浅层神经网络模型python实现

浅层神经网络模型python实现

文章目录

• 浅层神经网络模型python实现
• 注：
• 1.准备工作
• 导入需要的包
• testCases.py
• planar_utils.py
• 导入数据集
• 可视化数据集
• 2. 采用逻辑回归模型分类（可选）
• 3. 采用神经网络模型
• 获取每层size
• 初始化参数
• 前向传播
• 计算函数代价
• 反向传播
• 合成模型
• 预测函数
• 测试模型
• 计算正确率
• 尝试不同layer size（可选）
• 尝试其他数据集

注：

数据集及详细讲解请查找吴恩达深度学习第一课第三周，本篇博客为编程作业总结。
GitHub资料：https://github.com/TangZhaoXiang/deeplearning.ai.git

1.准备工作

导入需要的包

# Package imports
import numpy as np
import matplotlib.pyplot as plt
from testCases import *         # 自定义的testCases.py，包含测试实例，
import sklearn                  # ML神器，对一些常用的机器学习方法进行了封装
import sklearn.datasets         # sklearn中包含了大量的优质的数据集
import sklearn.linear_model     # sklearn的线性模型
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets    # 自定义的planar_utils.py

%matplotlib inline

np.random.seed(1) # set a seed so that the results are consistent

testCases.py

# TZX: testCases.py
import numpy as np

def layer_sizes_test_case():   # 测试每层宽度
    np.random.seed(1)
    X_assess = np.random.randn(5, 3)
    Y_assess = np.random.randn(2, 3)
    return X_assess, Y_assess

def initialize_parameters_test_case():
    n_x, n_h, n_y = 2, 4, 1
    return n_x, n_h, n_y

def forward_propagation_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)

    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    return X_assess, parameters

def compute_cost_test_case():
    np.random.seed(1)
    Y_assess = np.random.randn(1, 3)
    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    a2 = (np.array([[ 0.5002307 ,  0.49985831,  0.50023963]]))
    
    return a2, Y_assess, parameters

def backward_propagation_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    Y_assess = np.random.randn(1, 3)
    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    cache = {'A1': np.array([[-0.00616578,  0.0020626 ,  0.00349619],
         [-0.05225116,  0.02725659, -0.02646251],
         [-0.02009721,  0.0036869 ,  0.02883756],
         [ 0.02152675, -0.01385234,  0.02599885]]),
  'A2': np.array([[ 0.5002307 ,  0.49985831,  0.50023963]]),
  'Z1': np.array([[-0.00616586,  0.0020626 ,  0.0034962 ],
         [-0.05229879,  0.02726335, -0.02646869],
         [-0.02009991,  0.00368692,  0.02884556],
         [ 0.02153007, -0.01385322,  0.02600471]]),
  'Z2': np.array([[ 0.00092281, -0.00056678,  0.00095853]])}
    return parameters, cache, X_assess, Y_assess

def update_parameters_test_case():
    parameters = {'W1': np.array([[-0.00615039,  0.0169021 ],
        [-0.02311792,  0.03137121],
        [-0.0169217 , -0.01752545],
        [ 0.00935436, -0.05018221]]),
 'W2': np.array([[-0.0104319 , -0.04019007,  0.01607211,  0.04440255]]),
 'b1': np.array([[ -8.97523455e-07],
        [  8.15562092e-06],
        [  6.04810633e-07],
        [ -2.54560700e-06]]),
 'b2': np.array([[  9.14954378e-05]])}

    grads = {'dW1': np.array([[ 0.00023322, -0.00205423],
        [ 0.00082222, -0.00700776],
        [-0.00031831,  0.0028636 ],
        [-0.00092857,  0.00809933]]),
 'dW2': np.array([[ -1.75740039e-05,   3.70231337e-03,  -1.25683095e-03,
          -2.55715317e-03]]),
 'db1': np.array([[  1.05570087e-07],
        [ -3.81814487e-06],
        [ -1.90155145e-07],
        [  5.46467802e-07]]),
 'db2': np.array([[ -1.08923140e-05]])}
    return parameters, grads

