### 使用基础Python库实现MNIST手写数字识别 以下是一些使用基础Python库（如NumPy和Pandas）实现MNIST手写数字识别的算法示例代码。这些算法不依赖深度学习框架，而是通过传统机器学习方法完成任务。 --- #### 1. K-Nearest Neighbors (KNN) 实现 KNN是一种简单的分类算法，基于最近邻原则进行预测。 ```python import numpy as np from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score # 加载MNIST数据集 def load_mnist(): from keras.datasets import mnist (x_train, y_train), (x_test, y_test) = mnist.load_data() x_train = x_train.reshape(-1, 28 * 28) / 255.0 x_test = x_test.reshape(-1, 28 * 28) / 255.0 return x_train, y_train, x_test, y_test x_train, y_train, x_test, y_test = load_mnist() # 计算欧氏距离 def euclidean_distance(x1, x2): return np.sqrt(np.sum((x1 - x2) ** 2)) # KNN分类器 class KNN: def __init__(self, k=3): self.k = k def fit(self, X, y): self.X_train = X self.y_train = y def predict(self, X): y_pred = [self._predict(x) for x in X] return np.array(y_pred) def _predict(self, x): distances = [euclidean_distance(x, x_train) for x_train in self.X_train] k_indices = np.argsort(distances)[:self.k] k_nearest_labels = [self.y_train[i] for i in k_indices] most_common = np.bincount(k_nearest_labels).argmax() return most_common # 划分训练集和验证集 X_train, X_val, Y_train, Y_val = train_test_split(x_train, y_train, test_size=0.2, random_state=42) # 训练模型 knn = KNN(k=5) knn.fit(X_train, Y_train) predictions = knn.predict(X_val) # 评估模型 accuracy = accuracy_score(Y_val, predictions) print(f"KNN Accuracy: {accuracy * 100:.2f}%") ``` --- #### 2. Softmax回归实现 Softmax回归是一种多分类线性模型，适合处理像MNIST这样的分类问题。 ```python import numpy as np from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score # 加载MNIST数据集 def load_mnist(): from keras.datasets import mnist (x_train, y_train), (x_test, y_test) = mnist.load_data() x_train = x_train.reshape(-1, 28 * 28) / 255.0 x_test = x_test.reshape(-1, 28 * 28) / 255.0 return x_train, y_train, x_test, y_test x_train, y_train, x_test, y_test = load_mnist() # 转换为one-hot编码 def to_one_hot(y, num_classes=10): return np.eye(num_classes)[y] # Softmax函数 def softmax(z): exp_z = np.exp(z - np.max(z, axis=1, keepdims=True)) return exp_z / np.sum(exp_z, axis=1, keepdims=True) # 损失函数 def cross_entropy_loss(y_true, y_pred): m = y_true.shape[0] loss = -np.sum(y_true * np.log(y_pred + 1e-8)) / m return loss # Softmax回归模型 class SoftmaxRegression: def __init__(self, learning_rate=0.1, epochs=100): self.learning_rate = learning_rate self.epochs = epochs def fit(self, X, y): m, n = X.shape self.num_classes = y.shape[1] self.W = np.zeros((n, self.num_classes)) self.b = np.zeros((1, self.num_classes)) for epoch in range(self.epochs): z = np.dot(X, self.W) + self.b y_pred = softmax(z) loss = cross_entropy_loss(y, y_pred) if epoch % 10 == 0: print(f"Epoch {epoch}: Loss = {loss}") dw = np.dot(X.T, (y_pred - y)) / m db = np.sum((y_pred - y), axis=0) / m self.W -= self.learning_rate * dw self.b -= self.learning_rate * db def predict(self, X): z = np.dot(X, self.W) + self.b y_pred = softmax(z) return np.argmax(y_pred, axis=1) # 划分训练集和验证集 X_train, X_val, Y_train, Y_val = train_test_split(x_train, y_train, test_size=0.2, random_state=42) Y_train_one_hot = to_one_hot(Y_train) # 训练模型 softmax_reg = SoftmaxRegression(learning_rate=0.1, epochs=50) softmax_reg.fit(X_train, Y_train_one_hot) predictions = softmax_reg.predict(X_val) # 评估模型 accuracy = accuracy_score(Y_val, predictions) print(f"Softmax Regression Accuracy: {accuracy * 100:.2f}%") ``` --- #### 3. 主成分分析（PCA）+ KNN 实现 PCA可以用于降维，减少计算复杂度，同时结合KNN提高分类性能。 ```python import numpy as np from sklearn.decomposition import PCA from sklearn.neighbors import KNeighborsClassifier from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score # 加载MNIST数据集 def load_mnist(): from keras.datasets import mnist (x_train, y_train), (x_test, y_test) = mnist.load_data() x_train = x_train.reshape(-1, 28 * 28) / 255.0 x_test = x_test.reshape(-1, 28 * 28) / 255.0 return x_train, y_train, x_test, y_test x_train, y_train, x_test, y_test = load_mnist() # 应用PCA降维 pca = PCA(n_components=50) x_train_pca = pca.fit_transform(x_train) x_test_pca = pca.transform(x_test) # 划分训练集和验证集 X_train, X_val, Y_train, Y_val = train_test_split(x_train_pca, y_train, test_size=0.2, random_state=42) # 使用KNN分类器 knn = KNeighborsClassifier(n_neighbors=5) knn.fit(X_train, Y_train) predictions = knn.predict(X_val) # 评估模型 accuracy = accuracy_score(Y_val, predictions) print(f"PCA + KNN Accuracy: {accuracy * 100:.2f}%") ``` --- #### 4. 随机森林（Random Forest）实现 随机森林是一种基于决策树的集成学习方法，适合处理高维数据。 ```python import numpy as np from sklearn.ensemble import RandomForestClassifier from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score # 加载MNIST数据集 def load_mnist(): from keras.datasets import mnist (x_train, y_train), (x_test, y_test) = mnist.load_data() x_train = x_train.reshape(-1, 28 * 28) / 255.0 x_test = x_test.reshape(-1, 28 * 28) / 255.0 return x_train, y_train, x_test, y_test x_train, y_train, x_test, y_test = load_mnist() # 划分训练集和验证集 X_train, X_val, Y_train, Y_val = train_test_split(x_train, y_train, test_size=0.2, random_state=42) # 使用随机森林分类器 rf = RandomForestClassifier(n_estimators=100, random_state=42) rf.fit(X_train, Y_train) predictions = rf.predict(X_val) # 评估模型 accuracy = accuracy_score(Y_val, predictions) print(f"Random Forest Accuracy: {accuracy * 100:.2f}%") ``` --- ### 总结 上述代码展示了如何使用基础Python库（如NumPy、Pandas）实现MNIST手写数字识别。每种算法都有其特点和适用场景[^1]。例如，KNN简单但计算复杂度较高；Softmax回归适合线性可分数据；PCA+KNN通过降维提高了效率；随机森林则提供了更高的鲁棒性。