaussian Kernel between x1 = [1 2 1], x2 = [0 4 -1], sigma = %0.5f : ' \
'\t%f\n(this value should be about 0.324652)\n' % (sigma, sim)
raw_input("Program paused. Press Enter to continue...")
## =============== Part 4: Visualizing Dataset 2 ================
# The following code will load the next dataset into your environment and
# plot the data.
#
print 'Loading and Visualizing Data ...'
# Load from ex6data2:
# You will have X, y in your environment
#visualizeBoundaryLinear(X, y, clf)
#fprintf('Program paused. Press enter to continue.\n');
#% =============== Part 3: Implementing Gaussian Kernel ===============
# You will now implement the Gaussian kernel to use
# with the SVM. You should complete the code in gaussianKernel.m
#
print('\nEvaluating the Gaussian Kernel ...\n')
x1 = np.array([1, 2, 1])
x2 = np.array([0, 4, -1])
sigma = 2
sim = gaussianKernel(x1, x2, sigma)
print('Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = 0.5 :' ,
'\n\t%f\n(this value should be about 0.324652)\t', sim)
#%% =============== Part 4: Visualizing Dataset 2 ================
#% The following code will load the next dataset into your environment and
#% plot the data.
# Load from ex6data2:
# You will have X, y in your environment
#load('ex6data2.mat');
model = svmTrain(X, y, C, linearKernel, 1e-3, 20)
print(model)
visualizeBoundaryLinear(X, y, model)
input('Program paused. Press enter to continue.\n')
## =============== Part 3: Implementing Gaussian Kernel ===============
# You will now implement the Gaussian kernel to use
# with the SVM. You should complete the code in gaussianKernel.m
#
print('\nEvaluating the Gaussian Kernel ...\n')
x1 = np.array([1, 2, 1])
x2 = np.array([0, 4, -1])
sigma = 2
sim = gaussianKernel(x1, x2, sigma)
print('Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = 0.5 :' \
'\n\t%lf\n(this value should be about 0.324652)\n', sim)
input('Program paused. Press enter to continue.\n')
## =============== Part 4: Visualizing Dataset 2 ================
# The following code will load the next dataset into your environment and
# plot the data.
#
print('Loading and Visualizing Data ...\n')
# Load from ex6data2:
# You will have X, y in your environment
visualizeBoundaryLinear(X, y, model) fig.show() print 'Program paused. Press enter to continue.' raw_input() ## =============== Part 3: Implementing Gaussian Kernel =============== # You will now implement the Gaussian kernel to use # with the SVM. You should complete the code in gaussianKernel.m # print '\nEvaluating the Gaussian Kernel ...' x1 = array([1, 2, 1]) x2 = array([0, 4, -1]) sigma = 2.0 sim = gaussianKernel(x1, x2, sigma) print 'Gaussian Kernel between x1 = [1, 2, 1], x2 = [0, 4, -1], sigma = 0.5 :' print '\t%f\n(this value should be about 0.324652)' % sim print 'Program paused. Press enter to continue.' raw_input() ## =============== Part 4: Visualizing Dataset 2 ================ # The following code will load the next dataset into your environment and # plot the data. # print 'Loading and Visualizing Data ...' # Load from ex6data2:
def ex6():
# Machine Learning Online Class
# Exercise 6 | Support Vector Machines
#
# Instructions
# ------------
#
# This file contains code that helps you get started on the
# exercise. You will need to complete the following functions:
#
# gaussianKernel.m
# dataset3Params.m
# processEmail.m
# emailFeatures.m
#
# For this exercise, you will not need to change any code in this file,
# or any other files other than those mentioned above.
#
# Initialization
#clear ; close all; clc
# =============== Part 1: Loading and Visualizing Data ================
# We start the exercise by first loading and visualizing the dataset.
# The following code will load the dataset into your environment and plot
# the data.
#
print('Loading and Visualizing Data ...')
# Load from ex6data1:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data1.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
# Plot training data
plotData(X, y)
plt.savefig('figure1.png')
print('Program paused. Press enter to continue.')
#pause;
# ==================== Part 2: Training Linear SVM ====================
# The following code will train a linear SVM on the dataset and plot the
# decision boundary learned.
#
# Load from ex6data1:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data1.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
print('\nTraining Linear SVM ...')
# You should try to change the C value below and see how the decision
# boundary varies (e.g., try C = 1000)
C = 1
model = svmTrain(X, y, C, linearKernel, 1e-3, 20)
visualizeBoundaryLinear(X, y, model)
plt.savefig('figure2.png')
print('Program paused. Press enter to continue.')
#pause;
# =============== Part 3: Implementing Gaussian Kernel ===============
# You will now implement the Gaussian kernel to use
# with the SVM. You should complete the code in gaussianKernel.m
#
print('\nEvaluating the Gaussian Kernel ...')
x1 = np.array([
1,
2,
1,
])
x2 = np.array([0, 4, -1])
sigma = 2
sim = gaussianKernel(x1, x2, sigma)
print(
'Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = 0.5 :\n\t%f\n(this value should be about 0.324652)'
% sim)
print('Program paused. Press enter to continue.')
#pause;
# =============== Part 4: Visualizing Dataset 2 ================
# The following code will load the next dataset into your environment and
# plot the data.
#
fig = plt.figure()
print('Loading and Visualizing Data ...')
