朴素贝叶斯算法实现mnist数据集的读取与显示、数据集划分、算法实现的完整代码

好的，以下是用朴素贝叶斯算法实现MNIST数据集分类的完整代码：

import numpy as np
import struct
import matplotlib.pyplot as plt

# 读取MNIST数据集
def load_mnist(path, kind='train'):
    labels_path = path + '/' + kind + '-labels-idx1-ubyte'
    images_path = path + '/' + kind + '-images-idx3-ubyte'
    with open(labels_path, 'rb') as lbpath:
        magic, n = struct.unpack('>II', lbpath.read(8))
        labels = np.fromfile(lbpath, dtype=np.uint8)
    with open(images_path, 'rb') as imgpath:
        magic, num, rows, cols = struct.unpack('>IIII', imgpath.read(16))
        images = np.fromfile(imgpath, dtype=np.uint8).reshape(len(labels), 784)
    return images, labels

# 显示MNIST数据集中的一张图片
def show_image(image):
    plt.imshow(image.reshape(28, 28), cmap='gray')
    plt.show()

# 划分数据集为训练集和测试集
def split_dataset(dataset, labels, test_ratio=0.2):
    num_samples = dataset.shape[0]
    num_test = int(num_samples * test_ratio)
    indices = np.random.permutation(num_samples)
    test_indices = indices[:num_test]
    train_indices = indices[num_test:]
    train_dataset = dataset[train_indices]
    train_labels = labels[train_indices]
    test_dataset = dataset[test_indices]
    test_labels = labels[test_indices]
    return train_dataset, train_labels, test_dataset, test_labels

# 计算多项式分布概率密度函数
def multinomial_prob(x, theta):
    return np.exp(np.sum(x * np.log(theta), axis=1) + np.log(1 - theta.sum(axis=1)))

# 训练朴素贝叶斯算法模型
def train_naive_bayes(X, y):
    num_samples, num_features = X.shape
    num_classes = len(np.unique(y))
    priors = np.zeros(num_classes)
    theta = np.zeros((num_classes, num_features))
    for i in range(num_classes):
        X_i = X[y == i]
        priors[i] = len(X_i) / float(num_samples)
        theta[i] = (X_i.sum(axis=0) + 1) / (float(X_i.sum() + num_features))
    return priors, theta

# 使用朴素贝叶斯算法模型进行预测
def predict_naive_bayes(X, priors, theta):
    num_samples, num_features = X.shape
    num_classes = len(priors)
    log_probs = np.zeros((num_samples, num_classes))
    for i in range(num_classes):
        log_probs[:, i] = np.log(priors[i]) + np.sum(np.log(theta[i]) * X, axis=1)
    return np.argmax(log_probs, axis=1)

# 加载MNIST数据集
X_train, y_train = load_mnist('data', kind='train')
X_test, y_test = load_mnist('data', kind='t10k')

# 显示一张图片
show_image(X_train[0])

# 划分训练集和测试集
X_train, y_train, X_test, y_test = split_dataset(X_train, y_train, test_ratio=0.2)

# 训练朴素贝叶斯算法模型
priors, theta = train_naive_bayes(X_train, y_train)

# 使用朴素贝叶斯算法模型进行预测
y_pred = predict_naive_bayes(X_test, priors, theta)

# 计算预测精度
accuracy = np.mean(y_pred == y_test) * 100
print('Accuracy: %.2f%%' % accuracy)

这里采用了多项式分布作为特征的概率分布函数，实现了朴素贝叶斯算法模型的训练和预测，并计算了预测精度。