numpy反向传播算法示例
数据
通过 scikit-learn 库提供的便捷工具生成 2000 个线性不可分的 2 分类数据集
按着7: 3比例切分训练集和测试集
backpropagation.py
#!/usr/bin/env python
# encoding: utf-8
"""
@desc: 反向传播算法
"""
import pickle
import time
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
plt.rcParams['font.size'] = 16
# plt.rcParams['font.family'] = ['STKaiti']
plt.rcParams['axes.unicode_minus'] = False
def load_dataset():
# 采样点数
N_SAMPLES = 2000
# 测试数量比率
TEST_SIZE = 0.3
# 利用工具函数直接生成数据集
X, y = make_moons(n_samples=N_SAMPLES, noise=0.2, random_state=100)
# 将 2000 个点按着 7:3 分割为训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=TEST_SIZE, random_state=42)
return X, y, X_train, X_test, y_train, y_test
def make_plot(X, y, plot_name, XX=None, YY=None, preds=None, dark=False):
# 绘制数据集的分布， X 为 2D 坐标， y 为数据点的标签
if (dark):
plt.style.use('dark_background')
else:
sns.set_style("whitegrid")
plt.figure(figsize=(16, 12))
axes = plt.gca()
axes.set(xlabel="$x_1$", ylabel="$x_2$")
plt.title(plot_name, fontsize=30)
plt.subplots_adjust(left=0.20)
plt.subplots_adjust(right=0.80)
if XX is not None and YY is not None and preds is not None:
plt.contourf(XX, YY, preds.reshape(XX.shape), 25, alpha=1, cmap=plt.cm.Spectral)
plt.contour(XX, YY, preds.reshape(XX.shape), levels=[.5], cmap="Greys", vmin=0, vmax=.6)
# 绘制散点图，根据标签区分颜色
plt.scatter(X[:, 0], X[:, 1], c=y.ravel(), s=40, cmap=plt.cm.Spectral, edgecolors='none')
# plt.savefig('数据集分布.svg')
# plt.close()
plt.show()
class Layer:
# 全连接网络层
def __init__(self, n_input, n_neurons, activation=None, weights=None,
bias=None):
"""
:param int n_input: 输入节点数
:param int n_neurons: 输出节点数
:param str activation: 激活函数类型
:param weights: 权值张量，默认类内部生成
:param bias: 偏置，默认类内部生成
"""
# 通过正态分布初始化网络权值，初始化非常重要，不合适的初始化将导致网络不收敛
self.weights = weights if weights is not None else np.random.randn(n_input, n_neurons) * np.sqrt(1 / n_neurons)
self.bias = bias if bias is not None else np.random.rand(n_neurons) * 0.1
self.activation = activation # 激活函数类型，如’sigmoid’
self.last_activation = None # 激活函数的输出值o
self.error = None # 用于计算当前层的delta 变量的中间变量
self.delta = None # 记录当前层的delta 变量，用于计算梯度
# 网络层的前向传播函数实现如下，其中last_activation 变量用于保存当前层的输出值：
def activate(self, x):
# 前向传播函数
r = np.dot(x, self.weights) + self.bias # X@W+b
# 通过激活函数，得到全连接层的输出o
self.last_activation = self._apply_activation(r)
return self.last_activation
# 上述代码中的self._apply_activation 函数实现了不同类型的激活函数的前向计算过程，
# 尽管此处我们只使用Sigmoid 激活函数一种。代码如下：
def _apply_activation(self, r):
# 计算激活函数的输出
if self.activation is None:
return r # 无激活函数，直接返回
# ReLU 激活函数
elif self.activation == 'relu':
return np.maximum(r, 0)
# tanh 激活函数
elif self.activation == 'tanh':
return np.tanh(r)
# sigmoid 激活函数
elif self.activation == 'sigmoid':
return 1 / (1 + np.exp(-r))
return r
# 针对于不同类型的激活函数，它们的导数计算实现如下：
def apply_activation_derivative(self, r):
# 计算激活函数的导数
# 无激活函数，导数为1
if self.activation is None:
return np.ones_like(r)
# ReLU 函数的导数实现
elif self.activation == 'relu':
grad = np.array(r, copy=True)
grad[r > 0] = 1.
grad[r <= 0] = 0.