# Load from ex6data2:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data2.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
# Plot training data
plotData(X, y)
plt.savefig('figure3.png')
print('Program paused. Press enter to continue.')
#pause;
# ========== Part 5: Training SVM with RBF Kernel (Dataset 2) ==========
# After you have implemented the kernel, we can now use it to train the
# SVM classifier.
#
print('\nTraining SVM with RBF Kernel (this may take 1 to 2 minutes) ...')
# Load from ex6data2:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data2.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
# SVM Parameters
C = 1
sigma = 0.1
# We set the tolerance and max_passes lower here so that the code will run
# faster. However, in practice, you will want to run the training to
# convergence.
model = svmTrain(X, y, C, gaussianKernel, args=(sigma, ))
visualizeBoundary(X, y, model)
plt.savefig('figure4.png')
print('Program paused. Press enter to continue.')
#pause;
# =============== Part 6: Visualizing Dataset 3 ================
# The following code will load the next dataset into your environment and
# plot the data.
#
fig = plt.figure()
print('Loading and Visualizing Data ...')
# Load from ex6data3:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data3.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
# Plot training data
plotData(X, y)
plt.savefig('figure5.png')
print('Program paused. Press enter to continue.')
#pause;
# ========== Part 7: Training SVM with RBF Kernel (Dataset 3) ==========
# This is a different dataset that you can use to experiment with. Try
# different values of C and sigma here.
#
# Load from ex6data3:
# You will have X, y in your environment
mat = scipy.io.loadmat('ex6data3.mat')
X = mat['X'].astype(float)
y = mat['y'][:, 0]
Xval = mat['Xval'].astype(float)
yval = mat['yval'][:, 0]
# Try different SVM Parameters here
C, sigma = dataset3Params(X, y, Xval, yval)
# Train the SVM
model = svmTrain(X, y, C, gaussianKernel, args=(sigma, ))
visualizeBoundary(X, y, model)
plt.savefig('figure6.png')
print('Program paused. Press enter to continue.')
visualizeBoundaryLinear(X, y, model) fig.show() print 'Program paused. Press enter to continue.' raw_input() ## =============== Part 3: Implementing Gaussian Kernel =============== # You will now implement the Gaussian kernel to use # with the SVM. You should complete the code in gaussianKernel.m # print '\nEvaluating the Gaussian Kernel ...' x1 = array([1, 2, 1]) x2 = array([0, 4, -1]) sigma = 2.0 sim = gaussianKernel(x1, x2, sigma) print 'Gaussian Kernel between x1 = [1, 2, 1], x2 = [0, 4, -1], sigma = 0.5 :' print '\t%f\n(this value should be about 0.324652)' % sim print 'Program paused. Press enter to continue.' raw_input() ## =============== Part 4: Visualizing Dataset 2 ================ # The following code will load the next dataset into your environment and # plot the data. # print 'Loading and Visualizing Data ...' # Load from ex6data2:
yval = dataeval[:, 2]
# # Plot data
plt.plot(X[:, 0][y == 1], X[:, 1][y == 1], 'r+', label="c1")
plt.plot(X[:, 0][y == 0], X[:, 1][y == 0], 'bo', label="c2")
plt.legend(['y = 1', 'y = 0'], numpoints=1)
plt.show()
sigma = 0.2 # Gaussian kernel variance
C = 0.0 # SVM regularization parameter
# we create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
svc = SVC(C=C, kernel="precomputed")
svc.fit(gaussianKernel(X, X, sigma), y)
# Plot the decision boundary
u = linspace(min(X[:, 0]), max(X[:, 0]), 200)
v = linspace(min(X[:, 1]), max(X[:, 1]), 200)
z = zeros(shape=(len(u), len(v)))
for i in range(len(u)):
for j in range(len(v)):
z[i, j] = svc.predict(gaussianKernel(array([[u[i], v[j]]]), X, sigma))
plot(X[:, 0][y == 1], X[:, 1][y == 1], 'r+', label="c1")
plot(X[:, 0][y == 0], X[:, 1][y == 0], 'bo', label="c2")
contour(u, v, z.T, [0])
legend(['y = 1', 'y = 0', 'Decision boundary'], numpoints=1)
show()
# boundary varies (e.g., try C = 1000)
C = 1
model = svmTrain(X, y, C, linearKernel, 1e-3, 20)
print(model)
visualizeBoundaryLinear(X, y, model)
input('Program paused. Press enter to continue.\n')
## =============== Part 3: Implementing Gaussian Kernel ===============
# You will now implement the Gaussian kernel to use
# with the SVM. You should complete the code in gaussianKernel.m
#
print('\nEvaluating the Gaussian Kernel ...\n')
x1 = np.array([1,2,1]); x2 = np.array([0,4,-1]); sigma = 2
sim = gaussianKernel(x1, x2, sigma)
print('Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = 0.5 :' \
'\n\t%lf\n(this value should be about 0.324652)\n', sim)
input('Program paused. Press enter to continue.\n')
## =============== Part 4: Visualizing Dataset 2 ================
# The following code will load the next dataset into your environment and
# plot the data.
#
print('Loading and Visualizing Data ...\n')
# Load from ex6data2:
# You will have X, y in your environment