衡量嵌入相似度
了解支持向量搜索的距离与相似度指标，并学习如何选择合适的指标。
衡量嵌入相似度 是 CoddyKit 上的免费 LangChain / RAG / Vector DBs 课时。 这是第 4 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 LangChain / RAG / Vector DBs 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 LangChain / RAG / Vector DBs 课程共包含 4 节课。
本课时的部分内容尚未翻译，以英文显示。
From Vectors to Meaning
An embedding maps text to a list of numbers in high-dimensional space. Texts with similar meaning land close together. To rank results we need a way to measure that closeness.
Cosine Similarity
Cosine similarity measures the angle between two vectors, ignoring their length. It ranges from -1 (opposite) to 1 (identical direction).
import numpy as np
def cosine(a, b):
a, b = np.array(a), np.array(b)
return a.dot(b) / (np.linalg.norm(a) * np.linalg.norm(b))
print(cosine([1, 0], [1, 1])) # ~0.707Euclidean Distance
Euclidean (L2) distance is the straight-line distance between two points. Smaller means more similar. Unlike cosine, it is sensitive to magnitude.
import numpy as np
def l2(a, b):
return np.linalg.norm(np.array(a) - np.array(b))
print(l2([0, 0], [3, 4])) # 5.0Dot Product
The dot product multiplies matching dimensions and sums them. For normalized vectors it equals cosine similarity, which is why many stores normalize first.
import numpy as np
def dot(a, b):
return float(np.array(a).dot(np.array(b)))
print(dot([1, 2, 3], [4, 5, 6])) # 32.0Normalization
Dividing a vector by its length gives a unit vector. After normalization, dot product and cosine similarity become equivalent, simplifying the math.
import numpy as np
def normalize(v):
v = np.array(v, dtype=float)
return v / np.linalg.norm(v)
print(normalize([3, 4])) # [0.6 0.8]Choosing a Metric
Most modern text embedding models are trained for cosine similarity. Use cosine unless your provider documentation recommends otherwise.
- Cosine: direction matters, length ignored
- L2: absolute position matters
- Dot: cosine on normalized data
Similarity vs. Distance
Beware the inversion: higher cosine = more similar, but higher L2 = less similar. Vector stores expose this difference, sometimes returning a score you must interpret.
Why High Dimensions Help
Embeddings often have hundreds or thousands of dimensions. More dimensions give the model room to separate subtle differences in meaning, at the cost of more storage and compute.
Setting Metric in a Store
When creating a collection you declare the metric. Many libraries default to cosine.
import chromadb
client = chromadb.Client()
col = client.create_collection(
name="docs",
metadata={"hnsw:space": "cosine"}
)Ranking Search Results
Search computes the chosen metric between the query embedding and every stored vector, then returns the top-k closest. The metric directly shapes which documents win.
query_vec = embed("refund policy")
scored = [(cosine(query_vec, d.vec), d) for d in docs]
scored.sort(reverse=True)
top3 = scored[:3]Pitfall: Mixing Models
Vectors from different embedding models live in different spaces and are not comparable. Always embed your query with the same model you used to index the documents.
Quick Check
Test your grasp of similarity metrics.
Recap
You explored how similarity is measured:
- Cosine compares direction (most common for text)
- Euclidean compares position
- Dot product equals cosine on normalized vectors
- Always query and index with the same model
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常见问题解答
「衡量嵌入相似度」课时是免费的吗？
是的 — 「衡量嵌入相似度」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 LangChain / RAG / Vector DBs 课程的其余内容，请升级到 CoddyKit PRO。 LangChain / RAG / Vector DBs 课程共包含 4 节课。
「衡量嵌入相似度」这节课中我会学到什么？
了解支持向量搜索的距离与相似度指标，并学习如何选择合适的指标。 你通过在浏览器中直接运行的动手代码来练习 LangChain / RAG / Vector DBs，全天候 AI 导师会在你学习这节课的过程中回答你的问题。
学习 LangChain / RAG / Vector DBs 需要有经验吗？
无需任何先前经验。CoddyKit 上的 LangChain / RAG / Vector DBs 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 4 节课，共 4 节。
「衡量嵌入相似度」课时需要多长时间？
大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。
我能在这节 LangChain / RAG / Vector DBs 课中编写并运行代码吗？
能。每节 LangChain / RAG / Vector DBs 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。