2.非线性回归

import keras
import numpy as np
import matplotlib.pyplot as plt
# Sequential按顺序构成的模型
from keras.models import Sequential
# Dense全连接层
from keras.layers import Dense,Activation
from keras.optimizers import SGD

# 使用numpy生成200个随机点 
x_data = np.linspace(-0.5,0.5,200)
noise = np.random.normal(0,0.02,x_data.shape)
y_data = np.square(x_data) + noise

# 显示随机点
plt.scatter(x_data,y_data)
plt.show()

# 构建一个顺序模型
model = Sequential()
# 在模型中添加一个全连接层
# 1-10-1
model.add(Dense(units=10,input_dim=1,activation='relu'))
# model.add(Activation('tanh'))
model.add(Dense(units=1,activation='relu'))
# model.add(Activation('tanh'))
# 定义优化算法
sgd = SGD(lr=0.3)
# sgd:Stochastic gradient descent，随机梯度下降法
# mse:Mean Squared Error，均方误差
model.compile(optimizer=sgd,loss='mse')

# 训练3001个批次
for step in range(3001):
    # 每次训练一个批次
    cost = model.train_on_batch(x_data,y_data)
    # 每500个batch打印一次cost值
    if step % 500 == 0:
        print('cost:',cost)

# x_data输入网络中，得到预测值y_pred
y_pred = model.predict(x_data)

# 显示随机点
plt.scatter(x_data,y_data)
# 显示预测结果
plt.plot(x_data,y_pred,'r-',lw=3)
plt.show()