吴恩达 深度学习 1-3 课后作业 Planar data classification with one hidden layer
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# Package importsimport numpy as npimport matplotlib.pyplot as pltfrom testCases_v2 import *import sklearnimport sklearn.datasetsimport sklearn.linear_modelfrom planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets%matplotlib inline np.random.seed(1) # set a seed so that the results are consistent
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X, Y = load_planar_dataset()
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# Visualize the data:plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);
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### START CODE HERE ### (≈ 3 lines of code)shape_X = X.shapeshape_Y = Y.shapem = X.shape[1] # training set size### END CODE HERE ###print ('The shape of X is: ' + str(shape_X))print ('The shape of Y is: ' + str(shape_Y))print ('I have m = %d training examples!' % (m))
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# Train the logistic regression classifierclf = sklearn.linear_model.LogisticRegressionCV();clf.fit(X.T, Y.T);
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# Plot the decision boundary for logistic regressionplot_decision_boundary(lambda x: clf.predict(x), X, Y)plt.title("Logistic Regression")# Print accuracyLR_predictions = clf.predict(X.T)print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) + '% ' + "(percentage of correctly labelled datapoints)")
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# GRADED FUNCTION: layer_sizesdef layer_sizes(X, Y): """ Arguments: X -- input dataset of shape (input size, number of examples) Y -- labels of shape (output size, number of examples) Returns: n_x -- the size of the input layer n_h -- the size of the hidden layer n_y -- the size of the output layer """ ### START CODE HERE ### (≈ 3 lines of code) n_x = X.shape[0] # size of input layer n_h = 4 n_y = Y.shape[0] # size of output layer ### END CODE HERE ### return (n_x, n_h, n_y)
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X_assess, Y_assess = layer_sizes_test_case()(n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)print("The size of the input layer is: n_x = " + str(n_x))print("The size of the hidden layer is: n_h = " + str(n_h))print("The size of the output layer is: n_y = " + str(n_y))
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# GRADED FUNCTION: initialize_parametersdef initialize_parameters(n_x, n_h, n_y): """ Argument: n_x -- size of the input layer n_h -- size of the hidden layer n_y -- size of the output layer Returns: params -- python dictionary containing your parameters: W1 -- weight matrix of shape (n_h, n_x) b1 -- bias vector of shape (n_h, 1) W2 -- weight matrix of shape (n_y, n_h) b2 -- bias vector of shape (n_y, 1) """ np.random.seed(2) # we set up a seed so that your output matches ours although the initialization is random. ### START CODE HERE ### (≈ 4 lines of code) W1 = np.random.randn(n_h,n_x)*0.01 b1 = np.zeros((n_h,1)) W2 = np.random.randn(n_y,n_h)*0.01 b2 = np.zeros((n_y,1)) ### END CODE HERE ### assert (W1.shape == (n_h, n_x)) assert (b1.shape == (n_h, 1)) assert (W2.shape == (n_y, n_h)) assert (b2.shape == (n_y, 1)) parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2} return parameters
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n_x, n_h, n_y = initialize_parameters_test_case()parameters = initialize_parameters(n_x, n_h, n_y)print("W1 = " + str(parameters["W1"]))print("b1 = " + str(parameters["b1"]))print("W2 = " + str(parameters["W2"]))print("b2 = " + str(parameters["b2"]))
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# GRADED FUNCTION: forward_propagationdef forward_propagation(X, parameters): """ Argument: X -- input data of size (n_x, m) parameters -- python dictionary containing your parameters (output of initialization function) Returns: A2 -- The sigmoid output of the second activation cache -- a dictionary containing "Z1", "A1", "Z2" and "A2" """ # Retrieve each parameter from the dictionary "parameters" ### START CODE HERE ### (≈ 4 lines of code) W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] ### END CODE HERE ### # Implement Forward Propagation to calculate A2 (probabilities) ### START CODE HERE ### (≈ 4 lines of code) Z1 = np.dot(W1,X)+b1 A1 = np.tanh(Z1) Z2 = np.dot(W2,A1)+b2 A2 = sigmoid(Z2) #print(X.shape) #print(Z1.shape) #print(A1.shape) #print(Z2.shape) #print(A2.shape) ### END CODE HERE ### assert(A2.shape == (1, X.shape[1])) cache = {"Z1": Z1, "A1": A1, "Z2": Z2, "A2": A2} return A2, cache
