（1.2）Planar data classification.zip_usuallyrpr_分类_深度学习

# 1 Package imports import numpy as np import matplotlib.pyplot as plt from testCases_v2 import * import sklearn import sklearn.datasets import sklearn.linear_model from planar_utils import plot_decision_boundary, sigmoid, load_extra_datasets #%matplotlib inline np.random.seed(1) # set a seed so that the results are consistent #2 - Dataset def load_planar_dataset(): np.random.seed(1) m = 400 # 样本数量 N = int(m/2) # 每个类别的样本量 D = 2 # 维度数 X = np.zeros((m,D)) # 初始化X Y = np.zeros((m,1), dtype='uint8') # 初始化Y a = 4 # 花儿的最大长度 for j in range(2): ix = range(N*j,N*(j+1)) t = np.linspace(j*3.12,(j+1)*3.12,N) + np.random.randn(N)*0.2 # theta r = a*np.sin(4*t) + np.random.randn(N)*0.2 # radius X[ix] = np.c_[r*np.sin(t), r*np.cos(t)] Y[ix] = j X = X.T Y = Y.T return X, Y X, Y = load_planar_dataset() # Visualize the data: plt.scatter(X[0, :].reshape(Y.shape), X[1, :].reshape(Y.shape), c=Y, s=40, cmap=plt.cm.Spectral,alpha=0.5); plt.show() print ('The shape of X is: ' + str(X.shape)) print ('The shape of Y is: ' + str(Y.shape)) print ('I have m = %d training examples!' % (Y.size)) #3 - Simple Logistic Regression # Train the logistic regression classifier clf = sklearn.linear_model.LogisticRegressionCV(); clf.fit(X.T, Y.T); # Plot the decision boundary for logistic regression plot_decision_boundary(lambda x: clf.predict(x), X, Y) plt.title("Logistic Regression") plt.show() # 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)") #4.1 - Defining the neural network structure # 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)) #4.2 - Initialize the model’s parameters # 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) b1 = np.zeros((n_h, 1)) W2 = np.random.randn(n_y, n_h) 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"])) #4.3 - The Loop # 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'])) # 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(np.log(1-A2), (1-Y)) cost = -(1.0/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 A2, Y_assess, parameters = compute_cost_test_case() print("cost = " + str(compute_cost(A2, Y_assess, parameters))) # 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 = 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