python实现单隐层神经网络

功能：实现用神经网络对多样本数据进行分类训练

改进方法：应该把每次训练好的参数写入txt或json中，可以通过选择是否重新训练来调节 预测速度和 准确率的关系

demo.py

import numpy as np
import matplotlib.pyplot as plt
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset

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_y = Y.shape[0] # size of output layer
    ### END CODE HERE ###
    return (n_x, n_y)
    
    np.random.seed(1) # set a seed so that the results are consistent
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

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

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 = float(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 = -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

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 = float(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/m * np.dot(dZ2, A1.T)
    db2 =1/m * np.sum(dZ2, axis=1, keepdims=True)
    dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))
    dW1 = 1/m * np.dot(dZ1, X.T)
    db1 =1/m * np.sum(dZ1, axis=1, keepdims=True)
    ### END CODE HERE ###
    
    grads = {"dW1": dW1,
            "db1": db1,
            "dW2": dW2,
            "db2": db2}
    
    return grads

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 = W1 - learning_rate * dW1
    b1 = b1 - learning_rate * db1
    W2 = W2 - learning_rate * dW2
    b2 = b2 - learning_rate * db2
    ### END CODE HERE ###
    
    parameters = {"W1": W1,
    "b1": b1,
    "W2": W2,
    "b2": b2}
    
    return parameters
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)
    
    # 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)
    n_x, n_y = layer_sizes(X, Y)
    parameters = initialize_parameters(n_x, n_h, n_y)
    ### 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
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.array( [1 if x >0.5 else 0 for x in A2.reshape(-1,1)] ).reshape(A2.shape) # 这一行代码的作用详见下面代码示例
    ### END CODE HERE ###
    
    return predictions

X, Y = load_planar_dataset()

# print(X.shape) #(2, 400) 在load中进行了转置，其中2代表单个样本特征数，400 代表样本数
# print(Y.shape) #(1, 400) 在load中进行了转置，本例中1代表输出层个数，400 代表样本数

plt.scatter(X[0, :], X[1, :], c=Y, s=40); #c代表色彩或颜色序列 s代表标量或形如shape[n,]数组
# 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)

pre = predict(parameters, X)
print ('training accuracy: %.2f' % (np.mean(pre == Y[0])))

plt.title("Decision Boundary for hidden layer size " + str(4))
plt.show()

planar_utils.py

'''
Created on 2018年7月18日

@author: hcl
'''
import matplotlib.pyplot as plt
import numpy as np

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) 
    plt.ylabel('x2')
    plt.xlabel('x1')
    plt.scatter(X[0, :], X[1, :], c=y)
    
def sigmoid(x):
    """
    Compute the sigmoid of x

    Arguments:
    x -- A scalar or numpy array of any size.

    Return:
    s -- sigmoid(x)
    """
    s = 1/(1+np.exp(-x))
    return s

def load_planar_dataset():
    np.random.seed(1)
    m = 400 # number of examples
    N = int(m/2) # number of points per class
    D = 2 # dimensionality
    X = np.zeros((m,D)) # data matrix where each row is a single example
    Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue)
    a = 4 # maximum ray of the flower
    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

输出：

Cost after iteration 0: 0.693048
Cost after iteration 1000: 0.288083
Cost after iteration 2000: 0.254385
Cost after iteration 3000: 0.233864
Cost after iteration 4000: 0.226792
Cost after iteration 5000: 0.222644
Cost after iteration 6000: 0.219731
Cost after iteration 7000: 0.217504
Cost after iteration 8000: 0.219504
Cost after iteration 9000: 0.218571
training accuracy: 0.91

 

1：通过修改对应的X Y数据集 可以训练不同的数据

X = np.array([  [0,0,1],
                [1,1,1],
                [1,0,1],
                [0,1,1] ]).T
Y = np.array([[0,1,1,0]])

输出；

Cost after iteration 0: 0.693173
Cost after iteration 1000: 0.000294
Cost after iteration 2000: 0.000138
Cost after iteration 3000: 0.000090
Cost after iteration 4000: 0.000066
Cost after iteration 5000: 0.000052
Cost after iteration 6000: 0.000043
Cost after iteration 7000: 0.000037
Cost after iteration 8000: 0.000032
Cost after iteration 9000: 0.000028

2：在planar_utils.py中添加 

并在开头导入：import sklearn.datasets

def load_extra_datasets():  
    N = 200
    noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)
    noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)
    blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)
    gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)
    no_structure = np.random.rand(N, 2), np.random.rand(N, 2)
    
    return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure

在demo.py中 导入load_extra_datasets

并将X Y数据来源 改为：

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,
            }

dataset = 'noisy_moons'

X,Y = datasets[dataset]
X,Y = X.T, Y.reshape(1,Y.shape[0])
if dataset == 'blobs':
    Y = Y % 2
    
plt.scatter(X[0, :], X[1, :], c=Y, s=40)

训练输出：

Cost after iteration 0: 0.692994
Cost after iteration 1000: 0.299064
Cost after iteration 2000: 0.131752
Cost after iteration 3000: 0.124443
Cost after iteration 4000: 0.121406
Cost after iteration 5000: 0.118751
Cost after iteration 6000: 0.116311
Cost after iteration 7000: 0.114297
Cost after iteration 8000: 0.112747
Cost after iteration 9000: 0.111537
training accuracy: 0.95

3、查看不同隐藏层节点数对预测数据精确度的影响

 在获取X Y数据集以后：

plt.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))

plt.show()

输出：

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 20 hidden units: 90.0 %
Accuracy for 50 hidden units: 90.75 %