贝叶斯定理

贝叶斯分为：高斯贝叶斯，多项式贝叶斯，伯努利贝叶斯

高斯贝叶斯：先验为高斯分布的朴素贝叶斯

多项式贝叶斯：先验为多项式分布的朴素贝叶斯

伯努利贝叶斯：先验为伯努利的朴素贝叶斯，适用于样本特征是二元离散值或者很稀疏的多元离散值情况

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib

%matplotlib inline
matplotlib.rcParams['font.sans-serif'] = ['SimHei'] #显示中文
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号
#分析数据
data = pd.read_csv('010-data_multivar.csv',header=None)
dataset_X,dataset_Y = data.iloc[:,:-1],data.iloc[:,-1]

dataset_X = dataset_X.values
dataset_Y = dataset_Y.values
# print(dataset_Y)
classes = list(set(dataset_Y))# 去重
# classes = np.unique(dataset_Y)
print(classes)

[0, 1, 2, 3]

# 数据集可视化
def visual_2D_dataset(dataset_X,dataset_y):
    '''将二维数据集dataset_X和对应的类别dataset_y显示在散点图中'''
    assert dataset_X.shape[1]==2,'only support dataset with 2 features'
    plt.figure()
    classes=list(set(dataset_y)) 
    markers=['.',',','o','v','^','<','>','1','2','3','4','8'
             ,'s','p','*','h','H','+','x','D','d','|']
    colors=['b','c','g','k','m','w','r','y']
    for class_id in classes:
        one_class=np.array([feature for (feature,label) in 
                   zip(dataset_X,dataset_y) if label==class_id])
        plt.scatter(one_class[:,0],one_class[:,1],marker=np.random.choice(markers,1)[0],
                    c=np.random.choice(colors,1)[0],label='class_'+str(class_id))
    plt.legend()

visual_2D_dataset(dataset_X,dataset_Y)

# 将分类器绘制到图中
def plot_classifier(classifier, X, y):
    x_min, x_max = min(X[:, 0]) - 1.0, max(X[:, 0]) + 1.0 # 计算图中坐标的范围
    y_min, y_max = min(X[:, 1]) - 1.0, max(X[:, 1]) + 1.0
    step_size = 0.01 # 设置step size
    x_values, y_values = np.meshgrid(np.arange(x_min, x_max, step_size), np.arange(y_min, y_max, step_size))
    # 构建网格数据
    mesh_output = classifier.predict(np.c_[x_values.ravel(), y_values.ravel()])
    mesh_output = mesh_output.reshape(x_values.shape) 
    plt.figure()
    plt.pcolormesh(x_values, y_values, mesh_output, cmap=plt.cm.gray)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=80, edgecolors='black', linewidth=1, cmap=plt.cm.Paired)
    # specify the boundaries of the figure
    plt.xlim(x_values.min(), x_values.max())
    plt.ylim(y_values.min(), y_values.max())

    # specify the ticks on the X and Y axes
    plt.xticks((np.arange(int(min(X[:, 0])-1), int(max(X[:, 0])+1), 1.0)))
    plt.yticks((np.arange(int(min(X[:, 1])-1), int(max(X[:, 1])+1), 1.0)))
    plt.show()

构造高斯朴素贝叶斯

from sklearn.naive_bayes import GaussianNB
​
gaussian = GaussianNB()
gaussian.fit(dataset_X,dataset_Y)
​
#预测
pre_y = gaussian.predict(dataset_X)
# print(pre_y)
​
#判断预测结果和真实值的匹配数量
correct_count = (dataset_Y== pre_y).sum()
# print(correct_count)
​
#调用绘图函数
plot_classifier(gaussian,dataset_X,pre_y)

多项式朴素贝叶斯模型

from sklearn.naive_bayes import MultinomialNB
#范围缩放
from sklearn.preprocessing import MinMaxScaler
#要求所有特征必须是非负数，否则没法训练
#np.c_[x,y]列合并 np.r_[x,y]行合并
sclar = MinMaxScaler(feature_range=(0,1))

dataset = sclar.fit_transform(dataset_X)

mul_nb = MultinomialNB()
mul_nb.fit(dataset,dataset_Y)
print(np.c_[dataset,dataset_Y])
# print(dataset_Y.reshape(-1,2))
print(np.r_[dataset,dataset_Y.reshape(-1,2)])
y = mul_nb.predict([[0.51539855,0.27345309]])#预测
print(y)
y_pre = mul_nb.predict(dataset)

plot_classifier(mul_nb,dataset,dataset_Y)
from sklearn.naive_bayes import MultinomialNB
#范围缩放
from sklearn.preprocessing import MinMaxScaler
#要求所有特征必须是非负数，否则没法训练
#np.c_[x,y]列合并 np.r_[x,y]行合并
sclar = MinMaxScaler(feature_range=(0,1))
​
dataset = sclar.fit_transform(dataset_X)
​
mul_nb = MultinomialNB()
mul_nb.fit(dataset,dataset_Y)
print(np.c_[dataset,dataset_Y])
# print(dataset_Y.reshape(-1,2))
print(np.r_[dataset,dataset_Y.reshape(-1,2)])
y = mul_nb.predict([[0.51539855,0.27345309]])#预测
print(y)
y_pre = mul_nb.predict(dataset)
​
plot_classifier(mul_nb,dataset,dataset_Y)

伯努利贝叶斯

from sklearn.naive_bayes import BernoulliNB
​
bernou = BernoulliNB()
bernou.fit(dataset_X,dataset_Y)
y_re = bernou.predict(dataset_X)
plot_classifier(bernou,dataset_X,dataset_Y)
​