曼哈頓距離

manhattan

def manhattan(rating1, rating2):
    """計(jì)算曼哈頓距離，rating1 和 rating2均為字典對(duì)"""
    distance = 0
    for key in rating1:
        if key in rating2:
            distance = distance + abs(rating1[key] - rating2[key])
    return distance

歐幾里德距離

歐幾里德

def euclid(rating1, rating2):
    """計(jì)算歐幾里德距離"""
    distance = 0
    for key in rating1:
        if key in rating2:
            distance += pow(rating1[key] - rating2[key], 2)
    return sqrt(distance)

閔可夫斯基距離

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)

皮爾森相關(guān)系數(shù)

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

余弦距離

余弦相似度

分子x，y為向量的數(shù)量積

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))