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获取
运行结果： 
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获取
运行结果： 