任務： 使用tensorflow訓練一個神經網路作為分類器，分類的資料點如下：

螺旋形資料點

原理

資料點一共有三個類別，而且是螺旋形交織在一起，顯然是線性不可分的，需要一個非線性的分類器。這裡選擇神經網路。

輸入的資料點是二維的，因此每個點只有x,y座標這個原始特徵。這裡設計的神經網路有兩個隱藏層，每層有50個神經元，足夠抓住資料點的高維特徵（實際上每層10個都夠用了）。最後輸出層是一個邏輯迴歸，根據隱藏層計算出的50個特徵來預測資料點的分類（紅、黃、藍）。

一般訓練資料多的話，應該用隨機梯度下降來訓練神經網路，這裡訓練資料較少（300），就直接批量梯度下降了。

# 匯入包、初始化
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf  %matplotlib inline plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray
'# 生成螺旋形的線形不可分資料點
np.random.seed(0) N = 100 # 每個類的資料個數
D = 2 # 輸入維度
K = 3 # 類的個數
X = np.zeros((N*K,D)) num_train_examples = X.shape[0] y = np.zeros(N*K, dtype='uint8')
for j in xrange(K):   ix = range(N*j,N*(j+1))   r = np.linspace(0.0,1,N) # radius   t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta   X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]   y[ix] = j fig = plt.figure() plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral) plt.xlim([-1,1]) plt.ylim([-1,1])
 

螺旋形資料點

列印輸出輸入X和label的shape

num_label = 3
labels = (np.arange(num_label) == y[:,None]).astype(np.float32) labels.shape
(300, 3)
X.shape
(300, 2)

用tensorflow構建神經網路

import math  N = 100 # 每個類的資料個數
D = 2 # 輸入維度
num_label = 3 # 類的個數
num_data = N * num_label hidden_size_1 = 50
hidden_size_2 = 50
beta = 0.001 # L2 正則化係數
learning_rate = 0.1 # 學習速率
labels = (np.arange(num_label) == y[:,None]).astype(np.float32)  graph = tf.Graph()
with graph.as_default():     x = tf.constant(X.astype(np.float32))     tf_labels = tf.constant(labels)         # 隱藏層1     hidden_layer_weights_1 = tf.Variable(     tf.truncated_normal([D, hidden_size_1], stddev=math.sqrt(2.0/num_data)))     hidden_layer_bias_1 = tf.Variable(tf.zeros([hidden_size_1]))         # 隱藏層2     hidden_layer_weights_2 = tf.Variable(     tf.truncated_normal([hidden_size_1, hidden_size_2], stddev=math.sqrt(2.0/hidden_size_1)))     hidden_layer_bias_2 = tf.Variable(tf.zeros([hidden_size_2]))         # 輸出層     out_weights = tf.Variable(     tf.truncated_normal([hidden_size_2, num_label], stddev=math.sqrt(2.0/hidden_size_2)))     out_bias = tf.Variable(tf.zeros([num_label]))          z1 = tf.matmul(x, hidden_layer_weights_1) + hidden_layer_bias_1     h1 = tf.nn.relu(z1)          z2 = tf.matmul(h1, hidden_layer_weights_2) + hidden_layer_bias_2     h2 = tf.nn.relu(z2)          logits = tf.matmul(h2, out_weights) + out_bias         # L2正則化     regularization = tf.nn.l2_loss(hidden_layer_weights_1) + tf.nn.l2_loss(hidden_layer_weights_2) + tf.nn.l2_loss(out_weights)     loss = tf.reduce_mean(         tf.nn.softmax_cross_entropy_with_logits(labels=tf_labels, logits=logits) + beta * regularization)           optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)          train_prediction = tf.nn.softmax(logits)      weights = [hidden_layer_weights_1, hidden_layer_bias_1, hidden_layer_weights_2, hidden_layer_bias_2, out_weights, out_bias]  
 

上一步相當於搭建了神經網路的骨架，現在需要訓練。每1000步訓練，列印交叉熵損失和正確率。

num_steps = 50000

def accuracy(predictions, labels): return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1)) / predictions.shape[0])def relu(x): return np.maximum(0,x)

with tf.Session(graph=graph) as session: tf.global_variables_initializer().run() print('Initialized')

for step in range(num_steps): _, l, predictions = session.run([optimizer, loss, train_prediction]) if (step % 1000 == 0): print('Loss at step %d: %f' % (step, l)) print('Training accuracy: %.1f%%' % accuracy( predictions, labels)) w1, b1, w2, b2, w3, b3 = weights

