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_splitplt.rcParams['font.size'] = 16
# plt.rcParams['font.family'] = ['STKaiti']
plt.rcParams['axes.unicode_minus'] = Falsedef 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_testdef 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) * 0.1self.activation = activation # 激活函数类型,如’sigmoid’self.last_activation = None # 激活函数的输出值oself.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oself.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1if 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 Xdef 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_ratedef 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epochfor 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 Lossmse = 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, accuracysdef 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 = Noneaccuracys = None## make True to train or False to load trained modletrain = Falseif (train) :nn = NeuralNetwork() # 实例化网络类nn.add_layer(Layer(2, 25, 'sigmoid')) # 隐藏层 1, 2=>25nn.add_layer(Layer(25, 50, 'sigmoid')) # 隐藏层 2, 25=>50nn.add_layer(Layer(50, 25, 'sigmoid')) # 隐藏层 3, 50=>25nn.add_layer(Layer(25, 2, 'sigmoid')) # 输出层, 25=>2time1 = 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 modlewith 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 picklemodle = Nonewith 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()