利用tensorflow实现《神经网络与机器学习》一书中4.7模式分类练习
具体问题是将如下图所示双月牙数据集分类。
使用到的工具:
python3.5 tensorflow1.2.1 numpy matplotlib
1.产生双月环数据集
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def producedata(r,w,d,num):
r1 = r - w / 2
r2 = r + w / 2
#上半圆
theta1 = np.random.uniform( 0 , np.pi ,num)
x_col1 = np.random.uniform( r1 * np.cos(theta1),r2 * np.cos(theta1),num)[:, np.newaxis]
x_row1 = np.random.uniform(r1 * np.sin(theta1),r2 * np.sin(theta1),num)[:, np.newaxis]
y_label1 = np.ones(num) #类别标签为1
#下半圆
theta2 = np.random.uniform( - np.pi, 0 ,num)
x_col2 = (np.random.uniform( r1 * np.cos(theta2),r2 * np.cos(theta2),num) + r)[:, np.newaxis]
x_row2 = (np.random.uniform(r1 * np.sin(theta2), r2 * np.sin(theta2), num) - d)[:,np.newaxis]
y_label2 = - np.ones(num) #类别标签为-1,注意:由于采取双曲正切函数作为激活函数,类别标签不能为0
#合并
x_col = np.vstack((x_col1, x_col2))
x_row = np.vstack((x_row1, x_row2))
x = np.hstack((x_col, x_row))
y_label = np.hstack((y_label1,y_label2))
y_label.shape = (num * 2 , 1 )
return x,y_label
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其中r为月环半径,w为月环宽度,d为上下月环距离(与书中一致)
2.利用tensorflow搭建神经网络模型
2.1 神经网络层添加
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def add_layer(layername,inputs, in_size, out_size, activation_function = none):
# add one more layer and return the output of this layer
with tf.variable_scope(layername,reuse = none):
weights = tf.get_variable( "weights" ,shape = [in_size, out_size],
initializer = tf.truncated_normal_initializer(stddev = 0.1 ))
biases = tf.get_variable( "biases" , shape = [ 1 , out_size],
initializer = tf.truncated_normal_initializer(stddev = 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
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2.2 利用tensorflow建立神经网络模型
输入层大小:2
隐藏层大小:20
输出层大小:1
激活函数:双曲正切函数
学习率:0.1(与书中略有不同)
(具体的搭建过程可参考莫烦的视频,链接就不附上了自行搜索吧......)
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###define placeholder for inputs to network
xs = tf.placeholder(tf.float32, [none, 2 ])
ys = tf.placeholder(tf.float32, [none, 1 ])
###添加隐藏层
l1 = add_layer( "layer1" ,xs, 2 , 20 , activation_function = tf.tanh)
###添加输出层
prediction = add_layer( "layer2" ,l1, 20 , 1 , activation_function = tf.tanh)
###mse 均方误差
loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction), reduction_indices = [ 1 ]))
###优化器选取 学习率设置 此处学习率置为0.1
train_step = tf.train.gradientdescentoptimizer( 0.1 ).minimize(loss)
###tensorflow变量初始化,打开会话
init = tf.global_variables_initializer() #tensorflow更新后初始化所有变量不再用tf.initialize_all_variables()
sess = tf.session()
sess.run(init)
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2.3 训练模型
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###训练2000次
for i in range ( 2000 ):
sess.run(train_step, feed_dict = {xs: x_data, ys: y_label})
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3.利用训练好的网络模型寻找分类决策边界
3.1 产生二维空间随机点
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def produce_random_data(r,w,d,num):
x1 = np.random.uniform( - r - w / 2 , 2 * r + w / 2 , num)
x2 = np.random.uniform( - r - w / 2 - d, r + w / 2 , num)
x = np.vstack((x1, x2))
return x.transpose()
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3.2 用训练好的模型采集决策边界附近的点
向网络输入一个二维空间随机点,计算输出值大于-0.5小于0.5即认为该点落在决策边界附近(双曲正切函数)
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def collect_boundary_data(v_xs):
global prediction
x = np.empty([ 1 , 2 ])
x = list ()
for i in range ( len (v_xs)):
x_input = v_xs[i]
x_input.shape = [ 1 , 2 ]
y_pre = sess.run(prediction, feed_dict = {xs: x_input})
if abs (y_pre - 0 ) < 0.5 :
x.append(v_xs[i])
return np.array(x)
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3.3 用numpy工具将采集到的边界附近点拟合成决策边界曲线,用matplotlib.pyplot画图
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###产生空间随机数据
x_num = produce_random_data( 10 , 6 , - 4 , 5000 )
###边界数据采样
x_b = collect_boundary_data(x_num)
###画出数据
fig = plt.figure()
ax = fig.add_subplot( 1 , 1 , 1 )
###设置坐标轴名称
plt.xlabel( 'x1' )
plt.ylabel( 'x2' )
ax.scatter(x_data[:, 0 ], x_data[:, 1 ], marker = 'x' )
###用采样的边界数据拟合边界曲线 7次曲线最佳
z1 = np.polyfit(x_b[:, 0 ], x_b[:, 1 ], 7 )
p1 = np.poly1d(z1)
x = x_b[:, 0 ]
x.sort()
yvals = p1(x)
plt.plot(x, yvals, 'r' , label = 'boundray line' )
plt.legend(loc = 4 )
#plt.ion()
plt.show()
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4.效果
5.附上源码github链接
https://github.com/peakulorain/practices.git里的patternclassification.py文件
另注:分类问题还是用softmax去做吧.....我只是用这做书上的练习而已。
(初学者水平有限,有问题请指出,各位大佬轻喷)
以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持服务器之家。
原文链接:http://blog.csdn.net/Peakulorain/article/details/76944598