import numpy as np
import matplotlib.pyplot as plt
import planar_utils
1.3练习作业-自己编写的测试划分高斯分布的代码
0 准备神经网络需要的函数
0.1计算各个层的大小
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
"""
n_x = X.shape[0] # size of input layer
n_h = 4#the number of hiddrn is four
n_y = Y.shape[0] # size of output layer
return (n_x, n_h, n_y)
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.
W1 = np.random.randn(n_h, n_x) * 0.01#当n_h为4时W1为(4,2)
b1 = np.zeros((n_h, 1))#当n_h为4时b1为(4,1)
W2 = np.random.randn(n_y, n_h) * 0.01#当n_h为4时W2为(1,4)
b2 = np.zeros((n_y, 1))#b2为(1,1)
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"
W1 = parameters["W1"]#W1是4*2
b1 = parameters["b1"]#b1是4*1
W2 = parameters["W2"]#W2是1*4
b2 = parameters["b2"]#b2是1*1
# Implement Forward Propagation to calculate A2 (probabilities)
Z1 = np.dot(W1, X) + b1#W1为4*2,X为2*200,b1为4*1,Z1是4*200
A1 = np.tanh(Z1)#A1也是4*200
Z2 = np.dot(W2, A1) + b2#W2是1*4,A1是4*200，Z2是1*200
A2 = planar_utils.sigmoid(Z2)#A2是1*200
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 = Y.shape[1] # number of example Y为1*200,A2为1*200
# Compute the cross-entropy cost
logprobs = Y * np.log(A2) + (1 - Y) * np.log(1 - A2)#logprobs是1*200
cost = -1 / m * np.sum(logprobs)#cost值
cost = np.squeeze(cost) # makes sure cost is the dimension we expect.
#把1维的元素去掉
assert (isinstance(cost, float))#判断对象是否是已知类型
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 = X.shape[1]#X为2*200，m为200
#(1)retrieve W1 and W2 from the dictionary "parameters".
W1 = parameters["W1"]#W1为4*2
W2 = parameters["W2"]#W2为1*4
#(2)Retrieve also A1 and A2 from dictionary "cache".
A1 = cache["A1"]#A1为4*200
A2 = cache["A2"]#A2为1*200
#(3)Backward propagation: calculate dW1, db1, dW2, db2.书上有公式
dZ2 = A2 - Y#A2为1*200,Y为1*200，dZ2结果为1*200
dW2 = 1 / m * np.dot(dZ2, A1.T)#A1为4*200，A1.T为200*4,dW2结果为1*4
db2 = 1 / m * np.sum(dZ2, axis=1, keepdims=True)#db2为1*1
dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))#W2为1*4,W2.T为4*1,dZ2为1*200，np.dot(W2.T,dZ2)为4*200,A1为4*200，结果dZ1为4*200
dW1 = 1 / m * np.dot(dZ1, X.T)#dZ1为4*200,X为2*200,X.T为200*2，dW1为4*2
db1 = 1 / m * np.sum(dZ1, axis=1, keepdims=True)#db1为4*1
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"
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Retrieve each gradient from the dictionary "grads"
dW1 = grads["dW1"]
db1 = grads["db1"]
dW2 = grads["dW2"]
db2 = grads["db2"]
# Update rule for each parameter
W1 = W1 - learning_rate * dW1
b1 = b1 - learning_rate * db1
W2 = W2 - learning_rate * dW2
b2 = b2 - learning_rate * db2
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)
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".
parameters = initialize_parameters(n_x, n_h, n_y)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Loop (gradient descent)
#parameters={W1,b1,W2,b2}
for i in range(0, num_iterations):
# Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".
A2, cache = forward_propagation(X, parameters)
# A2是1 * 3,cache={Z1,A1,Z2,A2}
# Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".
cost = compute_cost(A2, Y, parameters)
# cost=0.692583903568
# Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".
grads = backward_propagation(parameters, cache, X, Y)
#grads = {dW1,db1,dW2,db2}
# Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".
parameters = update_parameters(parameters, grads)
# 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)
"""
#(1)Computes probabilities using forward propagation, and classifies to 0/1
# using 0.5 as the threshold.
A2, cache = forward_propagation(X, parameters)#根据X的值和parameters={W1,b1,W2,b2}预测
#预测结果A2为sigmoid(Z2),cache={Z1,A1,Z2,A2}
predictions = np.round(A2)#四舍五入
#(1)python 2中如果距离两端一样远，则保留到离0远的一边。所以
# round(0.5)会近似到1，而round(-0.5)会近似到-1。
#(2)python3中如果距离两边一样远，会保留到偶数的一边。比如
# round(0.5)和round(-0.5)都会保留到0，而round(1.5)会保留到2
return predictions
1、先观察测试数据的特征
print(“hello this is my first program!”)
noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = planar_utils.load_extra_datasets()
datasets = {“noisy_circles”: noisy_circles,#data为200*2,label为200
“noisy_moons”: noisy_moons,#data为200*2,label为200
“blobs”: blobs,#data为200*2,label为200
“gaussian_quantiles”: gaussian_quantiles}#data为200*2,label为200
dataset = “blobs”#可以更改不同的值，”noisy_circles”，”noisy_moons”
“blobs”，”gaussian_quantiles”看不同的分布
X, Y = datasets[dataset]#X是2*200数据,Ya是1*200标签
X, Y = X.T, Y.reshape(1, Y.shape[0])
make blobs binary，把Y变为0,1这样的数据
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);
plt.show()
2、构建神经网络并测试数据
2.1Build a model with a n_h-dimensionalhidden layer
parameters = nn_model(X, Y, n_h=4, num_iterations=10000, print_cost=True)
2.2Plot the decision boundary
planar_utils.plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title(“Decision Boundary for hidden layer size ” + str(4))
2.3Print accuracy
predictions = predict(parameters, X)#predictions是一个200个0或者1的向量
print(‘Accuracy: %d’ % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T))
/ float(Y.size) * 100) + ‘%’)