04 · 协同过滤：最简单的算法

小刚 ∩ 小明 = {A, B}      小刚 ∪ 小明 = {A, B, C}
sim(小刚, 小明) = 2/3 = 0.67

小刚 ∩ 小红 = {}          小刚 ∪ 小红 = {A, B, C, D}
sim(小刚, 小红) = 0/4 = 0

C 的得分 = 0.67 × 1(小明喜欢C) + 0 × 1(小红喜欢C) = 0.67
D 的得分 = 0.67 × 0(小明没看D) + 0 × 1(小红喜欢D) = 0

import numpy as np

def cosine(a, b):
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b) + 1e-8)

def jaccard(a, b):
    a, b = set(np.where(a > 0)[0]), set(np.where(b > 0)[0])
    return len(a & b) / (len(a | b) + 1e-8)

def pearson(a, b):
    mask = (a > 0) & (b > 0)          # 只在都评过分的物品上算
    if mask.sum() < 2: return 0
    return np.corrcoef(a[mask], b[mask])[0, 1]

import numpy as np
from collections import defaultdict

class ItemCF:
    def __init__(self, alpha=0.5, k=20):
        """
        alpha: 热门惩罚强度。0=不惩罚, 0.5=常用值, 1=强惩罚
        k:     每个物品只保留最相似的 k 个（截断，省内存 + 去噪）
        """
        self.alpha, self.k = alpha, k

    def fit(self, user_items):
        """user_items: {user_id: [item_id, ...]}"""
        # 1) 统计共现：多少人同时喜欢 i 和 j
        cooccur = defaultdict(lambda: defaultdict(float))
        popularity = defaultdict(int)

        for user, items in user_items.items():
            # 🔑 改进1: 活跃用户降权。一个买了1000本书的人，
            #    他的任意两本书之间的"关联"其实很弱
            weight = 1.0 / np.log1p(len(items))
            for i in items:
                popularity[i] += 1
                for j in items:
                    if i != j:
                        cooccur[i][j] += weight

        # 2) 共现 → 相似度（余弦形式 + 热门惩罚）
        self.sim = {}
        for i, related in cooccur.items():
            scores = {}
            for j, c in related.items():
                # 🔑 改进2: 除以流行度，惩罚"人人都喜欢"的热门物品
                scores[j] = c / ((popularity[i] ** self.alpha) *
                                 (popularity[j] ** (1 - self.alpha)))
            # 🔑 改进3: 只留 top-k，砍掉长尾噪声
            self.sim[i] = dict(sorted(scores.items(), key=lambda x: -x[1])[:self.k])
        return self

    def recommend(self, history, n=10):
        scores = defaultdict(float)
        seen = set(history)
        for i in history:
            for j, s in self.sim.get(i, {}).items():
                if j not in seen:
                    scores[j] += s
        return sorted(scores.items(), key=lambda x: -x[1])[:n]


# ---- 试一下 ----
data = {
    "u1": ["科幻A", "科幻B", "科幻C", "热门X"],
    "u2": ["科幻A", "科幻B", "热门X"],
    "u3": ["动画P", "动画Q", "热门X"],
    "u4": ["动画P", "动画Q", "动画R", "热门X"],
    "u5": ["科幻A", "科幻C", "热门X"],
}
model = ItemCF(alpha=0.5, k=10).fit(data)
print("看过 科幻A 的人，接下来推：")
for item, score in model.recommend(["科幻A"], n=3):
    print(f"  {item}: {score:.3f}")