Apriori 获取关联规则实现

前言

自己的一个Apriori 获取关联规则的python实现。具体原理不讲，代码添加了说明，还是很好理解的。

数据预处理

#最小置信度
min_conf = 0.5
#最小支持度
min_sup = 2
f=open('data.txt')
dataset = f.readlines()
print(dataset)

['T1	bread, cream, milk, tea
', 'T2	bread, cream, milk
', 'T3	cake, milk
', 'T4	milk, tea
', 'T5	bread, cake, milk
', 'T6	bread, tea
', 'T7	beer, milk, tea
', 'T8	bread, tea
', 'T9	bread, cream, milk, tea
', 'T10	bread, milk, tea']

dataset = [data.replace('
','').split('	') for data in dataset]
print(dataset)

[['T1', 'bread, cream, milk, tea'], ['T2', 'bread, cream, milk'], ['T3', 'cake, milk'], ['T4', 'milk, tea'], ['T5', 'bread, cake, milk'], ['T6', 'bread, tea'], ['T7', 'beer, milk, tea'], ['T8', 'bread, tea'], ['T9', 'bread, cream, milk, tea'], ['T10', 'bread, milk, tea']]

dataset = [tuple([data[0],sorted(data[1].replace(' ', '').split(','))]) for data in dataset]
print(dataset)

[('T1', ['bread', 'cream', 'milk', 'tea']), ('T2', ['bread', 'cream', 'milk']), ('T3', ['cake', 'milk']), ('T4', ['milk', 'tea']), ('T5', ['bread', 'cake', 'milk']), ('T6', ['bread', 'tea']), ('T7', ['beer', 'milk', 'tea']), ('T8', ['bread', 'tea']), ('T9', ['bread', 'cream', 'milk', 'tea']), ('T10', ['bread', 'milk', 'tea'])]

terms = [term for data in dataset for term in data[1]]
terms.sort()
terms = [terms[i] for i in range(0,len(terms)) if i==0 or terms[i]!=terms[i-1]]
print(terms)

['beer', 'bread', 'cake', 'cream', 'milk', 'tea']

Aprior寻找频繁项集

def is_sub_seq(P, T):
    '''判断P是否为T的子序列
    Parameters
    --------
    P: 一个有序序列
    T: 一个有序序列
    '''
    i, j = 0, 0
    while(i<len(P) and j<len(T)):
        if(P[i]==T[j]):
            i+=1
        j+=1
    return i==len(P)

def Aprior_sieve(L):
    '''从一个项集组成的序列中中筛选出频繁项集
    Parameters
    ---
    L: 一个项集组成的序列
    
    Returns
    ---
    一个频繁项集和它支持度组成的序列
    '''
    L = [[l,0] for l in L]
    for l in L:
        for data in dataset:
            if(is_sub_seq(l[0], data[1])):
                l[1] += 1
    L = [l for l in L if l[1]>=minsup]
    return L
    

def Aprior_gen(L,k):
    '''通过k项集构造k+1项集
    Parameters
    ---
    L:一个频繁k项集和它支持度组成的序列
    k:频繁k项集的项数
    
    Returns
    ---
    一个k+1项集组成的序列
    '''
    print(k,":	",L)
    NL = []
    myset = {tuple(l[0]) for l in L}
    for i in range(0, len(L)):
        for j in range(i+1, len(L)):
            if(L[i][0][:k-1]==L[j][0][:k-1]):
                nl = L[i][0].copy()
                nl.append(L[j][0][k-1])
                ok = True
                for r in range(0, k-1):
                    tmp = nl.copy()
                    tmp.pop(r)
                    tmp = tuple(tmp)
                    if(tmp not in myset):
                        ok = False
                        break
                if(ok):
                    NL.append(nl)
            else:
                break
    return NL
                

L = [[term] for term in terms]
L = Aprior_sieve(L)
print(L)

[[['bread'], 7], [['cake'], 2], [['cream'], 3], [['milk'], 8], [['tea'], 7]]

Ans = []
Ans.append(L)
for i in range(1,len(terms)):
    L = Aprior_gen(Ans[i-1],i)
    L = Aprior_sieve(L)
    if(len(L)==0):
        break
    Ans.append(L)
print(Ans)