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X_assess, parameters = forward_propagation_test_case()A2, cache = forward_propagation(X_assess, parameters)# Note: we use the mean here just to make sure that your output matches ours. print(np.mean(cache['Z1']) ,np.mean(cache['A1']),np.mean(cache['Z2']),np.mean(cache['A2']))
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# GRADED FUNCTION: compute_costdef compute_cost(A2, Y, parameters): """ Computes the cross-entropy cost given in equation (13) Arguments: A2 -- The sigmoid output of the second activation, of shape (1, number of examples) Y -- "true" labels vector of shape (1, number of examples) parameters -- python dictionary containing your parameters W1, b1, W2 and b2 Returns: cost -- cross-entropy cost given equation (13) """ m = Y.shape[1] # number of example # Compute the cross-entropy cost ### START CODE HERE ### (≈ 2 lines of code) logprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1-A2),1-Y) cost = -1/m * np.sum(logprobs) ### END CODE HERE ### cost = np.squeeze(cost) # makes sure cost is the dimension we expect. # E.g., turns [[17]] into 17 assert(isinstance(cost, float)) return cost
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A2, Y_assess, parameters = compute_cost_test_case()print("cost = " + str(compute_cost(A2, Y_assess, parameters)))
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# GRADED FUNCTION: backward_propagationdef backward_propagation(parameters, cache, X, Y): """ Implement the backward propagation using the instructions above. Arguments: parameters -- python dictionary containing our parameters cache -- a dictionary containing "Z1", "A1", "Z2" and "A2". X -- input data of shape (2, number of examples) Y -- "true" labels vector of shape (1, number of examples) Returns: grads -- python dictionary containing your gradients with respect to different parameters """ m = X.shape[1] # First, retrieve W1 and W2 from the dictionary "parameters". ### START CODE HERE ### (≈ 2 lines of code) W1 = parameters["W1"] W2 = parameters["W2"] ### END CODE HERE ### # Retrieve also A1 and A2 from dictionary "cache". ### START CODE HERE ### (≈ 2 lines of code) A1 = cache["A1"] A2 = cache["A2"] ### END CODE HERE ### # Backward propagation: calculate dW1, db1, dW2, db2. ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above) dZ2 = A2-Y dW2 = 1.0/m*np.dot(dZ2,A1.T) db2 = 1.0/m*np.sum(dZ2,axis=1,keepdims=True) dZ1 = np.dot(W2.T,dZ2)*(1-np.power(A1,2)) dW1 = 1.0/m*np.dot(dZ1,X.T) db1 = 1.0/m*np.sum(dZ1,axis=1,keepdims=True) ### END CODE HERE ### grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2} return grads
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parameters, cache, X_assess, Y_assess = backward_propagation_test_case()grads = backward_propagation(parameters, cache, X_assess, Y_assess)print ("dW1 = "+ str(grads["dW1"]))print ("db1 = "+ str(grads["db1"]))print ("dW2 = "+ str(grads["dW2"]))print ("db2 = "+ str(grads["db2"]))
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# GRADED FUNCTION: update_parametersdef update_parameters(parameters, grads, learning_rate = 1.2): """ Updates parameters using the gradient descent update rule given above Arguments: parameters -- python dictionary containing your parameters grads -- python dictionary containing your gradients Returns: parameters -- python dictionary containing your updated parameters """ # Retrieve each parameter from the dictionary "parameters" ### START CODE HERE ### (≈ 4 lines of code) W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] ### END CODE HERE ### # Retrieve each gradient from the dictionary "grads" ### START CODE HERE ### (≈ 4 lines of code) dW1 = grads["dW1"] db1 = grads["db1"] dW2 = grads["dW2"] db2 = grads["db2"] ## END CODE HERE ### # Update rule for each parameter ### START CODE HERE ### (≈ 4 lines of code) W1 = W1 - learning_rate*dW1 b1 = b1 - learning_rate*db2 W2 = W2 - learning_rate*dW2 b2 = b2 - learning_rate*db2 ### END CODE HERE ### parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2} return parameters
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parameters, grads = update_parameters_test_case()parameters = update_parameters(parameters, grads)print("W1 = " + str(parameters["W1"]))print("b1 = " + str(parameters["b1"]))print("W2 = " + str(parameters["W2"]))print("b2 = " + str(parameters["b2"]))
