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  • Planar data classification with one hidden layer

    如果直接看代码对你来说有困难: 参考 https://blog.csdn.net/u013733326/article/details/79702148
    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)
    

    在这里插入图片描述

    ### 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)")
    

    在这里插入图片描述

    # 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))
    

    在这里插入图片描述

    # 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 %
    

    在这里插入图片描述

    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);
    

    在这里插入图片描述

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  • 原文地址:https://www.cnblogs.com/wanghongze95/p/13842547.html
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