为何使用曼哈顿距离与余弦距离返回相同文本块但得分不同？

问题背景 #

我正在构建RAG的PoC，使用Qdrant数据库及客户端进行文档嵌入。发现用曼哈顿距离构建向量集合时，查询得分高于余弦距离，但返回的文本块完全相同，对此原因存在疑问。

查询与响应示例 #

用户查询 #

What is DoS?

余弦距离响应 #

response: [
ScoredPoint(id=0, 
version=10, 
score=0.17464592, 
payload={
'chunk': "It also includes overhead bytes for operations, 
administration, and maintenance (OAM) purposes.\nOptical Network Unit 
(ONU)\nONU is a device used in Passive Optical Networks (PONs). It converts 
optical signals transmitted via fiber optic cables into electrical signals that 
can be used by end-user devices, such as computers and telephones. The ONU is 
located at the end user's premises and serves as the interface between the optical 
network and the user's local network."
}, 
vector=None, shard_key=None)
]

曼哈顿距离响应 #

response: [
ScoredPoint(id=0, 
version=10, 
score=103.86209, 
payload={
'chunk': "It also includes overhead bytes for operations, administration, 
and maintenance (OAM) purposes.\nOptical Network Unit 
(ONU)\nONU is a device used in Passive Optical Networks (PONs). It converts 
optical signals transmitted via fiber optic cables into electrical signals that 
can be used by end-user devices, such as computers and telephones. The ONU is 
located at the end user's premises and serves as the interface between the optical 
network and the user's local network."
}, 
vector=None, shard_key=None)
]

原因解析 #

1. 唯一匹配结果限制
   你的向量集合中仅存在这一个与查询向量最接近的文档块（id=0），无论采用哪种距离算法，它都是当前数据集中的最优匹配项，因此返回结果必然一致。另外注意：查询是关于DoS的问题，但返回的是ONU相关内容，说明集合中根本没有DoS相关文档，只能返回现有数据里最接近的条目。

2. 两种距离的得分体系差异

• 余弦距离：Qdrant中采用1 - 余弦相似度作为得分，范围通常在[0,2]之间，得分越低代表相似度越高。这里的0.1746说明该文档块与查询的相似度很高。
• 曼哈顿距离（L1距离）：得分是向量各维度差值的绝对值之和，没有固定范围，数值取决于向量维度和取值规模，得分越高代表向量差异越大。这里的103.86是该距离的直接计算值，反映的是向量间的绝对差异程度。

两者得分的含义完全不同，不能直接通过数值大小判断匹配度高低，需结合各自的规则解读。

内容的提问来源于stack exchange，提问作者raikumardipak