朴素贝叶斯

使用朴素贝叶斯，特征向量为离散型
x1，x2是两个特征向量，Y是类别

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
x1	1	1	1	1	1	2	2	2	2	2	3	3	3	3	3
x2	S	M	M	S	S	S	M	M	L	L	L	M	M	L	L
Y	-1	-1	1	1	-1	-1	-1	1	1	1	1	1	1	1	-1

手算过程见文末参考博客

思想：

1. 创建数据集
2. 计算各类概率
2.1 算p(y = -1)，p（y = 1）， 即算各类概率
2.2 根据输入特征向量x = (2, 'S'), 计算p(x向量 | y) = 累乘 p(xi | y)
3. 预测：给一个特征向量，按照2中算出的值相乘，各类概率大的获胜

代码：

def createDataSet():
    dataSet = [[1, 'S', -1],
               [1, 'M', -1],
               [1, 'M', 1],
               [1, 'S', 1],
               [1, 'S', -1],
               [2, 'S', -1],
               [2, 'M', -1],
               [2, 'M', 1],
               [2, 'L', 1],
               [2, 'L', 1],
               [3, 'L', 1],
               [3, 'M', 1],
               [3, 'M', 1],
               [3, 'L', 1],
               [3, 'L', -1]]
    labels = ['x1', 'x2', 'y']
    return dataSet, labels

# 统计yi的个数
def typeCount(typeList, t):
    cnt = 0
    for tL in typeList:
        if tL == t:
            cnt += 1
    return cnt

# 计算Y=-1或1的条件下，X等于某值 个数
def featCount(dataSet, i, feat, y):
    cnt = 0
    #print(i, feat, y)
    for row in dataSet:
        if row[i] == feat and row[-1] == y:
            cnt += 1
    return cnt

def calcBayes(dataSet):
    # 以 x = (2, 'S') 为例
    X = [2 , 'S']
    
    lenDataSet = len(dataSet)
    typeList = [row[-1] for row in dataSet] 
    typeSet = set(typeList) # 类别集合
    print(typeList, typeSet)
    typeLen = len(typeSet)
    # 遍历一类 t=1; t=-1
    pList = [] # 记录预计 各类类别 概率
    for t in typeSet:
        yNum = typeCount(typeList, t)# 计算yi的个数
        print(f'{t} num =',yNum)
        py = yNum / lenDataSet
        print(f'P(Y = {t}) =', py)
        pSum = py
        # 对每个特征分量计数
        for i in range(len(X)):
            xiNum = featCount(dataSet, i, X[i], t) # 统计Y条件下 Xi取相应特征 的数量
            print(f'特征{X[i]} num =',xiNum)
            # 条件概率P{X = xi | Y = yi}
            pxy = xiNum / yNum
            print(f'条件概率 =', pxy)
            pSum *= pxy
        pList.append(pSum)
    #print(pList)
    return pList, typeSet

# 就是找最大的概率，记录下标
def predict(pList, typeList):
    for i in range(len(pList)):
        if pList[i] == max(pList):
            print('*'*50)
            print(f'预测类 为 = {typeList[i]}')
            
if __name__ == '__main__':
    dataSet, labels = createDataSet()
    pList, typeSet = calcBayes(dataSet)
    predict(pList, list(typeSet))