1 :	 [[['bread'], 7], [['cake'], 2], [['cream'], 3], [['milk'], 8], [['tea'], 7]]
2 :	 [[['bread', 'cream'], 3], [['bread', 'milk'], 5], [['bread', 'tea'], 5], [['cake', 'milk'], 2], [['cream', 'milk'], 3], [['cream', 'tea'], 2], [['milk', 'tea'], 5]]
3 :	 [[['bread', 'cream', 'milk'], 3], [['bread', 'cream', 'tea'], 2], [['bread', 'milk', 'tea'], 3], [['cream', 'milk', 'tea'], 2]]
4 :	 [[['bread', 'cream', 'milk', 'tea'], 2]]
[[[['bread'], 7], [['cake'], 2], [['cream'], 3], [['milk'], 8], [['tea'], 7]], [[['bread', 'cream'], 3], [['bread', 'milk'], 5], [['bread', 'tea'], 5], [['cake', 'milk'], 2], [['cream', 'milk'], 3], [['cream', 'tea'], 2], [['milk', 'tea'], 5]], [[['bread', 'cream', 'milk'], 3], [['bread', 'cream', 'tea'], 2], [['bread', 'milk', 'tea'], 3], [['cream', 'milk', 'tea'], 2]], [[['bread', 'cream', 'milk', 'tea'], 2]]]

获取关联规则

mydict = { tuple(l[0]):l[1] for i in range(0, len(Ans)) for l in Ans[i]}
print(mydict)
R=set()

{('bread',): 7, ('cake',): 2, ('cream',): 3, ('milk',): 8, ('tea',): 7, ('bread', 'cream'): 3, ('bread', 'milk'): 5, ('bread', 'tea'): 5, ('cake', 'milk'): 2, ('cream', 'milk'): 3, ('cream', 'tea'): 2, ('milk', 'tea'): 5, ('bread', 'cream', 'milk'): 3, ('bread', 'cream', 'tea'): 2, ('bread', 'milk', 'tea'): 3, ('cream', 'milk', 'tea'): 2, ('bread', 'cream', 'milk', 'tea'): 2}

def conf(rule):
    return mydict[rule[1]]/mydict[rule[0]]

def gen_rule(X, Y):
    for item in Y:
        if item not in X:
            nX = X.copy()
            nX.append(item)
            nX.sort()
            rule = (tuple(nX),Y)
            if(rule not in R and conf(rule)>=min_conf):
                R.add(rule)
                gen_rule(nX, Y)

for l in mydict.keys():
    gen_rule([],l)

R = [(f, tuple(set(b)-set(f))) for f, b in R]
R.sort()
print(R)

[(('bread',), ()), (('bread',), ('milk',)), (('bread',), ('tea',)), (('bread', 'cream'), ()), (('bread', 'cream'), ('milk',)), (('bread', 'cream'), ('milk', 'tea')), (('bread', 'cream'), ('tea',)), (('bread', 'cream', 'milk'), ()), (('bread', 'cream', 'milk'), ('tea',)), (('bread', 'cream', 'milk', 'tea'), ()), (('bread', 'cream', 'tea'), ()), (('bread', 'cream', 'tea'), ('milk',)), (('bread', 'milk'), ()), (('bread', 'tea'), ()), (('cake',), ()), (('cake',), ('milk',)), (('cake', 'milk'), ()), (('cream',), ()), (('cream',), ('bread',)), (('cream',), ('bread', 'milk')), (('cream',), ('bread', 'milk', 'tea')), (('cream',), ('bread', 'tea')), (('cream',), ('milk',)), (('cream',), ('milk', 'tea')), (('cream',), ('tea',)), (('cream', 'milk'), ()), (('cream', 'milk'), ('bread',)), (('cream', 'milk'), ('bread', 'tea')), (('cream', 'milk'), ('tea',)), (('cream', 'milk', 'tea'), ()), (('cream', 'milk', 'tea'), ('bread',)), (('cream', 'tea'), ()), (('cream', 'tea'), ('bread',)), (('cream', 'tea'), ('bread', 'milk')), (('cream', 'tea'), ('milk',)), (('milk',), ()), (('milk',), ('bread',)), (('milk',), ('tea',)), (('milk', 'tea'), ()), (('tea',), ()), (('tea',), ('bread',)), (('tea',), ('milk',))]

print(len(mydict), len(R))

17 42

感想

算法的原理还是比较简单的，但实现起来还是要花些功夫。另外使用python的一些特性可以极大简化代码实现，如列表解析（学到了一种多重循环的解析），容器转换。踩了一波语法特性的坑，比如copy,dict的键为容器的话只能用tuple