# 顯示分類器 h = 0.02 x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1 y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) Z = np.dot(relu(np.dot(relu(np.dot(np.c_[xx.ravel(), yy.ravel()], w1.eval()) + b1.eval()), w2.eval()) + b2.eval()), w3.eval()) + b3.eval() Z = np.argmax(Z, axis=1) Z = Z.reshape(xx.shape) fig = plt.figure() plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8) plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral) plt.xlim(xx.min(), xx.max()) plt.ylim(yy.min(), yy.max())

Initialized

Loss at step 0: 1.132545
Training accuracy: 43.7%
Loss at step 1000: 0.257016
Training accuracy: 94.0%
Loss at step 2000: 0.165511
Training accuracy: 98.0%
Loss at step 3000: 0.149266
Training accuracy: 99.0%
Loss at step 4000: 0.142311
Training accuracy: 99.3%
Loss at step 5000: 0.137762
Training accuracy: 99.3%
Loss at step 6000: 0.134356
Training accuracy: 99.3%
Loss at step 7000: 0.131588
Training accuracy: 99.3%
Loss at step 8000: 0.129299
Training accuracy: 99.3%
Loss at step 9000: 0.127340
Training accuracy: 99.3%
Loss at step 10000: 0.125686
Training accuracy: 99.3%
Loss at step 11000: 0.124293
Training accuracy: 99.3%
Loss at step 12000: 0.123130
Training accuracy: 99.3%
Loss at step 13000: 0.122149
Training accuracy: 99.3%
Loss at step 14000: 0.121309
Training accuracy: 99.3%
Loss at step 15000: 0.120542
Training accuracy: 99.3%
Loss at step 16000: 0.119895
Training accuracy: 99.3%
Loss at step 17000: 0.119335
Training accuracy: 99.3%
Loss at step 18000: 0.118836
Training accuracy: 99.3%
Loss at step 19000: 0.118376
Training accuracy: 99.3%
Loss at step 20000: 0.117974
Training accuracy: 99.3%
Loss at step 21000: 0.117601
Training accuracy: 99.3%
Loss at step 22000: 0.117253
Training accuracy: 99.3%
Loss at step 23000: 0.116887
Training accuracy: 99.3%
Loss at step 24000: 0.116561
Training accuracy: 99.3%
Loss at step 25000: 0.116265
Training accuracy: 99.3%
Loss at step 26000: 0.115995
Training accuracy: 99.3%
Loss at step 27000: 0.115750
Training accuracy: 99.3%
Loss at step 28000: 0.115521
Training accuracy: 99.3%
Loss at step 29000: 0.115310
Training accuracy: 99.3%
Loss at step 30000: 0.115111
Training accuracy: 99.3%
Loss at step 31000: 0.114922
Training accuracy: 99.3%
Loss at step 32000: 0.114743
Training accuracy: 99.3%
Loss at step 33000: 0.114567
Training accuracy: 99.3%
Loss at step 34000: 0.114401
Training accuracy: 99.3%
Loss at step 35000: 0.114242
Training accuracy: 99.3%
Loss at step 36000: 0.114086
Training accuracy: 99.3%
Loss at step 37000: 0.113933
Training accuracy: 99.3%
Loss at step 38000: 0.113785
Training accuracy: 99.3%
Loss at step 39000: 0.113644
Training accuracy: 99.3%
Loss at step 40000: 0.113504
Training accuracy: 99.3%
Loss at step 41000: 0.113366
Training accuracy: 99.3%
Loss at step 42000: 0.113229
Training accuracy: 99.3%
Loss at step 43000: 0.113096
Training accuracy: 99.3%
Loss at step 44000: 0.112966
Training accuracy: 99.3%
Loss at step 45000: 0.112838
Training accuracy: 99.3%
Loss at step 46000: 0.112711
Training accuracy: 99.3%
Loss at step 47000: 0.112590
Training accuracy: 99.3%
Loss at step 48000: 0.112472
Training accuracy: 99.3%
Loss at step 49000: 0.112358
Training accuracy: 99.3%

分類器.png