运行环境

• Pyhton3
• numpy(科学计算包)
• matplotlib(画图所需，不画图可不必)
• sklearn(人工智能包，生成数据使用)

计算过程

输入样例

none

代码实现

# -*- coding:utf-8 -*-

#!python3

__author__ = 'Wsine'

import numpy as np

import sklearn

import sklearn.datasets

import sklearn.linear_model

import matplotlib.pyplot as plt

import matplotlib

import operator

import time

def createData(dim=200, cnoise=0.20):

"""

输出：数据集, 对应的类别标签

描述：生成一个数据集和对应的类别标签

"""

np.random.seed(0)

X, y = sklearn.datasets.make_moons(dim, noise=cnoise)

plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)

#plt.show()

return X, y

def plot_decision_boundary(pred_func, X, y):

"""

输入：边界函数, 数据集, 类别标签

描述：绘制决策边界(画图用)

"""

# 设置最小最大值, 加上一点外边界

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 = 0.01

# 根据最小最大值和一个网格距离生成整个网格

xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

# 对整个网格预测边界值

Z = pred_func(np.c_[xx.ravel(), yy.ravel()])

Z = Z.reshape(xx.shape)

# 绘制边界和数据集的点

plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)

plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)

def calculate_loss(model, X, y):

"""

输入：训练模型, 数据集, 类别标签

输出：误判的概率

描述：计算整个模型的性能

"""

W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']

# 正向传播来计算预测的分类值

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)

# 计算误判概率

corect_logprobs = -np.log(probs[range(num_examples), y])

data_loss = np.sum(corect_logprobs)

# 加入正则项修正错误(可选)

data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))

return 1./num_examples * data_loss

def predict(model, x):

"""

输入：训练模型, 预测向量

输出：判决类别

描述：预测类别属于(0 or 1)

"""

W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']

# 正向传播计算

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)

return np.argmax(probs, axis=1)

def initParameter(X):

"""

输入：数据集

描述：初始化神经网络算法的参数

必须初始化为全局函数！

这里需要手动设置！

"""

global num_examples

num_examples = len(X) # 训练集的大小

global nn_input_dim

nn_input_dim = 2 # 输入层维数

global nn_output_dim

nn_output_dim = 2 # 输出层维数

# 梯度下降参数

global epsilon

epsilon = 0.01 # 梯度下降学习步长

global reg_lambda

reg_lambda = 0.01 # 修正的指数

def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False):

"""

输入：数据集, 类别标签, 隐藏层层数, 迭代次数, 是否输出误判率

输出：神经网络模型

描述：生成一个指定层数的神经网络模型

"""

# 根据维度随机初始化参数

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))

model = {}

# 梯度下降

for i in range(0, num_passes):

# 正向传播

z1 = X.dot(W1) + b1

a1 = np.tanh(z1) # 激活函数使用tanh = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

z2 = a1.dot(W2) + b2

exp_scores = np.exp(z2) # 原始归一化

probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)

# 后向传播

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)

# 加入修正项

dW2 += reg_lambda * W2

dW1 += reg_lambda * W1

# 更新梯度下降参数

W1 += -epsilon * dW1

b1 += -epsilon * db1

W2 += -epsilon * dW2

b2 += -epsilon * db2

# 更新模型

model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}

# 一定迭代次数后输出当前误判率

if print_loss and i % 1000 == 0:

print("Loss after iteration %i: %f" % (i, calculate_loss(model, X, y)))

plot_decision_boundary(lambda x: predict(model, x), X, y)

plt.title("Decision Boundary for hidden layer size %d" % nn_hdim)

#plt.show()

return model

def main():

dataSet, labels = createData(200, 0.20)

initParameter(dataSet)

nnModel = build_model(dataSet, labels, 3, print_loss=False)

print("Loss is %f" % calculate_loss(nnModel, dataSet, labels))

if __name__ == '__main__':

start = time.clock()

main()

end = time.clock()

print('finish all in %s' % str(end - start))

plt.show()

输出样例

Loss is 0.071316

finish all in 7.221354361552228

来源：邵寒峰