def nn_model_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    Y_assess = np.random.randn(1, 3)
    return X_assess, Y_assess

def predict_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    parameters = {'W1': np.array([[-0.00615039,  0.0169021 ],
        [-0.02311792,  0.03137121],
        [-0.0169217 , -0.01752545],
        [ 0.00935436, -0.05018221]]),
     'W2': np.array([[-0.0104319 , -0.04019007,  0.01607211,  0.04440255]]),
     'b1': np.array([[ -8.97523455e-07],
        [  8.15562092e-06],
        [  6.04810633e-07],
        [ -2.54560700e-06]]),
     'b2': np.array([[  9.14954378e-05]])}
    return parameters, X_assess

planar_utils.py

# 自定义的planar_utils.py
import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model

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=np.squeeze(y), cmap=plt.cm.Spectral)
    

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

def load_planar_dataset():   # 创建数据集
    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))  # 分段：j=0时，,[00,200），j=1时，[200，400）
        #j=0：划分[0，3.12，200]的结果 + 符合正态分布的一维数组（200，）* 0.2
        t = np.linspace(j*3.12,(j+1)*3.12,N) + np.random.randn(N)*0.2 # theta  (200,)
        # r = 4sin(4t) + 随机数组（200，） * 0.2
        r = a*np.sin(4*t) + np.random.randn(N)*0.2  # radius半径  (200,)  什么东西？ 
        X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]   # 拼接
        Y[ix] = j
        # print(X[ix],Y[ix])    
        
    X = X.T
    Y = Y.T
    
    return X, Y

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

导入数据集

X, Y = load_planar_dataset() 

可视化数据集

# Visualize the data:
plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral);

说明：可以看到，这朵花的红蓝花瓣相互交叉，很难区分开。——线性不可分

2. 采用逻辑回归模型分类（可选）

这里采用sklearn里面的逻辑回归模型进行分类（两步就搞定！）

# Train the logistic regression classifier
clf = sklearn.linear_model.LogisticRegressionCV();  # sklearn的逻辑回归模型
clf.fit(X.T, Y.T);  # 拟合数据

# 画出决策边界
plot_decision_boundary(lambda x: clf.predict(x), X, Y)   # planar_utils.py的函数
plt.title("Logistic Regression")

# 打印正确率
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)")

3. 采用神经网络模型

Here is our model:

Mathematically:

For one example $x^{(i)}$x(i):
$z^{[1] (i)} = W^{[1]} x^{(i)} + b^{[1] (i)}\tag{1}$z[1](i)=W[1]x(i)+b[1](i)(1)
$a^{[1] (i)} = \tanh(z^{[1] (i)})\tag{2}$a[1](i)=tanh(z[1](i))(2)
$z^{[2] (i)} = W^{[2]} a^{[1] (i)} + b^{[2] (i)}\tag{3}$z[2](i)=W[2]a[1](i)+b[2](i)(3)
$\hat{y}^{(i)} = a^{[2] (i)} = \sigma(z^{ [2] (i)})\tag{4}$y^​(i)=a[2](i)=σ(z[2](i))(4)
KaTeX parse error: Expected & or \\ or \cr or \end at position 42: …gin{cases} 1 & \̲m̲b̲o̲x̲{if } a^{[2](i)…

Given the predictions on all the examples, you can also compute the cost $J$J as follows:
$J = - \frac{1}{m} \sum\limits_{i = 0}^{m} \large\left(\small y^{(i)}\log\left(a^{[2] (i)}\right) + (1-y^{(i)})\log\left(1- a^{[2] (i)}\right) \large \right) \small \tag{6}$J=−m1​i=0∑m​(y(i)log(a[2](i))+(1−y(i))log(1−a[2](i)))(6)

获取每层size

# GRADED FUNCTION: layer_sizes
# X(2,400),Y(1,400)

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]
    n_h = 4
    n_y = Y.shape[0] # 0和1

