### BP神经网络处理图像数据的Python代码示例 以下是基于Python实现的一个简单的BP（反向传播）神经网络用于处理图像分类任务的代码示例。此代码使用`numpy`库来构建模型并训练MNIST手写数字数据集[^2]。 ```python import numpy as np from sklearn.datasets import fetch_openml from sklearn.model_selection import train_test_split from sklearn.preprocessing import LabelBinarizer import matplotlib.pyplot as plt class NeuralNetwork: def __init__(self, layers, alpha=0.1): self.layers = layers self.alpha = alpha self.W = [] for i in range(len(layers) - 1): w = np.random.randn(layers[i], layers[i + 1]) self.W.append(w / np.sqrt(layers[i])) def sigmoid(self, x): return 1.0 / (1 + np.exp(-x)) def predict(self, X, add_bias=True): p = np.atleast_2d(X) if add_bias: p = np.c_[p, np.ones((p.shape[0]))] for layer in self.W: p = self.sigmoid(np.dot(p, layer)) return p def fit(self, X, y, epochs=1000, displayUpdate=100): X = np.c_[X, np.ones((X.shape[0]))] for epoch in range(epochs): for (x, target) in zip(X, y): self.fit_partial(x, target) if epoch == 0 or (epoch + 1) % displayUpdate == 0: loss = self.calculate_loss(X, y) print("[INFO] epoch={}, loss={:.7f}".format(epoch + 1, loss)) def calculate_loss(self, X, targets): targets = np.atleast_2d(targets) predictions = self.predict(X, add_bias=False) loss = 0.5 * np.sum((predictions - targets) ** 2) return loss def fit_partial(self, x, y): A = [np.atleast_2d(x)] for layer in self.W: net = A[-1].dot(layer) out = self.sigmoid(net) A.append(out) error = A[-1] - y D = [error * self.sigmoid_derivative(A[-1])] for layer in range(len(A) - 2, 0, -1): delta = D[-1].dot(self.W[layer].T) delta *= self.sigmoid_derivative(A[layer]) D.append(delta) D = D[::-1] for layer in range(len(self.W)): self.W[layer] += -self.alpha * A[layer].T.dot(D[layer]) def sigmoid_derivative(self, x): return x * (1 - x) # 加载MNIST数据集 mnist = fetch_openml('mnist_784', version=1) data = mnist["data"].astype(float) / 255.0 labels = mnist["target"].astype(int) # 将标签转换为one-hot编码形式 lb = LabelBinarizer() labels = lb.fit_transform(labels) # 划分训练集和测试集 train_x, test_x, train_y, test_y = train_test_split(data, labels, test_size=0.2, random_state=42) # 初始化神经网络并进行训练 nn = NeuralNetwork([train_x.shape[1], 32, 16, 10], alpha=0.01) nn.fit(train_x, train_y, epochs=1000) # 测试预测效果 predictions = nn.predict(test_x) predictions = np.argmax(predictions, axis=1) actuals = np.argmax(test_y, axis=1) print(f"[INFO] Accuracy: {np.mean(predictions == actuals)}") # 可视化部分结果 for i in range(10): pred = np.argmax(nn.predict(test_x[i])) actual = np.argmax(test_y[i]) img = (test_x[i] * 255).reshape((28, 28)).astype("uint8") title = f"Actual:{actual}, Pred:{pred}" plt.imshow(img, cmap="gray") plt.title(title) plt.show() ``` 上述代码展示了如何通过自定义类创建一个三层BP神经网络，并将其应用于MNIST数据集上的图像分类任务。该网络具有输入层、隐藏层以及输出层，其中激活函数采用了Sigmoid函数[^1]。 #### 关键点说明 - 数据预处理阶段将像素值标准化到 `[0, 1]` 范围内以便于优化收敛速度。 - 使用 `LabelBinarizer` 对类别标签进行了独热编码操作以适配多分类场景下的损失计算需求。 - 自定义实现了前馈传播与反向传播算法逻辑，在每次迭代过程中更新权重参数直至达到指定的最大轮次或者满足停止条件为止。