Step1:
目标：
使用线性模拟器模拟指定的直线：y = 0.1*x + 0.3
代码：
1 import tensorflow as tf 2 import numpy as np 3 import matplotlib.pyplot as plt 4 5 def show_data(x,y,w,b): 6 ''' 7 绘图函数 8 :param x: 横坐标散点 9 :param y: 纵坐标散点 10 :param w: 权重 11 :param b: 偏移量 12 :return: 无 13 ''' 14 plt.figure() 15 plt.scatter(x,y,marker='.') 16 plt.scatter(x,(w*x+b),marker='.') 17 plt.show() 18 19 ### 生成数据 ### 20 x_data = np.random.rand(100).astype(np.float32) 21 y_data = 0.1*x_data + 0.3 22 23 24 ### 创建结构 ### 25 26 Weights = tf.Variable(tf.random_uniform([1],-1.0,1.0)) 27 biases = tf.Variable(tf.zeros([1])) 28 29 y = Weights*x_data + biases 30 31 loss = tf.reduce_mean(tf.square(y-y_data)) # 损失函数 32 optimizer = tf.train.GradientDescentOptimizer(0.5) # 优化器&学习率选择 33 train = optimizer.minimize(loss) # 优化器优化目标选择 34 35 init = tf.global_variables_initializer() # 初始化全变量节点 36 37 38 ### 训练部分 39 40 with tf.Session() as sess: 41 sess.run(init) 42 for step in range(200): 43 sess.run(train) 44 if step % 20 == 0: 45 print(step,sess.run(Weights),sess.run(biases)) 46 show_data(x_data, y_data, sess.run(Weights), sess.run(biases))
返回：
/home/hellcat/anaconda2/envs/python3_6/bin/python /home/hellcat/PycharmProjects/data_analysis/TensorFlow/line_polyfit.py 2017-05-16 14:30:21.054380: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.1 instructions, but these are available on your machine and could speed up CPU computations. 2017-05-16 14:30:21.054405: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.2 instructions, but these are available on your machine and could speed up CPU computations. 2017-05-16 14:30:21.054412: W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX instructions, but these are available on your machine and could speed up CPU computations. 0 [-0.04776853] [ 0.48895872] 20 [ 0.05342153] [ 0.32313728] 40 [ 0.08880574] [ 0.30556062] 60 [ 0.09730968] [ 0.30133641] 80 [ 0.09935342] [ 0.30032119] 100 [ 0.0998446] [ 0.3000772] 120 [ 0.09996266] [ 0.30001855] 140 [ 0.09999102] [ 0.30000448] 160 [ 0.09999786] [ 0.30000108] 180 [ 0.09999949] [ 0.30000028] Process finished with exit code 0
给出第一次（左）和最后一次（右）的图，直观的感受一下拟合效果(蓝色为标准，黄色为拟合)：
step2:
目标：
使用神经网络拟合二次函数（加噪声）
代码：
1 import numpy as np 2 import tensorflow as tf 3 4 def add_layer(input,in_size,out_size,activation_function=None): 5 Weights = tf.Variable(tf.random_normal([in_size,out_size])) 6 biases = tf.Variable(tf.zeros([1,out_size]) + 0.1) 7 # [in]*[[out]*in]+[out] 8 Wx_plus_b = tf.matmul(input,Weights) + biases 9 if activation_function is None: 10 outputs = Wx_plus_b 11 else: 12 outputs = activation_function(Wx_plus_b) 13 return outputs 14 15 x_data = np.linspace(-1,1,300)[:,np.newaxis] # 插入新维度(300)->(300,1) 16 noise = np.random.normal(0,0.05,x_data.shape) 17 y_data = np.square(x_data) - 0.5 + noise # 平方 18 19 # 这样也可以在feed时修改标准数据的类型 20 xs = tf.placeholder(tf.float32,[None,1]) 21 ys = tf.placeholder(tf.float32,[None,1]) 