    ### END CODE HERE ###
    return (n_x, n_h, n_y)

初始化参数

# 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 ###
    
    # 确保程序shape正确非常重要！
    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))
    
    # 这种导出方式很赞
    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    
    return parameters

前向传播

# 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']
    # print("W1,b1,W2,b2的shape：",W1.shape,b1.shape,W2.shape,b2.shape)
    ### END CODE HERE ###
    
    # Implement Forward Propagation to calculate A2 (probabilities)
    ### START CODE HERE ### (≈ 4 lines of code)
    Z1 = np.matmul(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.matmul(W2, A1) + b2
    A2 = sigmoid(Z2)
    # print("Z1,A1,Z2,A2的shape：",Z1.shape,A1.shape,Z2.shape,A2.shape)
    ### END CODE HERE ###
    
    assert(A2.shape == (1, X.shape[1]))   # 断言功能强大，帮助错误定位
    
    cache = {"Z1": Z1,
             "A1": A1,
             "Z2": Z2,
             "A2": A2}
    
    return A2, cache

计算函数代价

# 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(Y, np.log(A2)) + np.multiply(1 - Y, np.log(1 - A2))
    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

反向传播

# 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                                         # **函数为sigmoid
    dW2 = np.matmul(dZ2, A1.T) / m
    db2 = np.sum(dZ2, axis=1, keepdims= True) / m
    dZ1 = np.matmul(W2.T, dZ2) * (1 - np.power(A1, 2))   # **函数为tanh
    dW1 = np.matmul(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

合成模型

# 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]   # 2
    n_y = layer_sizes(X, Y)[2]   # 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

预测函数

# 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 = (A2 > 0.5)
    ### END CODE HERE ###
    
    return predictions

测试模型

# Build a model with a n_h-dimensional hidden layer
parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)

# 画出决策边界
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title("Decision Boundary for hidden layer size " + str(4))

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: 0.219456
Cost after iteration 9000: 0.218558

计算正确率

# 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%

尝试不同layer size（可选）

# This may take about 2 minutes to run

plt.figure(figsize=(16, 32))
hidden_layer_sizes = [1, 2, 3, 4, 5, 10, 20]    # n_h数量
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))

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: 90.0 %

可以看出：当size =5时，效果最好，而当size增大到20时，已经开始出现过拟合现象。
以后也可以通过这种方式来决定隐藏层单元个数！

一些经验是：

• 隐藏层中至少有一层，其单元数必须大于输入层单元数，才能发挥NN的效果。
• 总的来说，隐藏层单元数越多，越能拟合数据集，但是过多会导致过拟合，如上面的size=20
• 使用正则化，可以是size很大的模型也能避免过拟合

尝试其他数据集

# 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)
dataset = "gaussian_quantiles"
### END CODE HERE ###

X, Y = datasets[dataset]
X, Y = X.T, Y.reshape(1, Y.shape[0])

# make blobs binary
if dataset == "blobs":
    Y = Y%2

# Visualize the data
plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral);

# Build a model with a n_h-dimensional hidden layer
parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)
#print(parameters)

# 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))

Cost after iteration 0: 0.693139
Cost after iteration 1000: 0.126985
Cost after iteration 2000: 0.130040
Cost after iteration 3000: 0.130737
Cost after iteration 4000: 0.131268
Cost after iteration 5000: 0.189943
Cost after iteration 6000: 0.165035
Cost after iteration 7000: 0.187770
Cost after iteration 8000: 0.249635
Cost after iteration 9000: 0.098592

# This may take about 2 minutes to run

plt.figure(figsize=(16, 32))
hidden_layer_sizes = [1, 2, 3, 4, 5, 10, 20]    # n_h数量
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))

Accuracy for 1 hidden units: 67.0 %
Accuracy for 2 hidden units: 80.0 %
Accuracy for 3 hidden units: 95.0 %
Accuracy for 4 hidden units: 90.0 %
Accuracy for 5 hidden units: 92.5 %
Accuracy for 10 hidden units: 98.5 %
Accuracy for 20 hidden units: 97.5 %