MNIST3_numpy手写全连接神经网络

本文主要是介绍MNIST3_numpy手写全连接神经网络，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

一、链式求导

二、numpy layer和反向传播

全部脚本见笔者github: numpynn.py

import numpy as npclass npLayer():def __init__(self, n_input, n_out, activation=None, weights=None,bias=None):self.weights = weights if weights is not None else np.random.randn(n_input, n_out) * np.sqrt(1 / n_out)self.bias = bias if bias is not None else np.random.randn(n_out) * 0.1self.activation = activation self.last_activation = None self.error = None self.delta = None def activate(self, x):# 前向传播r = np.dot(x, self.weights) + self.biasself.last_activation = self.apply_activation(r)return self.last_activation def apply_activation(self, r):# 计算激活函数的输出if self.activation is None:return relif self.activation == 'relu':return np.maximum(r, 0)elif self.activation == 'tanh':return np.tanh(r)elif self.activation == 'sigmoid':return 1/(1 + np.exp(-r))return rdef apply_activation_derivative(self, act_r):# 计算激活函数的导数if self.activation is None:return np.ones_like(act_r)elif self.activation == 'relu':return (act_r > 0) * 1elif self.activation == 'tanh':return 1 - act_r ** 2elif self.activation == 'sigmoid':return act_r * (1 - act_r)return act_rdef __call__(self, x):return self.activate(x)

反向传播

    def backpropagation(self, x, y, learning_rate):# 反向传播算法实现## 从后向前计算梯度 output = self.feed_forward(x) # 最后层输出layer_len = len(self._layers)for i in reversed(range(layer_len)):layer = self._layers[i] # 如果是输出层if layer  == self._layers[-1]:delta_i = layer.apply_activation_derivative(output)layer.error = output - ylayer.delta = layer.error * delta_ielse:next_layer = self._layers[i + 1]delta_i = layer.apply_activation_derivative(layer.last_activation)layer.error = np.dot(next_layer.weights, next_layer.delta)layer.delta = layer.error * delta_i# 梯度下降for i in range(layer_len):layer = self._layers[i]o_i = np.atleast_2d(x if i == 0 else self._layers[i - 1].last_activation)layer.weights -= layer.delta * o_i.T * learning_rate

三、MNIST训练及测试

if __name__ == '__main__':mnistdf = get_ministdata()te_index = mnistdf.sample(frac=0.8).index.tolist()mnist_te = mnistdf.loc[te_index, :]mnist_tr = mnistdf.loc[~mnistdf.index.isin(te_index), :]x_tr, y_tr = mnist_tr.iloc[:, :-1].values, mnist_tr.iloc[:, -1].valuesx_te, y_te = mnist_te.iloc[:, :-1].values, mnist_te.iloc[:, -1].valuesprint(x_te.shape)nn = NeuralNetwork()nn.add_layer(npLayer(784, 128, 'relu')) nn.add_layer(npLayer(128, 10, 'sigmoid'))st = time.perf_counter()mses, accs = nn.train(x_tr, x_te, y_tr, y_te, 0.01, 150)cost_ = time.perf_counter() - stprint(f'cost: {cost_:.2f}s',accs)

 ================================================================================
Epoch: # 85, MSE: 0.00713
Accuracy: 93.93 % ================================================================================
Epoch: # 90, MSE: 0.00654
Accuracy: 94.09 % ================================================================================
Epoch: # 95, MSE: 0.00600
Accuracy: 94.27 % ================================================================================
Epoch: # 100, MSE: 0.00558
Accuracy: 94.41 % ================================================================================
Epoch: # 105, MSE: 0.00514
Accuracy: 94.53 % ================================================================================
Epoch: # 110, MSE: 0.00479
Accuracy: 94.65 % ================================================================================
Epoch: # 115, MSE: 0.00447
Accuracy: 94.75 % ================================================================================
Epoch: # 120, MSE: 0.00417
Accuracy: 94.84 % ================================================================================
Epoch: # 125, MSE: 0.00393
Accuracy: 94.93 % ================================================================================
Epoch: # 130, MSE: 0.00370
Accuracy: 94.98 % ================================================================================
Epoch: # 135, MSE: 0.00350
Accuracy: 95.03 %================================================================================
Epoch: # 140, MSE: 0.00332
Accuracy: 95.08 %================================================================================
Epoch: # 145, MSE: 0.00316
Accuracy: 95.12 %================================================================================
Epoch: # 150, MSE: 0.00303
Accuracy: 95.14 %
cost: 1104.11s [0.2034285714285714, 0.5135714285714286, 0.5907142857142857, 0.6798928571428572, 0.74375, 0.7954285714285715
, 0.8364821428571428, 0.863125, 0.8833571428571428, 0.8975178571428571, 0.9077857142857142, 0.9149285714285714, 0.9213214285714286
, 0.9264821428571427, 0.9302142857142858, 0.9336071428571429, 0.9372678571428571, 0.9392857142857143, 0.9408928571428572, 0.9427321428571429
, 0.9440535714285714, 0.94525, 0.9465178571428572, 0.9475178571428572, 0.9483571428571429, 0.9493035714285715, 0.9498214285714286
, 0.9502857142857143, 0.95075, 0.9511607142857144, 0.9513571428571429]

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