本文通过TensorFlow生成双层神经网络，对二次函数进行拟合。
双层神经网络如下图所示。
weights代表神经元的权重，activation_function是激活函数sgn或sigmoid或relu函数
构建神经网络的函数
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def add_layer(inputs, in_size, out_size, activation_function=None): Weights = tf.Variable(tf.random_normal([in_size, out_size])) biases = tf.Variable(tf.zeros([1, out_size]) + 0.1) Wx_plus_b = tf.matmul(inputs, Weights) + biases if activation_function is None: outputs = Wx_plus_b else: outputs = activation_function(Wx_plus_b) return outputs |
主要步骤：
①生成测试数据集，利用numpy来生成坐标轴的点，并在点上添加噪音。
②添加占位符
③添加隐藏层与输出层
④定义loss function，计算误差，并用梯度下降使得误差最小
⑤训练数据，拟合曲线
源码：
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from __future__ import print_function import tensorflow as tf import numpy as np import matplotlib.pyplot as plt import time def add_layer(inputs, in_size, out_size, activation_function=None): Weights = tf.Variable(tf.random_normal([in_size, out_size])) biases = tf.Variable(tf.zeros([1, out_size]) + 0.1) Wx_plus_b = tf.matmul(inputs, Weights) + biases if activation_function is None: outputs = Wx_plus_b else: outputs = activation_function(Wx_plus_b) return outputs # 数据集的生成，利用np来生成-1~2的300个点 x_data = np.linspace(-1, 2, num=300)[:, np.newaxis] # 添加噪音 noise = np.random.normal(0, 0.05, x_data.shape) # 计算Y轴的值 y_data = np.square(x_data) - 0.5 + noise # 添加占位符 xs = tf.placeholder(tf.float32, [None, 1]) ys = tf.placeholder(tf.float32, [None, 1]) # 添加隐藏层 l1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu) # 添加输出层 prediction = add_layer(l1, 10, 1, activation_function=None) # 由此生成了两层神经网络 # 计算误差，并用梯度下降使得误差最小 loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction), reduction_indices=[1])) train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss) # important step init = tf.initialize_all_variables() sess = tf.Session() sess.run(init) # 画出原始值 fig = plt.figure() ax = fig.add_subplot(1, 1, 1) ax.scatter(x_data, y_data) plt.ion() plt.show() lines = None time.sleep(4) # 显示拟合 for i in range(1000): sess.run(train_step, feed_dict={xs: x_data, ys: y_data}) try: ax.lines.remove(lines[0]) except Exception: pass prediction_value = sess.run(prediction, feed_dict={xs: x_data}) lines = ax.plot(x_data, prediction_value, 'r-', lw=5) plt.pause(0.1) writer = tf.train.SummaryWriter("logs/", sess.graph) |
结果：
