Neural_network_example
import numpy as np
from sklearn.datasets import make_moons
import matplotlib.pyplot as plt
# 手动生成一个随机的平面点分布，并画出来
#np.random.seed(0)
X, y = make_moons(200, noise=0.3)
print(X.shape,y.shape)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)
plt.show()
# 咱们先顶一个一个函数来画决策边界
def plot_decision_boundary(pred_func):# 设定最大最小值，附加一点点边缘填充
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
h = 0.01xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# 用预测函数预测一下
Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)# 然后画出图
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)
from sklearn.linear_model import LogisticRegressionCV
#咱们先来瞄一眼逻辑斯特回归对于它的分类效果
clf = LogisticRegressionCV()
clf.fit(X, y)
# 画一下决策边界
plot_decision_boundary(lambda x: clf.predict(x))
plt.title("Logistic Regression")
plt.show()
num_examples = len(X) # 样本数
nn_input_dim = 2 # 输入的维度
nn_output_dim = 2 # 输出的类别个数
# 梯度下降参数
epsilon = 0.01 # 学习率
reg_lambda = 0.01 # 正则化参数# 定义损失函数(才能用梯度下降啊...)
def calculate_loss(model):
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
# 向前推进，前向运算
z1 = X.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
# 计算损失
corect_logprobs = -np.log(probs[range(num_examples), y])
data_loss = np.sum(corect_logprobs)
# 也得加一下正则化项
data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
return 1./num_examples * data_loss
# 完整的训练建模函数定义
def build_model(nn_hdim, num_passes=20000, print_loss=False):
'''
参数：
1) nn_hdim: 隐层节点个数
2）num_passes: 梯度下降迭代次数
3）print_loss: 设定为True的话，每1000次迭代输出一次loss的当前值
'''
# 随机初始化一下权重呗
np.random.seed(0)
W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
b1 = np.zeros((1, nn_hdim))
W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
b2 = np.zeros((1, nn_output_dim))
# 这是咱们最后学到的模型
model = {}
# 开始梯度下降...
for i in xrange(0, num_passes):
# 前向运算计算loss
z1 = X.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
# 反向传播
delta3 = probs
delta3[range(num_examples), y] -= 1
dW2 = (a1.T).dot(delta3)
db2 = np.sum(delta3, axis=0, keepdims=True)
delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
dW1 = np.dot(X.T, delta2)
db1 = np.sum(delta2, axis=0)
# 加上正则化项
dW2 += reg_lambda * W2
dW1 += reg_lambda * W1
# 梯度下降更新参数
W1 += -epsilon * dW1
b1 += -epsilon * db1
W2 += -epsilon * dW2
b2 += -epsilon * db2
# 得到的模型实际上就是这些权重
model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
# 如果设定print_loss了，那我们汇报一下中间状况
if print_loss and i % 1000 == 0:
print "Loss after iteration %i: %f" %(i, calculate_loss(model))
return model
# 判定结果的函数
def predict(model, x):
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
# 前向运算
z1 = x.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2)
# 计算概率输出最大概率对应的类别
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
return np.argmax(probs, axis=1)
# 建立隐层有3个节点(神经元)的神经网络
model = build_model(3, print_loss=True)
# 然后再把决策/判定边界画出来
plot_decision_boundary(lambda x: predict(model, x))
plt.title("Decision Boundary for hidden layer size 3")
plt.show()
# 然后听闻你想知道不同的隐层节点个数对结果的影响？
# 那咱们来一起看看吧
plt.figure(figsize=(16, 32))
# 设定不同的隐层节点(神经元)个数
hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]
for i, nn_hdim in enumerate(hidden_layer_dimensions):
plt.subplot(5, 2, i+1)
plt.title('Hidden Layer size %d' % nn_hdim)
model = build_model(nn_hdim)
plot_decision_boundary(lambda x: predict(model, x))
plt.show()