tensorflow学习笔记二——建立一个简单的神经网络

本笔记目的是通过tensorflow实现一个两层的神经网络。目的是实现一个二次函数的拟合。

如何添加一层网络

代码如下：

def add_layer(inputs, in_size, out_size, activation_function=None):    # add one more layer and return the output of this layer    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

注意该函数中是xW+b，而不是Wx+b。所以要注意乘法的顺序。x应该定义为[类别数量， 数据数量]， W定义为[数据类别，类别数量]。

创建一些数据

# Make up some real datax_data = np.linspace(-1,1,300)[:, np.newaxis]noise = np.random.normal(0, 0.05, x_data.shape)y_data = np.square(x_data) - 0.5 + noise

numpy的linspace函数能够产生等差数列。start,stop决定等差数列的起止值。endpoint参数指定包不包括终点值。
numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)[source]
Return evenly spaced numbers over a specified interval.
Returns num evenly spaced samples, calculated over the interval [start, stop].

noise函数为添加噪声所用，这样二次函数的点不会与二次函数曲线完全重合。

numpy的newaxis可以新增一个维度而不需要重新创建相应的shape在赋值，非常方便，如上面的例子中就将x_data从一维变成了二维。

添加占位符，用作输入

# define placeholder for inputs to networkxs = tf.placeholder(tf.float32, [None, 1])ys = tf.placeholder(tf.float32, [None, 1])

添加隐藏层和输出层

# add hidden layerl1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)# add output layerprediction = add_layer(l1, 10, 1, activation_function=None)

计算误差，并用梯度下降使得误差最小

# the error between prediciton and real dataloss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),reduction_indices=[1]))train_step =  tf.train.GradientDescentOptimizer(0.1).minimize(loss)

完整代码如下：

from __future__ import print_functionimport tensorflow as tfimport numpy as npimport matplotlib.pyplot as pltdef add_layer(inputs, in_size, out_size, activation_function=None):    # add one more layer and return the output of this layer    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# Make up some real datax_data = np.linspace(-1,1,300)[:, np.newaxis]noise = np.random.normal(0, 0.05, x_data.shape)y_data = np.square(x_data) - 0.5 + noise# define placeholder for inputs to networkxs = tf.placeholder(tf.float32, [None, 1])ys = tf.placeholder(tf.float32, [None, 1])# add hidden layerl1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)# add output layerprediction = add_layer(l1, 10, 1, activation_function=None)# the error between prediciton and real dataloss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),                     reduction_indices=[1]))train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)# important stepinit = tf.initialize_all_variables()sess = tf.Session()sess.run(init)# plot the real datafig = plt.figure()ax = fig.add_subplot(1,1,1)ax.scatter(x_data, y_data)plt.ion()plt.show()for i in range(1000):    # training    sess.run(train_step, feed_dict={xs: x_data, ys: y_data})    if i % 50 == 0:        # to visualize the result and improvement        try:            ax.lines.remove(lines[0])        except Exception:            pass        prediction_value = sess.run(prediction, feed_dict={xs: x_data})        # plot the prediction        lines = ax.plot(x_data, prediction_value, 'r-', lw=5)        plt.pause(0.1)

运行结果：