李航《统计学习方法》——第四章朴素贝叶斯法

忘是亡心i 2022-05-30 10:27 153阅读 0赞

由于网上资料很多，这里就不再对算法原理进行推导，仅给出博主用Python实现的代码，供大家参考

**适用问题**：多类分类  
  
**基于贝叶斯定理和特征条件独立假设**  
  
**常用的三个模型有**：  
\- 高斯模型：处理特征是连续型变量的情况  
\- 多项式模型：最常见，要求特征是离散数据  
\- 伯努利模型：要求特征是离散的，且为布尔类型，即true和false，或者1和0

**测试数据集**：[train.csv][]  
  
**实现代码（基于多项式模型）**：

# encoding=utf-8
    
    import pandas as pd
    import numpy as np
    import cv2
    import time
    
    from sklearn.cross_validation import train_test_split
    from sklearn.metrics import accuracy_score
    
    # 二值化处理
    def binaryzation(img):
        cv_img = img.astype(np.uint8)  # 类型转化成Numpy中的uint8型
        cv2.threshold(cv_img, 50, 1, cv2.THRESH_BINARY_INV, cv_img)  # 大于50的值赋值为0,不然赋值为1
        return cv_img
    
    # 训练，计算出先验概率和条件概率
    def Train(trainset, train_labels):
        prior_probability = np.zeros(class_num)                         # 先验概率
        conditional_probability = np.zeros((class_num, feature_len, 2))   # 条件概率
    
        # 计算
        for i in range(len(train_labels)):
            img = binaryzation(trainset[i])     # 图片二值化，让每一个特征都只有0，1两种取值
            label = train_labels[i]
    
            prior_probability[label] += 1
    
            for j in range(feature_len):
                conditional_probability[label][j][img[j]] += 1
    
        # 将条件概率归到[1,10001]
        for i in range(class_num):
            for j in range(feature_len):
    
                # 经过二值化后图像只有0，1两种取值
                pix_0 = conditional_probability[i][j][0]
                pix_1 = conditional_probability[i][j][1]
    
                # 计算0，1像素点对应的条件概率
                probalility_0 = (float(pix_0)/float(pix_0+pix_1))*10000 + 1
                probalility_1 = (float(pix_1)/float(pix_0+pix_1))*10000 + 1
    
                conditional_probability[i][j][0] = probalility_0
                conditional_probability[i][j][1] = probalility_1
    
        return prior_probability, conditional_probability
    
    # 计算概率
    def calculate_probability(img, label):
        probability = int(prior_probability[label])
    
        for j in range(feature_len):
            probability *= int(conditional_probability[label][j][img[j]])
    
        return probability
    
    # 预测
    def Predict(testset, prior_probability, conditional_probability):
        predict = []
    
        # 对每个输入的x，将后验概率最大的类作为x的类输出
        for img in testset:
    
            img = binaryzation(img)  # 图像二值化
    
            max_label = 0
            max_probability = calculate_probability(img, 0)
    
            for j in range(1, class_num):
                probability = calculate_probability(img, j)
    
                if max_probability < probability:
                    max_label = j
                    max_probability = probability
    
            predict.append(max_label)
    
        return np.array(predict)
    
    
    class_num = 10  # MINST数据集有10种labels，分别是“0,1,2,3,4,5,6,7,8,9”
    feature_len = 784  # MINST数据集每个image有28*28=784个特征（pixels）
    
    if __name__ == '__main__':
    
        print("Start read data")
        time_1 = time.time()
    
        raw_data = pd.read_csv('../data/train.csv', header=0)  # 读取csv数据
        data = raw_data.values
    
        features = data[::, 1::]
        labels = data[::, 0]
    
        # 避免过拟合，采用交叉验证，随机选取33%数据作为测试集，剩余为训练集
        train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33, random_state=0)
    
        time_2 = time.time()
        print('read data cost %f seconds' % (time_2 - time_1))
    
    
        print('Start training')
        prior_probability, conditional_probability = Train(train_features, train_labels)
        time_3 = time.time()
        print('training cost %f seconds' % (time_3 - time_2))
    
    
        print('Start predicting')
        test_predict = Predict(test_features, prior_probability, conditional_probability)
        time_4 = time.time()
        print('predicting cost %f seconds' % (time_4 - time_3))
    
    
        score = accuracy_score(test_labels, test_predict)
    print("The accruacy score is %f" % score)

代码可从这里[naive\_bayes/naive\_bayes.py][naive_bayes_naive_bayes.py]获取  
  
**运行结果**：  
  
![naive_bayes_result.png][]  
  
  
**实现代码（基于多项式模型，用sklearn实现）**：

# encoding=utf-8
    
    import pandas as pd
    import numpy as np
    import time
    
    from sklearn.naive_bayes import MultinomialNB
    
    from sklearn.cross_validation import train_test_split
    from sklearn.metrics import accuracy_score
    
    
    if __name__ == '__main__':
    
        print("Start read data...")
        time_1 = time.time()
    
        raw_data = pd.read_csv('../data/train.csv', header=0)  # 读取csv数据
        data = raw_data.values
    
        features = data[::, 1::]
        labels = data[::, 0]
    
        # 随机选取33%数据作为测试集，剩余为训练集
        train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33, random_state=0)
    
        time_2 = time.time()
        print('read data cost %f seconds' % (time_2 - time_1))
    
    
        print('Start training...')
        clf = MultinomialNB(alpha=1.0) # 加入laplace平滑
        clf.fit(train_features, train_labels)
        time_3 = time.time()
        print('training cost %f seconds' % (time_3 - time_2))
    
    
        print('Start predicting...')
        test_predict = clf.predict(test_features)
        time_4 = time.time()
        print('predicting cost %f seconds' % (time_4 - time_3))
    
    
        score = accuracy_score(test_labels, test_predict)
    print("The accruacy score is %f" % score)

代码可从这里[naive\_bayes/naive\_bayes\_sklearn.py][naive_bayes_naive_bayes_sklearn.py]获取  
  
**运行结果**：  
  
![naive_bayes_sklearn_result.png][]

[train.csv]: https://github.com/fuqiuai/lihang_algorithms/blob/master/data/train.csv
[naive_bayes_naive_bayes.py]: https://github.com/fuqiuai/lihang_algorithms/blob/master/naive_bayes/naive_bayes.py
[naive_bayes_result.png]: /images/20220530/53d219604f6847a89095223a231095fa.png
[naive_bayes_naive_bayes_sklearn.py]: https://github.com/fuqiuai/lihang_algorithms/blob/master/naive_bayes/naive_bayes_sklearn.py
[naive_bayes_sklearn_result.png]: /images/20220530/6a898b75a58c4cb6bf8ae0beeae8a507.png