import numpy as np import gzip import pickle import pandas as pd class Network(object): def __init__(self, sizes): self.num_layers = len(sizes) self.sizes = sizes self.biases = [np.random.randn(y, 1) for y in sizes[1:]] self.weights = [np.random.randn(y, x) for x,y in zip(sizes[:-1], sizes[1:])] def feedforward(self, a): for b, w in zip(self.biases, self.weights): a = sigmoid(np.dot(w, a) + b) return a def SGD(self, training_data, epochs, mini_batch_size, eta, k, test_data=None): if test_data: n_test = len(test_data) for j in range(epochs): np.random.shuffle(training_data) k_fold = self.k_fold_split(training_data, k) for fold in range(k): validation_data = k_fold[fold] train_data = [item for sublist in k_fold[:fold] + k_fold[fold + 1:] for item in sublist] for mini_batch in [train_data[k:k+mini_batch_size] for k in range(0, len(train_data), mini_batch_size)]: self.update_mini_batch(mini_batch, eta) print(f"Epoch {j}, Fold {fold}: {self.evaluate(validation_data)}/{len(validation_data)}") if test_data: print(f"Epoch {j}: {self.evaluate(test_data)}/{n_test}") def k_fold_split(self, data, k): fold_size = len(data) // k return [data[i*fold_size:(i+1)*fold_size] for i in range(k)] def update_mini_batch(self, mini_batch, eta): nabla_b = [np.zeros(b.shape) for b in self.biases] nabla_w = [np.zeros(w.shape) for w in self.weights] for x, y in mini_batch: delta_nabla_b, delta_nabla_w = self.backdrop(x, y) nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)] nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)] self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)] self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)] def evaluate(self, test_data): test_results = [(np.argmax(self.feedforward(x)), np.argmax(y)) for (x, y) in test_data] return sum(int(x == y) for (x, y) in test_results) def cost_derivative(self, output_activations, y): return output_activations - y def backdrop(self, x, y): nabla_b = [np.zeros(b.shape) for b in self.biases] nabla_w = [np.zeros(w.shape) for w in self.weights] activation = x activations = [x] zs = [] for b, w in zip(self.biases, self.weights): z = np.dot(w, activation)+b zs.append(z) activation = sigmoid(z) activations.append(activation) delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1]) nabla_b[-1] = delta nabla_w[-1] = np.dot(delta, activations[-2].transpose()) for l in range(2, self.num_layers): z = zs[-l] sp = sigmoid_prime(z) delta = np.dot(self.weights[-l+1].transpose(), delta) * sp nabla_b[-l] = delta nabla_w[-l] = np.dot(delta, activations[-l-1].transpose()) return (nabla_b, nabla_w) def sigmoid(z): sig = np.zeros_like(z) sig[z >= 0] = 1 / (1 + np.exp(-z[z >= 0])) sig[z < 0] = np.exp(z[z < 0]) / (1 + np.exp(z[z < 0])) return sig def sigmoid_prime(z): return sigmoid(z)*(1-sigmoid(z)) def load_data(): with gzip.open('C:\\Users\\tt235\\Desktop\\Code\\code\\代码复现\\BP神经网络\\mnist.pkl.gz', 'rb') as f: training_data, validation_data, test_data = pickle.load(f, encoding='latin1') return (training_data, validation_data, test_data) def load_data_wrapper(): tr_d, va_d, te_d = load_data() training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]] training_results = [vectorized_result(y) for y in tr_d[1]] training_data = list(zip(training_inputs, training_results)) validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]] validation_data = list(zip(validation_inputs, va_d[1])) test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]] test_results = [vectorized_result(y) for y in te_d[1]] test_data = list(zip(test_inputs, test_results)) return (training_data, validation_data, test_data) def vectorized_result(j): e = np.zeros((10, 1)) e[j] = 1.0 return e training_data, validation_data, test_data = load_data_wrapper() net = Network([784, 41, 10]) net.SGD(training_data, 3, 8, 3.0, 5, test_data=test_data)