向量嵌入(Embedding)完全指南：从原理到实践【2026】

from gensim.models import Word2Vec

sentences = [
    ["机器", "学习", "是", "人工智能", "的", "分支"],
    ["深度", "学习", "是", "机器", "学习", "的", "子集"],
    ["神经网络", "是", "深度", "学习", "的", "基础"]
]

model = Word2Vec(sentences, vector_size=100, window=5, min_count=1)

similar_words = model.wv.most_similar("学习", topn=3)
print(similar_words)

word_vector = model.wv["机器"]
print(f"向量维度: {len(word_vector)}")

import numpy as np

def sentence_embedding_average(sentence, word2vec_model):
    words = sentence.split()
    vectors = [word2vec_model.wv[w] for w in words if w in word2vec_model.wv]
    if vectors:
        return np.mean(vectors, axis=0)
    return np.zeros(word2vec_model.vector_size)

from openai import OpenAI

client = OpenAI()

def get_embedding(text, model="text-embedding-3-small", dimensions=None):
    params = {"input": text, "model": model}
    if dimensions:
        params["dimensions"] = dimensions
    
    response = client.embeddings.create(**params)
    return response.data[0].embedding

text = "向量嵌入是AI应用的核心技术"
embedding = get_embedding(text, dimensions=256)
print(f"嵌入维度: {len(embedding)}")

from sentence_transformers import SentenceTransformer

model = SentenceTransformer('all-MiniLM-L6-v2')

sentences = [
    "向量嵌入技术非常重要",
    "Embedding是AI的基础",
    "今天的天气真不错"
]

embeddings = model.encode(sentences)
print(f"嵌入形状: {embeddings.shape}")

from sentence_transformers import SentenceTransformer

model = SentenceTransformer('BAAI/bge-base-zh-v1.5')

texts = ["什么是向量嵌入？", "Embedding技术详解"]
embeddings = model.encode(texts, normalize_embeddings=True)

import numpy as np
from numpy.linalg import norm

def cosine_similarity(vec1, vec2):
    return np.dot(vec1, vec2) / (norm(vec1) * norm(vec2))

vec_a = np.array([0.1, 0.2, 0.3, 0.4])
vec_b = np.array([0.15, 0.25, 0.28, 0.38])
vec_c = np.array([0.9, 0.1, 0.05, 0.02])

print(f"A与B的相似度: {cosine_similarity(vec_a, vec_b):.4f}")
print(f"A与C的相似度: {cosine_similarity(vec_a, vec_c):.4f}")

def euclidean_distance(vec1, vec2):
    return np.sqrt(np.sum((vec1 - vec2) ** 2))

distance_ab = euclidean_distance(vec_a, vec_b)
distance_ac = euclidean_distance(vec_a, vec_c)

print(f"A与B的距离: {distance_ab:.4f}")
print(f"A与C的距离: {distance_ac:.4f}")

from sentence_transformers import SentenceTransformer, util

model = SentenceTransformer('all-MiniLM-L6-v2')

documents = [
    "Python是一种流行的编程语言",
    "机器学习需要大量数据",
    "深度学习使用神经网络",
    "自然语言处理分析文本",
    "向量数据库存储嵌入向量"
]

doc_embeddings = model.encode(documents, convert_to_tensor=True)

def semantic_search(query, top_k=3):
    query_embedding = model.encode(query, convert_to_tensor=True)
    scores = util.cos_sim(query_embedding, doc_embeddings)[0]
    top_results = scores.argsort(descending=True)[:top_k]
    
    results = []
    for idx in top_results:
        results.append({
            "document": documents[idx],
            "score": scores[idx].item()
        })
    return results

query = "如何处理文本数据"
results = semantic_search(query)
for r in results:
    print(f"相似度: {r['score']:.4f} - {r['document']}")

class EmbeddingRecommender:
    def __init__(self, model_name='all-MiniLM-L6-v2'):
        self.model = SentenceTransformer(model_name)
        self.items = []
        self.embeddings = None
    
    def add_items(self, items):
        self.items = items
        self.embeddings = self.model.encode(items, convert_to_tensor=True)
    
    def recommend(self, user_history, top_k=5):
        history_embedding = self.model.encode(
            user_history, 
            convert_to_tensor=True
        ).mean(dim=0)
        
        scores = util.cos_sim(history_embedding, self.embeddings)[0]
        top_indices = scores.argsort(descending=True)[:top_k]
        
        return [self.items[i] for i in top_indices]

recommender = EmbeddingRecommender()
recommender.add_items([
    "Python机器学习实战",
    "深度学习入门指南",
    "Web开发最佳实践",
    "数据科学手册",
    "算法与数据结构"
])

user_history = ["Python编程基础", "数据分析入门"]
recommendations = recommender.recommend(user_history, top_k=3)
print("推荐内容:", recommendations)

from sklearn.cluster import KMeans
import numpy as np

texts = [
    "Python是最流行的编程语言",
    "JavaScript用于Web开发",
    "机器学习改变了AI领域",
    "深度学习需要GPU加速",
    "React是前端框架",
    "神经网络模拟大脑"
]

model = SentenceTransformer('all-MiniLM-L6-v2')
embeddings = model.encode(texts)

kmeans = KMeans(n_clusters=2, random_state=42)
clusters = kmeans.fit_predict(embeddings)

for i, (text, cluster) in enumerate(zip(texts, clusters)):
    print(f"聚类 {cluster}: {text}")

from sklearn.decomposition import PCA

original_dim = 768
target_dim = 256

embeddings_768 = model.encode(texts)

pca = PCA(n_components=target_dim)
embeddings_256 = pca.fit_transform(embeddings_768)

print(f"原始维度: {embeddings_768.shape}")
print(f"降维后: {embeddings_256.shape}")
print(f"保留方差比例: {sum(pca.explained_variance_ratio_):.4f}")

import chromadb
from chromadb.utils import embedding_functions

client = chromadb.Client()

ef = embedding_functions.SentenceTransformerEmbeddingFunction(
    model_name="all-MiniLM-L6-v2"
)

collection = client.create_collection(
    name="documents",
    embedding_function=ef
)

collection.add(
    documents=[
        "向量嵌入是AI的基础技术",
        "语义搜索理解查询意图",
        "推荐系统提供个性化内容"
    ],
    ids=["doc1", "doc2", "doc3"]
)

results = collection.query(
    query_texts=["如何实现智能搜索"],
    n_results=2
)
print(results)