運行環境
- Pyhton3
- numpy(科學計算包)
- matplotlib(畫圖所需，不畫圖可不必)
- sklearn(人工智能包，生成數據使用)
計算過程
輸入樣例
none
代碼實現
# -*- coding:utf-8 -*-
#!python3
__author__ = 'Wsine'
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
import matplotlib.pyplot as plt
import matplotlib
import operator
import time
def createData(dim=200, cnoise=0.20):
"""
輸出：數據集, 對應的類別標籤
描述：生成一個數據集和對應的類別標籤
"""
np.random.seed(0)
X, y = sklearn.datasets.make_moons(dim, noise=cnoise)
plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)
#plt.show()
return X, y
def plot_decision_boundary(pred_func, X, y):
"""
輸入：邊界函數, 數據集, 類別標籤
描述：繪製決策邊界(畫圖用)
"""
# 設置最小最大值, 加上一點外邊界
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
h = 0.01
# 根據最小最大值和一個網格距離生成整個網格
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# 對整個網格預測邊界值
Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
# 繪製邊界和數據集的點
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)
def calculate_loss(model, X, y):
"""
輸入：訓練模型, 數據集, 類別標籤
輸出：誤判的概率
描述：計算整個模型的性能
"""
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
# 正向傳播來計算預測的分類值
z1 = X.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
# 計算誤判概率
corect_logprobs = -np.log(probs[range(num_examples), y])
data_loss = np.sum(corect_logprobs)
# 加入正則項修正錯誤(可選)
data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
return 1./num_examples * data_loss
def predict(model, x):
"""
輸入：訓練模型, 預測向量
輸出：判決類別
描述：預測類別屬於(0 or 1)
"""
W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
# 正向傳播計算
z1 = x.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
return np.argmax(probs, axis=1)
def initParameter(X):
"""
輸入：數據集
描述：初始化神經網絡算法的參數
必須初始化為全局函數！
這裡需要手動設置！
"""
global num_examples
num_examples = len(X) # 訓練集的大小
global nn_input_dim
nn_input_dim = 2 # 輸入層維數
global nn_output_dim
nn_output_dim = 2 # 輸出層維數
# 梯度下降參數
global epsilon
epsilon = 0.01 # 梯度下降學習步長
global reg_lambda
reg_lambda = 0.01 # 修正的指數
def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False):
"""
輸入：數據集, 類別標籤, 隱藏層層數, 迭代次數, 是否輸出誤判率
輸出：神經網絡模型
描述：生成一個指定層數的神經網絡模型
"""
# 根據維度隨機初始化參數
np.random.seed(0)
W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
b1 = np.zeros((1, nn_hdim))
W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
b2 = np.zeros((1, nn_output_dim))
model = {}# 梯度下降
for i in range(0, num_passes):
# 正向傳播
z1 = X.dot(W1) + b1
a1 = np.tanh(z1) # 激活函數使用tanh = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
z2 = a1.dot(W2) + b2
exp_scores = np.exp(z2) # 原始歸一化
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
# 後向傳播
delta3 = probs
delta3[range(num_examples), y] -= 1
dW2 = (a1.T).dot(delta3)
db2 = np.sum(delta3, axis=0, keepdims=True)
delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
dW1 = np.dot(X.T, delta2)
db1 = np.sum(delta2, axis=0)
# 加入修正項
dW2 += reg_lambda * W2
dW1 += reg_lambda * W1
# 更新梯度下降參數
W1 += -epsilon * dW1
b1 += -epsilon * db1
W2 += -epsilon * dW2
b2 += -epsilon * db2
# 更新模型
model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}# 一定迭代次數後輸出當前誤判率
if print_loss and i % 1000 == 0:
print("Loss after iteration %i: %f" % (i, calculate_loss(model, X, y)))plot_decision_boundary(lambda x: predict(model, x), X, y)
plt.title("Decision Boundary for hidden layer size %d" % nn_hdim)#plt.show()
return model
def main():
dataSet, labels = createData(200, 0.20)
initParameter(dataSet)
nnModel = build_model(dataSet, labels, 3, print_loss=False)
print("Loss is %f" % calculate_loss(nnModel, dataSet, labels))if __name__ == '__main__':
start = time.clock()
main()
end = time.clock()
print('finish all in %s' % str(end - start))plt.show()
輸出樣例
Loss is 0.071316
finish all in 7.221354361552228
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