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# GRADED FUNCTION: nn_modeldef nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False): """ Arguments: X -- dataset of shape (2, number of examples) Y -- labels of shape (1, number of examples) n_h -- size of the hidden layer num_iterations -- Number of iterations in gradient descent loop print_cost -- if True, print the cost every 1000 iterations Returns: parameters -- parameters learnt by the model. They can then be used to predict. """ np.random.seed(3) n_x = layer_sizes(X,Y)[0] n_y = layer_sizes(X,Y)[2] # Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y". Outputs = "W1, b1, W2, b2, parameters". ### START CODE HERE ### (≈ 5 lines of code) parameters = initialize_parameters(n_x, n_h, n_y) W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] ### END CODE HERE ### # Loop (gradient descent) for i in range(0, num_iterations): ### START CODE HERE ### (≈ 4 lines of code) # Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache". A2, cache = forward_propagation(X, parameters) # Cost function. Inputs: "A2, Y, parameters". Outputs: "cost". cost = compute_cost(A2, Y, parameters) # Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads". grads = backward_propagation(parameters, cache, X, Y) # Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters". parameters = update_parameters(parameters, grads, learning_rate = 1.2) ### END CODE HERE ### # Print the cost every 1000 iterations if print_cost and i % 1000 == 0: print ("Cost after iteration %i: %f" %(i, cost)) return parameters
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X_assess, Y_assess = nn_model_test_case()parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=True)print("W1 = " + str(parameters["W1"]))print("b1 = " + str(parameters["b1"]))print("W2 = " + str(parameters["W2"]))print("b2 = " + str(parameters["b2"]))
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# GRADED FUNCTION: predictdef predict(parameters, X): """ Using the learned parameters, predicts a class for each example in X Arguments: parameters -- python dictionary containing your parameters X -- input data of size (n_x, m) Returns predictions -- vector of predictions of our model (red: 0 / blue: 1) """ # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold. ### START CODE HERE ### (≈ 2 lines of code) A2, cache = forward_propagation(X, parameters) predictions = (A2 > 0.5) ### END CODE HERE ### return predictions
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parameters, X_assess = predict_test_case()predictions = predict(parameters, X_assess)print("predictions mean = " + str(np.mean(predictions)))
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# Build a model with a n_h-dimensional hidden layerparameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)# Plot the decision boundaryplot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)plt.title("Decision Boundary for hidden layer size " + str(4))
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# Print accuracypredictions = predict(parameters, X)print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')
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# This may take about 2 minutes to runplt.figure(figsize=(16, 32))hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]for i, n_h in enumerate(hidden_layer_sizes): plt.subplot(5, 2, i+1) plt.title('Hidden Layer of size %d' % n_h) parameters = nn_model(X, Y, n_h, num_iterations = 5000) plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y) predictions = predict(parameters, X) accuracy = float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) print ("Accuracy for {} hidden units: {} %".format(n_h, accuracy))
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# Datasetsnoisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()datasets = {"noisy_circles": noisy_circles, "noisy_moons": noisy_moons, "blobs": blobs, "gaussian_quantiles": gaussian_quantiles}### START CODE HERE ### (choose your dataset)dataset = "noisy_moons"### END CODE HERE ###X, Y = datasets[dataset]X, Y = X.T, Y.reshape(1, Y.shape[0])# make blobs binaryif dataset == "blobs": Y = Y%2# Visualize the dataplt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);
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