常用用户相似度距离计算函数

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曼哈顿距离

manhattan

def manhattan(rating1, rating2):
    """计算曼哈顿距离，rating1 和 rating2均为字典对"""
    distance = 0
    for key in rating1:
        if key in rating2:
            distance = distance + abs(rating1[key] - rating2[key])
    return distance

欧几里德距离

欧几里德

def euclid(rating1, rating2):
    """计算欧几里德距离"""
    distance = 0
    for key in rating1:
        if key in rating2:
            distance += pow(rating1[key] - rating2[key], 2)
    return sqrt(distance)

闵可夫斯基距离

minkowski

def minkowski(rating1, rating2, r):
    distance = 0
    for key in rating1:
        if key in rating2:
            distance += pow(abs(rating1[key] - rating2[key]), r)
    return pow(distance, 1.0 / r)

皮尔森相关系数

Pearson

def pearson(rating1, rating2):
    sum_x = 0
    sum_y = 0
    sum_xy = 0
    sum_x2 = 0
    sum_y2 = 0
    n = 0
    for key in rating1:
        if key in rating2:
            n += 1
            sum_x += rating1[key]
            sum_y += rating2[key]
            sum_xy += rating1[key] * rating2[key]  #-->sum_xy += sum_x * sum_y
            sum_x2 += rating1[key] ** 2
            sum_y2 += rating2[key] ** 2

    fenmu = sqrt(sum_x2 - (sum_x ** 2) / n) * sqrt(sum_y2 - (sum_y ** 2) / n)
    if fenmu == 0:
        return 0
    else:
        return (sum_xy - (sum_x * sum_y) / n) / fenmu

余弦距离

余弦相似度

分子x，y为向量的数量积

def cosine_similarity(rating1, rating2):
    sum_xy = 0
    sum_x2 = 0
    sum_y2 = 0
    for key in rating1:
        if key in rating2:
            sum_xy += rating1[key] * rating2[key]
            sum_x2 += rating1[key] ** 2
            sum_y2 += rating2[key] ** 2
    return sum_xy / (sqrt(sum_x2) * sqrt(sum_y2))