22 23 l1 = add_layer(xs,1,10,activation_function=tf.nn.relu) 24 prediction =add_layer(l1,10,1,activation_function=None) 25 26 loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys-prediction),reduction_indices=[1])) 27 train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss) 28 29 init = tf.global_variables_initializer() 30 31 with tf.Session() as sess: 32 sess.run(init) 33 for i in range(1000): 34 sess.run(train_step,feed_dict={xs:x_data,ys:y_data}) 35 if i % 50 == 0: 36 print(sess.run(loss,feed_dict={xs:x_data,ys:y_data})) 37 # print(sess.run(tf.reduce_sum(tf.square(ys-prediction),reduction_indices=[1]), feed_dict={xs: x_data, ys: y_data}))
返回：
10.3325 0.0496612 0.0166555 0.0104833 0.00823758 0.00722597 0.00659782 0.00605279 0.0056059 0.00526385 0.00496126 0.00471807 0.00449589 0.00431383 0.00418103 0.00405819 0.00395102 0.00385027 0.0037683 0.00369631
np.newaxis维度扩充：
1 import numpy as np 2 a = np.array([1,2,3,4,5]) 3 a[:,np.newaxis] 4 # Out[7]: 5 # array([[1], 6 # [2], 7 # [3], 8 # [4], 9 # [5]]) 10 a[np.newaxis,:] 11 # Out[8]: 12 # array([[1, 2, 3, 4, 5]]) 13 a.shape 14 # Out[12]: 15 # (5,) 16 a[:,np.newaxis].shape 17 # Out[10]: 18 # (5, 1) 19 a[np.newaxis,:].shape 20 # Out[11]: 21 # (1, 5)
loss函数计算分析：
将输出改成下面：
1 with tf.Session() as sess: 2 sess.run(init) 3 for i in range(1000): 4 sess.run(train_step,feed_dict={xs:x_data,ys:y_data}) 5 if i % 50 == 0: 6 #print(sess.run(loss,feed_dict={xs:x_data,ys:y_data})) 7 print(sess.run(tf.square(ys - prediction),feed_dict={xs:x_data,ys:y_data})) # 300行 8 print(sess.run(tf.reduce_sum(tf.square(ys-prediction),reduction_indices=[1]), feed_dict={xs: x_data, ys: y_data})) # 300列
会发现tf.square(ys - prediction)输出：
[[ 1.27196927e-02] [ 3.22369207e-03] [ 1.74964982e-04] .... [ 1.06449667e-02] [ 4.93255538e-05] [ 3.47382086e-03]]
共计300个元素[300,1]。
而tf.reduce_sum(tf.square(ys-prediction),reduction_indices=[1])输出：
[ 1.27196927e-02 3.22369207e-03 1.74964982e-04 3.40620875e-02
1.67742800e-02 7.89122283e-03 8.79658014e-03 3.09832394e-04
2.58327164e-02 8.12971615e-04 3.06550064e-03 2.16252869e-04
.....
7.49099301e-04 9.10352624e-04 1.99158350e-03 2.43023387e-04
5.97979059e-04 8.30261386e-04 1.25318235e-02 1.10179959e-02
5.22381114e-03 1.06449667e-02 4.93255538e-05 3.47382086e-03]
共计300个元素[300]。
修改如下的话：
1 with tf.Session() as sess: 2 sess.run(init) 3 for i in range(1000): 4 sess.run(train_step,feed_dict={xs:x_data,ys:y_data}) 5 if i % 50 == 0: 6 #print(sess.run(loss,feed_dict={xs:x_data,ys:y_data})) 7 print(sess.run(tf.square(ys - prediction),feed_dict={xs:x_data,ys:y_data}).shape) # 300行 8 print(sess.run(tf.reduce_sum(tf.square(ys-prediction),reduction_indices=[1]), feed_dict={xs: x_data, ys: y_data}).shape) # 300列
(300, 1)
(300,)
有意思的发现是sess.run的输出是numpy.ndarray类型。
查询reduction_indices=[1]可知是指定操作坐标轴的函数：
即把[300,1]按行求和后拼接为新的数组，也就是[300]的尺寸。
step3:
之前学习的记忆渐渐复苏，感觉，还真的恰是故人归。