给定数据利用神经网络算法模型进行计算，利用FP、BP算法，求得模型最优值。

神经网络初步学习使用。

import numpy as np
import matplotlib.pylab as plt
from numpy import *
from pylab import *

from sklearn.neural_network import MLPClassifier

# 中文 负号
mpl.rcParams['font.sans-serif']=['SimHei']
matplotlib.rcParams['axes.unicode_minus']=False

X1 = [0.697,0.774,0.634,0.608,0.556,0.403,0.481,0.437,0.666,0.243,0.245,0.343,0.639,0.657,0.360,0.593,0.719]
X2 = [0.460,0.376,0.264,0.318,0.215,0.237,0.149,0.211,0.091,0.267,0.057,0.099,0.161,0.198,0.370,0.042,0.103]
Y = [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]

# 数据初始化
m = len(X1)
X = np.c_[np.ones(m),X1,X2]
y = np.c_[Y]

# 数据重新洗牌/打乱
np.random.seed(3)
order=np.random.permutation(m)
X=X[order]
y=y[order]

# 将数据切割 分为训练集和测试集
d = int(m*0.75)
train_X,test_X=np.split(X,[d,])
train_y,test_y=np.split(y,[d,])

# 定义Sigmoid函数g(z)函数
def g(z,deriv=False):
    if deriv == True:
        return z*(1-z)
    return 1.0/(1.0+np.exp(-z))

# 初始化theta值 定义神经网络网格结构  L1=3,L2=17,L3=1
np.random.seed(3)
theta1=2*np.random.random((3,17))-1
theta2=2*np.random.random((17,1))-1

# 初始化代价值
J_hietory = np.zeros(15000)

# 开始神经网络迭代
for i in range(15000):
    # 前项传播算法
    a1 = train_X
    z2 = a1.dot(theta1)
    a2 = g(z2)
    z3 = a2.dot(theta2)
    a3 = g(z3)
    h = a3


    # 记录每次代价
    J_hietory[i] = -1.0/m*(np.dot(train_y.T,np.log(h))+np.dot((1-train_y).T,np.log((1-h))))

    # 反向传播算法

    # 每层的delta
    delta_L3 = a3-train_y
    delta_L2 = delta_L3.dot(theta2.T)*g(a2,True)
    # 每层的deltatheta
    deltatheta2 = 1.0/m*np.dot(a2.T,delta_L3)
    deltatheta1 = 1.0/m*np.dot(a1.T,delta_L2)
    # 每层的theta更新
    theta2 -= 0.8*deltatheta2
    theta1 -= 0.8*deltatheta1

plt.plot(J_hietory)
plt.show()


# 定义准确率函数
def testAccuracy(X,y):
    m = X.shape[0]
    count = 0

    for i in range(m):
        a1 = X[i]
        z2 = a1.dot(theta1)
        a2 = g(z2)
        z3 = a2.dot(theta2)
        a3 = g(z3)
        h = a3

        if bool(np.where(h>=0.5,1,0)) == bool(y[i]):
            count += 1
    return count/m

# 分别计算训练集和测试集的准确率
print('训练集的准确率：',testAccuracy(train_X,train_y)*100,'%')
print('训练集的准确率：',testAccuracy(test_X,test_y)*100,'%')