Planar data classification with one hidden layer - 吴恩达深度学习视频第三周作业
如果直接看代码对你来说有困难: 参考 http://www.javashuo.com/article/p-wwkrzsse-c.html
完成时间 2018年11月26日 19:48:44 没有任何报错
# Package imports import numpy as np import matplotlib.pyplot as plt from testCases import * import sklearn import sklearn.datasets import sklearn.linear_model from 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 X, Y = load_planar_dataset() # Visualize the data: # plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral); plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral)
### START CODE HERE ### (≈ 3 lines of code) shape_X = X.shape# (2, 400) shape_Y = Y.shape# (1, 400) m = shape_X[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))
The shape of X is: (2, 400) The shape of Y is: (1, 400) I have m = 400 training examples!
# Train the logistic regression classifier clf = sklearn.linear_model.LogisticRegressionCV(); clf.fit(X.T, Y.T); # Plot the decision boundary for logistic regression def plot_decision_boundary(model, X, y): # Set min and max values and give it some padding x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1 y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1 h = 0.01 # Generate a grid of points with distance h between them xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Predict the function value for the whole grid Z = model(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot the contour and training examples plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) plt.ylabel('x2') plt.xlabel('x1') plt.scatter(X[0, :], X[1, :], c=y.reshape(X[0,:].shape), cmap=plt.cm.Spectral) plot_decision_boundary(lambda x: clf.predict(x), X, Y) plt.title("Logistic Regression") # Print accuracy LR_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)")
# GRADED FUNCTION: layer_sizes def 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) 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))
The size of the input layer is: n_x = 5 The size of the hidden layer is: n_h = 4 The size of the output layer is: n_y = 2
# GRADED FUNCTION: initialize_parameters def 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 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"]))
W1 = [[-0.00416758 -0.00056267] [-0.02136196 0.01640271] [-0.01793436 -0.00841747] [ 0.00502881 -0.01245288]] b1 = [[0.] [0.] [0.] [0.]] W2 = [[-0.01057952 -0.00909008 0.00551454 0.02292208]] b2 = [[0.]]
# GRADED FUNCTION: forward_propagation def 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) ### END CODE HERE ### assert(A2.shape == (1, X.shape[1])) cache = {"Z1": Z1, "A1": A1, "Z2": Z2, "A2": A2} return A2, cache 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']))
-0.0004997557777419902 -0.000496963353231779 0.00043818745095914653 0.500109546852431
# GRADED FUNCTION: compute_cost def 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((1-Y), np.log(1-A2)) cost = - np.sum(logprobs) / m ### 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 A2, Y_assess, parameters = compute_cost_test_case() print("cost = " + str(compute_cost(A2, Y_assess, parameters)))
cost = 0.6929198937761266
# GRADED FUNCTION: backward_propagation def 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 = np.dot(dZ2, A1.T) / m db2 = np.sum(dZ2, axis=1, keepdims=True) / m dZ1 = np.multiply(np.dot(W2.T, dZ2), 1-np.power(A1, 2)) dW1 = np.dot(dZ1, X.T) / m db1 = np.sum(dZ1, axis=1, keepdims=True) / m ### END CODE HERE ### grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2} return grads 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"]))
dW1 = [[ 0.01018708 -0.00708701] [ 0.00873447 -0.0060768 ] [-0.00530847 0.00369379] [-0.02206365 0.01535126]] db1 = [[-0.00069728] [-0.00060606] [ 0.000364 ] [ 0.00151207]] dW2 = [[ 0.00363613 0.03153604 0.01162914 -0.01318316]] db2 = [[0.06589489]]
# GRADED FUNCTION: update_parameters def 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 -= learning_rate * dW1 b1 -= learning_rate * db1 W2 -= learning_rate * dW2 b2 -= learning_rate * db2 ### END CODE HERE ### parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2} return parameters 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"]))
W1 = [[-0.00643025 0.01936718] [-0.02410458 0.03978052] [-0.01653973 -0.02096177] [ 0.01046864 -0.05990141]] b1 = [[-1.02420756e-06] [ 1.27373948e-05] [ 8.32996807e-07] [-3.20136836e-06]] W2 = [[-0.01041081 -0.04463285 0.01758031 0.04747113]] b2 = [[0.00010457]]
# GRADED FUNCTION: nn_model def 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) ### 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 X_assess, Y_assess = nn_model_test_case() parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=False) print("W1 = " + str(parameters["W1"])) print("b1 = " + str(parameters["b1"])) print("W2 = " + str(parameters["W2"])) print("b2 = " + str(parameters["b2"]))
W1 = [[-4.18494502 5.33220306] [-7.52989352 1.24306198] [-4.19295477 5.32631754] [ 7.52983748 -1.24309404]] b1 = [[ 2.32926814] [ 3.79459053] [ 2.3300254 ] [-3.79468789]] W2 = [[-6033.83672183 -6008.12981297 -6033.10095335 6008.0663689 ]] b2 = [[-52.666077]]
# GRADED FUNCTION: predict def 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 = np.round(A2) ### END CODE HERE ### return predictions parameters, X_assess = predict_test_case() predictions = predict(parameters, X_assess) print("predictions mean = " + str(np.mean(predictions)))
predictions mean = 0.6666666666666666
# Build a model with a n_h-dimensional hidden layer parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True) # Plot the decision boundary plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y) plt.title("Decision Boundary for hidden layer size " + str(4))
# Print accuracy predictions = predict(parameters, X) print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%'
Accuracy: 90%
# This may take about 2 minutes to run plt.figure(figsize=(16, 32)) hidden_layer_sizes = [1, 2, 3, 4, 5, 10, 20] for i, n_h in enumerate(hidden_layer_sizes): # i denote index of array 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))
Accuracy for 1 hidden units: 67.5 % Accuracy for 2 hidden units: 67.25 % Accuracy for 3 hidden units: 90.75 % Accuracy for 4 hidden units: 90.5 % Accuracy for 5 hidden units: 91.25 % Accuracy for 10 hidden units: 90.25 % Accuracy for 20 hidden units: 90.5 %
Performance on other datasets
# Datasets noisy_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) plt.figure(figsize=(16, 32)) for i, dataset in enumerate(datasets.values()): ### END CODE HERE ### X, Y = dataset X, Y = X.T, Y.reshape(1, Y.shape[0]) # make blobs binary if dataset == "blobs": Y = Y%2 plt.subplot(5, 2, i+1) # Visualize the data plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral);