🧬 第11课：知识图谱推荐

🎯 学习目标

🗂️ 课程定位

📖 核心理论

知识图谱（Knowledge Graph, KG）推荐利用结构化的外部知识（物品属性、实体关系）增强推荐效果。知识图谱可以提供物品间的语义关联、可解释的推理路径，以及缓解冷启动问题。

知识图谱的核心价值：语义增强（提供物品间关联）、可解释性（推理路径）、冷启动（新物品有属性信息）。

📐 数学公式

💻 代码实现

import numpy as np
np.random.seed(42)
print("="*60+"\n知识图谱推荐系统\n"+"="*60)
# 构建简单知识图谱
entities=[];relations=[];triples=[]
# 用户实体
for i in range(15):entities.append(f"User_{i}")
# 物品实体
for i in range(12):entities.append(f"Item_{i}")
# 属性实体
attrs=["Action","Comedy","Drama","SciFi","Romance","Thriller",
       "Director_A","Director_B","Director_C","Actor_X","Actor_Y","Actor_Z"]
entities.extend(attrs)
print(f"实体数:{len(entities)}")
# 知识图谱三元组
triples=[
    ("Item_0","genre","Action"),("Item_0","director","Director_A"),
    ("Item_1","genre","Comedy"),("Item_1","actor","Actor_X"),
    ("Item_2","genre","Drama"),("Item_2","director","Director_B"),
    ("Item_3","genre","SciFi"),("Item_3","actor","Actor_Y"),
    ("Item_4","genre","Action"),("Item_4","actor","Actor_Z"),
    ("Item_5","genre","Romance"),("Item_5","director","Director_C"),
    ("Item_6","genre","Comedy"),("Item_6","director","Director_A"),
    ("Item_7","genre","Thriller"),("Item_7","actor","Actor_X"),
    ("Item_8","genre","Action"),("Item_8","actor","Actor_Y"),
    ("Item_9","genre","Drama"),("Item_9","director","Director_B"),
    ("Item_10","genre","SciFi"),("Item_10","actor","Actor_Z"),
    ("Item_11","genre","Romance"),("Item_11","director","Director_C"),
]
# 用户-物品交互
interactions=[]
for u in range(15):
    n=np.random.randint(2,5)
    for i in np.random.choice(12,size=min(n,12),replace=False):
        interactions.append((f"User_{u}",f"Item_{i}"))
        triples.append((f"User_{u}","interact",f"Item_{i}"))
print(f"交互数:{len(interactions)} 三元组数:{len(triples)}")
# TransE知识图谱嵌入
n_ent=len(entities);n_rel=20;emb_size=16
ent2idx={e:i for i,e in enumerate(entities)}
rel2idx={"genre":0,"director":1,"actor":2,"interact":3}
ent_emb=np.random.randn(n_ent,emb_size)*0.1
rel_emb=np.random.randn(n_rel,emb_size)*0.1
print("\n--- TransE训练 ---")
lr_te=0.01;margin=1.0
for ep in range(50):
    total_loss=0
    for h,r,t in triples:
        h_idx=ent2idx[h];t_idx=ent2idx[t];r_idx=rel2idx.get(r,4)
        # 负采样
        t_neg=ent2idx[np.random.choice(entities)]
        while t_neg==t_idx:t_neg=ent2idx[np.random.choice(entities)]
        pos_score=np.linalg.norm(ent_emb[h_idx]+rel_emb[r_idx]-ent_emb[t_idx])
        neg_score=np.linalg.norm(ent_emb[h_idx]+rel_emb[r_idx]-ent_emb[t_neg])
        loss=max(0,margin+pos_score-neg_score)
        total_loss+=loss
        if loss>0:
            grad_h=2*(ent_emb[h_idx]+rel_emb[r_idx]-ent_emb[t_idx])-2*(ent_emb[h_idx]+rel_emb[r_idx]-ent_emb[t_neg])
            ent_emb[h_idx]-=lr_te*grad_h
            rel_emb[r_idx]-=lr_te*grad_h
            ent_emb[t_idx]+=lr_te*2*(ent_emb[h_idx]+rel_emb[r_idx]-ent_emb[t_idx])
    if(ep+1)%10==0:print(f"  Epoch{ep+1}:Loss={total_loss:.4f}")
# KG增强推荐
print("\n--- KG增强推荐 ---")
# 用户画像(基于交互物品的属性)
user_profiles={}
for u in range(15):
    profile=np.zeros(emb_size)
    count=0
    for uu,item in interactions:
        if uu==f"User_{u}":
            profile+=ent_emb[ent2idx[item]]
            count+=1
    if count>0:user_profiles[u]=profile/count
    else:user_profiles[u]=np.random.randn(emb_size)*0.01
# 推荐得分(用户画像 vs 物品embedding + 知识增强)
for u in range(5):
    scores={}
    for i in range(12):
        item_emb=ent_emb[ent2idx[f"Item_{i}"]]
        # 基础得分
        base_score=np.dot(user_profiles[u],item_emb)
        # 知识增强：考虑物品的属性关联
        kg_bonus=0
        for h,r,t in triples:
            if h==f"Item_{i}" and r in ["genre","director","actor"]:
                t_idx=ent2idx[t]
                kg_bonus+=0.1*np.dot(user_profiles[u],ent_emb[t_idx])
        scores[i]=base_score+kg_bonus
    top3=sorted(scores.items(),key=lambda x:-x[1])[:3]
    print(f"  User_{u}推荐:{[(f'Item_{i}',f'{s:.3f}')for i,s in top3]}")
# 知识推理路径
print("\n知识推理路径示例:")
for item in ["Item_0","Item_1"]:
    paths=[]
    for h,r,t in triples:
        if h==item:paths.append(f"{h}--[{r}]-->{t}")
    print(f"  {item}的知识路径: {paths}")

🔴 运行结果

✅ 验证通过

🔍 代码解读

💡 关键洞察

📝 本章小结

🧪 练习

📚 延伸阅读

💼 面试考点

🏭 工业案例