return grad
# tanh 函数的导数实现
elif self.activation == 'tanh':
return 1 - r ** 2
# Sigmoid 函数的导数实现
elif self.activation == 'sigmoid':
return r * (1 - r)
return r
# 神经网络模型
class NeuralNetwork:
def __init__(self):
self._layers = [] # 网络层对象列表
def add_layer(self, layer):
# 追加网络层
self._layers.append(layer)
# 网络的前向传播只需要循环调各个网络层对象的前向计算函数即可，代码如下：
# 前向传播
def feed_forward(self, X):
for layer in self._layers:
# 依次通过各个网络层
X = layer.activate(X)
return X
def backpropagation(self, X, y, learning_rate):
# 反向传播算法实现
# 前向计算，得到输出值
output = self.feed_forward(X)
for i in reversed(range(len(self._layers))): # 反向循环
layer = self._layers[i] # 得到当前层对象
# 如果是输出层
if layer == self._layers[-1]: # 对于输出层
layer.error = y - output # 计算2 分类任务的均方差的导数
# 关键步骤：计算最后一层的delta，参考输出层的梯度公式
layer.delta = layer.error * layer.apply_activation_derivative(output)
else: # 如果是隐藏层
next_layer = self._layers[i + 1] # 得到下一层对象
layer.error = np.dot(next_layer.weights, next_layer.delta)
# 关键步骤：计算隐藏层的delta，参考隐藏层的梯度公式
layer.delta = layer.error * layer.apply_activation_derivative(layer.last_activation)
# 循环更新权值
for i in range(len(self._layers)):
layer = self._layers[i]
# o_i 为上一网络层的输出
o_i = np.atleast_2d(X if i == 0 else self._layers[i - 1].last_activation)
# 梯度下降算法，delta 是公式中的负数，故这里用加号
layer.weights += layer.delta * o_i.T * learning_rate
def train(self, X_train, X_test, y_train, y_test, learning_rate, max_epochs):
# 网络训练函数
# one-hot 编码
y_onehot = np.zeros((y_train.shape[0], 2))
y_onehot[np.arange(y_train.shape[0]), y_train] = 1
# 将One-hot 编码后的真实标签与网络的输出计算均方误差，并调用反向传播函数更新网络参数，循环迭代训练集1000 遍即可
mses = []
accuracys = []
for i in range(max_epochs + 1): # 训练1000 个epoch
for j in range(len(X_train)): # 一次训练一个样本
self.backpropagation(X_train[j], y_onehot[j], learning_rate)
if i % 10 == 0:
# 打印出MSE Loss
mse = np.mean(np.square(y_onehot - self.feed_forward(X_train)))
mses.append(mse)
accuracy = self.accuracy(self.predict(X_test), y_test.flatten())
accuracys.append(accuracy)
print('Epoch: #%s, MSE: %f' % (i, float(mse)))
# 统计并打印准确率
print('Accuracy: %.2f%%' % (accuracy * 100))
return mses, accuracys
def predict(self, X):
return self.feed_forward(X)
def accuracy(self, X, y):
return np.sum(np.equal(np.argmax(X, axis=1), y)) / y.shape[0]
def main():
X, y, X_train, X_test, y_train, y_test = load_dataset()
# 调用 make_plot 函数绘制数据的分布，其中 X 为 2D 坐标， y 为标签
# make_plot(X, y, "Classification Dataset Visualization ")
mses = None
accuracys = None
## make True to train or False to load trained modle
train = False
if (train) :
nn = NeuralNetwork() # 实例化网络类
nn.add_layer(Layer(2, 25, 'sigmoid')) # 隐藏层 1, 2=>25
nn.add_layer(Layer(25, 50, 'sigmoid')) # 隐藏层 2, 25=>50
nn.add_layer(Layer(50, 25, 'sigmoid')) # 隐藏层 3, 50=>25
nn.add_layer(Layer(25, 2, 'sigmoid')) # 输出层, 25=>2
time1 = time.perf_counter()
mses, accuracys = nn.train(X_train, X_test, y_train, y_test, 0.01, 1000)
time2 = time.perf_counter()
print (f"train time : {time2-time1} s ")
#--- save trained modle
with open('trained_model.pickle', 'wb') as f:
pickle.dump(nn, f)
# 绘制MES曲线
x = [i for i in range(0, 101, 10)]
ax = plt.subplot(1,2,1)
ax.set_title("MES Loss")
plt.plot(x, mses[:11], color='blue')
plt.xlabel('Epoch')
plt.ylabel('MSE')
# plt.savefig('训练误差曲线.svg')
# plt.close()
# 绘制Accuracy曲线
ax = plt.subplot(1,2,2)
ax.set_title("Accuracy")
plt.plot(x, accuracys[:11], color='blue')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
# plt.savefig('网络测试准确率.svg')
# plt.close()
plt.savefig('训练曲线.svg')
else :
#--- load modle from pickle
modle = None
with open('trained_model.pickle', 'rb') as f:
modle = pickle.load(f)
# 预测
out = modle.predict(X_test)
# 预测标签
pred = np.argmax(out, axis=1)
# 正确率
accuracy = modle.accuracy(out, y_test.flatten())
print(f"accuracy : {accuracy}")
# 绘制散点图,根据标签区分颜色
ax = plt.subplot(1,2,1)
ax.set_title("X_test Classification by y_test")
plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test.ravel(), s=40, cmap=plt.cm.Spectral, edgecolors='#356')
# 绘制散点图,根据模型预测标签,正确的绿色/错误的红色
ax = plt.subplot(1,2,2)
ax.set_title("X_test Classification by pred ,error mark red,correct mark green")
t_x = X_test[:, 0]
t_y = X_test[:, 1]
acc_points = []
err_points = []
for i in range(0,y_test.shape[0]):
if np.equal(pred[i],y_test[i]):
# print(f"pred[{i}]:{pred[i]} \t y_test[{i}]: {y_test[i]}")
acc_points.append(i)
else :
err_points.append(i)
# print(f"pred[{i}]:{pred[i]} \t y_test[{i}]: {y_test[i]}")
plt.scatter(t_x[acc_points],t_y[acc_points],s=40,c="green" , edgecolors='#356')
plt.scatter(t_x[err_points],t_y[err_points],s=80,c="red" , edgecolors='#789')
plt.show()
if __name__ == '__main__':
main()
