# 导入必要的库
import numpy as np
import os
import struct
import matplotlib.pyplot as plt# 定义导入函数
def load_images(path):with open(path, "rb") as f:data = f.read()magic_number, num_items, rows, cols = struct.unpack(">iiii", data[:16])return np.asanyarray(bytearray(data[16:]), dtype=np.uint8).reshape(num_items, 28, 28)def load_labels(file):with open(file, "rb") as f:data = f.read()return np.asanyarray(bytearray(data[8:]), dtype=np.int32)# 定义sigmoid函数
def sigmoid(x):result = np.zeros_like(x)positive_mask = x >= 0result[positive_mask] = 1 / (1 + np.exp(-x[positive_mask]))negative_mask = x < 0exp_x = np.exp(x[negative_mask])result[negative_mask] = exp_x / (1 + exp_x)return result# 定义softmax函数
def softmax(x):max_x = np.max(x, axis=-1, keepdims=True)x = x - max_xex = np.exp(x)sum_ex = np.sum(ex, axis=1, keepdims=True)result = ex / sum_exresult = np.clip(result, 1e-10, 1e10)return result# 定义独热编码函数
def make_onehot(labels, class_num):result = np.zeros((labels.shape[0], class_num))for idx, cls in enumerate(labels):result[idx, cls] = 1return result# 定义dataset类
class Dataset:def __init__(self, all_images, all_labels):self.all_images = all_imagesself.all_labels = all_labelsdef __getitem__(self, index):image = self.all_images[index]label = self.all_labels[index]return image, labeldef __len__(self):return len(self.all_images)# 定义dataloader类
class DataLoader:def __init__(self, dataset, batch_size, shuffle=True):self.dataset = datasetself.batch_size = batch_sizeself.shuffle = shuffleself.idx = np.arange(len(self.dataset))def __iter__(self):# 如果需要打乱，则在每个 epoch 开始时重新排列索引if self.shuffle:np.random.shuffle(self.idx)self.cursor = 0return selfdef __next__(self):if self.cursor >= len(self.dataset):raise StopIteration# 使用索引来获取数据batch_idx = self.idx[self.cursor : min(self.cursor + self.batch_size, len(self.dataset))]batch_images = self.dataset.all_images[batch_idx]batch_labels = self.dataset.all_labels[batch_idx]self.cursor += self.batch_sizereturn batch_images, batch_labels# 主函数
if __name__ == "__main__":# 加载训练集图片、标签train_images = (load_images(os.path.join("Python", "NLP basic", "data", "minist", "train-images.idx3-ubyte"))/ 255)train_labels = make_onehot(load_labels(os.path.join("Python", "NLP basic", "data", "minist", "train-labels.idx1-ubyte")),10,)# 加载测试集图片、标签dev_images = (load_images(os.path.join("Python", "NLP basic", "data", "minist", "t10k-images.idx3-ubyte"))/ 255)dev_labels = load_labels(os.path.join("Python", "NLP basic", "data", "minist", "t10k-labels.idx1-ubyte"))# 设置超参数epochs = 10lr = 0.08batch_size = 200shuffle = True# 展开图片数据train_images = train_images.reshape(60000, 784)dev_images = dev_images.reshape(-1, 784)# 调用dataset类和dataloader类train_dataset = Dataset(train_images, train_labels)train_dataloader = DataLoader(train_dataset, batch_size, shuffle)dev_dataset = Dataset(dev_images, dev_labels)dev_dataloader = DataLoader(dev_dataset, batch_size, shuffle)# 权重和偏置w1 = np.random.normal(0, 1, size=(784, 512)) # 第一层权重w3 = np.random.normal(0, 1, size=(512, 256)) # 第三层权重w4 = np.random.normal(0, 1, size=(256, 10)) # 第四层权重b1 = np.random.normal(0, 1, size=(1, 512)) # 第一层偏置b3 = np.random.normal(0, 1, size=(1, 256)) # 第三层偏置b4 = np.random.normal(0, 1, size=(1, 10)) # 第四层偏置# 训练集训练过程for e in range(epochs):for batch_images, batch_labels in train_dataloader:# 前向传播H1 = np.dot(batch_images, w1) + b1 # 第一层输出H2 = sigmoid(H1) # 第二层输出，使用sigmoid激活函数H3 = np.dot(H2, w3) + b3 # 第三层输出H4 = np.dot(H3, w4) + b4 # 第四层输出p = softmax(H4) # 输出层输出，使用softmax激活函数# 计算损失loss = -np.mean(np.sum(batch_labels * np.log(p), axis=1))# 反向传播# 第四层G4 = (p - batch_labels) / batch_images.shape[0] # 第四层误差dw4 = np.dot(H3.T, G4) # 第四层权重梯度db4 = np.mean(G4, axis=0, keepdims=True) # 第四层偏置梯度# 第三层G3 = np.dot(G4, w4.T) # 第三层误差dw3 = np.dot(H2.T, G3) # 第三层权重梯度db3 = np.mean(G3, axis=0, keepdims=True) # 第三层偏置梯度# 第二层G2 = np.dot(G3, w3.T) # 第二层误差# 第一层G1 = G2 * (H2 * (1 - H2)) # 第一层误差dw1 = np.dot(batch_images.T, G1) # 第一层权重梯度db1 = np.mean(G1, axis=0, keepdims=True) # 第一层偏置梯度# 更新权重和偏置w1 -= lr * dw1b1 -= lr * db1w3 -= lr * dw3b3 -= lr * db3w4 -= lr * dw4b4 -= lr * db4# 验证集验证并输出预测准确率right_num = 0for bictc_images, bictc_labels in dev_dataloader:H1 = np.dot(bictc_images, w1) + b1 # 第一层输出H2 = sigmoid(H1) # 第二层输出，使用sigmoid激活函数H3 = np.dot(H2, w3) + b3 # 第三层输出H4 = np.dot(H3, w4) + b4 # 第四层输出p = softmax(H4) # 输出层输出，使用softmax激活函数pre_idx = np.argmax(p, axis=-1) # 预测类别right_num += np.sum(pre_idx == bictc_labels) # 统计正确个数acc = right_num / len(dev_images) # 计算准确率print(f"Epoch {e + 1}, Acc: {acc:.4f}")
