讲解：Python：CS4006 Support Vector

代写实现SVM分类器。RequirementIn this assignment, we use the scikit-learn package to train an SVM classifier. To do so, we need to tune 2 hyperparameters: the cost C and precision γ (gamma). We are going to use K-fold cross-validation to determine the best combination of values for this pair.Question 0Have a look at the 3 first cells. In the third one, take note of how the SVC object is instantiated and trained, how labels are predicted, and finally how the fitting error is computed. In this assignment, the prediction error after a given training is simply defined as the number of misclassified labels.Question 1Using an SVM classifier with an RBF kernel, use 10-fold cross-validation to find the best cost and precision parameters. The range of test values for each parameter is provided. a. First compute the cross-validation error matrix: for each parameter combination, instantiate an SVM classifier; for each split provided by the KFold object, re-train this classifier and compute the prediction error; the cross- validation error is the average of these errors over all splits. b. Use the error matrix to select the best parameter combination. c. Visualize the error matrix using imshow and the ‘hot’ colormap.Question 2Plot the decision boundaries of this classifier, by appropriately modifying the code from the previous assignments. Display the support vectors on the same figure.Question 3Evaluate and print the generalization error of this classifier, computed on the test set.Codeimports12345import matplotlib.pyplot as pltimport numpy as npfrom sklearn.model_selection import KFoldfrom sklearn.svm import SVC%matplotlib inlineLoad and display the training data123456789101112131415161718192021features = np.load(&"features.npy&")labels = np.load(&"labels.npy&")print(&"features size:&", features.shape)print(&"labels size:&", labels.shape)# Extract features for both classespos = labels == 1 # 1D array of booleans, with pos[i] = True if labels[i] == 1features_pos = features[pos] # filter the array with the boolean arrayneg = labels != 1features_neg = features[neg]# Display datafig, ax = plt.subplots()ax.scatter(features_pos[:, 0], features_pos[:, 1], c=&"red&", label=&"Posit ive class&")ax.scatter(features_neg[:, 0], features_neg[:, 1], c=&"blue&", label=&"Nega tive class&")ax.set_title(&"Training data&")ax.set_xlabel(&"Feature 1&")ax.set_ylabel(&"Feature 2&")ax.legend()plt.show()features size: (500, 2)labels size: (500,)Training the SVM classifier with arbitrary hyperparameters1234567891011121314151617cost = 1gamma = 1# Train the SVM classifier.svm = SVC(C=cost, kernel=rbf, gamma=gamma)svm.fit(features, labels)# Predict labels.# Note that here we use the same set for training and testing,# which is not the case in the remainder of the assignment.predicted_labels = svm.predict(features)# Compute the error.# Note: since in Python, True and False are equivalent to 1 and 0, we ca n# directly sum over the boolean array returned by the comparison operato r.error = sum(labels != predicted_labels)print(&"Prediction error:&", error)Prediction error: 98Training with K-fold cross-validationDefine test values for the cost and precision parameters1234567def logsample(start, end, num): return np.logspace(np.log10(start), np.log10(end), num, base=10.0)num_gammas = 20num_costs = 20gamma_range = logsample(1e-1, 1e3, num_gammas)cost_range = logsample(1e-1, 1e3, num_costs)Compute the cross-validation error for each parameter combinationThe KFold class from scikit-learn is a “cross-validation” object, initialized with a number of folds. For each fold, it randomly partitions the input data into a training set and a validation set. The documentation (http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) provides an example of use.123456K = 10 # number of folds for cross validationkf = KFold(n_splits=K)cv_error = np.zeros((num_gammas, num_costs)) # error matrix# TODO (Question 1)# /TODO (Question 1)& Train the classifier with the best parameter combination123456789# Find gamma and cost giving the smallest error# TODO (Question 1)# /TODO (Question 1)# Train the SVM classifier using these parameterssvm = SVC(C=cost, kernel=rbf, gamma=gamma)svm.fit(features, labels)support_vectors = svm.support_vectors_Display cross-validation results and decision function12345678910111213141516171819202122232425262728293031323334353637# Sample points on a gridnum_points = 100x_rng = np.linspace(0, 1, num_points)y_rng = np.linspace(0, 1, num_points)grid_x, grid_y = np.meshgrid(x_rng, y_rng)# Evaluate decision function for each pointxy_list = np.column_stack((grid_x.flat, grid_y.flat))values = svm.decision_function(xy_list)values = values.reshape((num_points, num_points))# Displayfig = plt.figure(figsize=plt.figaspect(0.25))ax = fig.add_subplot(1, 3, 1)ax.set_title(&"Cross-validation error&")ax.set_xlabel(&"Log10 of the cost parameter&")ax.set_ylabel(&"Log10 of the precision parameter&")# TODO (Question 1)# /TODO (Question 1)ax = fig.add_subplot(1, 3, 2)ax.set_title(&"Decision function&")ax.set_xlabel(&"Feature 1&")ax.set_ylabel(&"Feature 2&")ax.imshow(values, extent=[0, 1, 0, 1], origin=lower)ax = fig.add_subplot(1, 3, 3)ax.set_title(&"Support vectors and isolevels of the decision function&")ax.set_xlabel(&"Feature 1&")ax.set_ylabel(&"Feature 2&")# TODO (Question 2)# /TODO (Question 2)plt.show()Generalization errorLoad the test data12345# Load the training datatest_features = np.load(&"test_features.npy&")test_labels = np.load(&"test_labels.npy&")print(test_features.shape)print(test_labels.shape)(500, 2)(500,)Print the number of misclassified points in the test set123# TODO (Question 3)# /TODO (Question 3)90转自：http://www.3daixie.com/contents/11/3444.html