【协同过滤推荐算法】欧氏距离表示用户或物品相似度

Prefer = {"jim": {"War": 1.9, "the big bang": 1.0, "The lord of wings": 4.0, "Beautiful America": 4.7}, "lily": {"War": 2.0, "Kongfu": 4.1, "The lord of wings": 3.6}, "tommy": {"War": 2.3, "Kongfu": 5.0, "The lord of wings": 3.0}, "jack": {"War": 2.8, "Kongfu": 5.5, "The lord of wings": 3.5}}
#欧式距离及几何距离，有m个物品就有m维度的空间，把用户u定位到这个m维度的空间里
#用户u在m维度空间里的第i维度的坐标值表示用户对此物品的评分
#这里只计算2维度的情况
def EuclidDistance(prefer, person1, person2):   
    sim = {}
    for item in prefer[person1]:
        if item in prefer[person2]:
            sim[item] = 1#添加共同项到字典中
    #无共同项，返回0
    if len(sim)==0:         
        return 0
    #计算所有共有项目的差值的平方和
    sum_all = sum([pow(prefer[person1][item]-prefer[person2][item], 2) for item in sim])
    #返回改进的相似度函数，距离越大相似度越小
    #两个点完全重合相似度为1    
    return 1/(1+(sum_all**0.5))

#测试
print("\n欧氏距离表示相似度....")
print("EuclidDistance(Prefer,'tommy','jim') = ",EuclidDistance(Prefer, 'tommy', 'jim'))
print("EuclidDistance(Prefer,'tommy','lily') = ",EuclidDistance(Prefer, 'tommy', 'lily'))
print("EuclidDistance(Prefer,'tommy','jack') = ",EuclidDistance(Prefer, 'tommy', 'jack'))

结果：

欧氏距离表示相似度....

EuclidDistance(Prefer,'tommy','jim') = 0.48145600891813006

EuclidDistance(Prefer,'tommy','lily') = 0.471143138585317

EuclidDistance(Prefer,'tommy','jack') = 0.5358983848622454