在文本使用三维向量的相似度时，对三种相似度的对比。 当前基于已经搭建好的Elasticsearch、Kibana。 

1、创建索引库

PUT my-index-000002
{"mappings": {"properties": {"my_dense_vector": {"type": "dense_vector","dims": 3},"status" : {"type" : "keyword"}}}
}

创建成功：

{"acknowledged": true,"shards_acknowledged": true,"index": "my-index-000002"
}

2、放入数据

PUT my-index-000002/_doc/1
{"my_dense_vector": [1, 0,0],"status" : "published"
}

PUT my-index-000002/_doc/2
{"my_dense_vector": [0,1,0],"status" : "published"
}

PUT my-index-000002/_doc/3
{"my_dense_vector": [0,0,1],"status" : "published"
}

返回结果类似如下

{"_index": "my-index-000002","_id": "3","_version": 1,"result": "created","_shards": {"total": 2,"successful": 1,"failed": 0},"_seq_no": 2,"_primary_term": 1
}

3、查看所有数据

GET my-index-000002/_search

结果如下： 

{"took": 2,"timed_out": false,"_shards": {"total": 1,"successful": 1,"skipped": 0,"failed": 0},"hits": {"total": {"value": 3,"relation": "eq"},"max_score": 1,"hits": [{"_index": "my-index-000002","_id": "1","_score": 1,"_source": {"my_dense_vector": [1,0,0],"status": "published"}},{"_index": "my-index-000002","_id": "2","_score": 1,"_source": {"my_dense_vector": [0,1,0],"status": "published"}},{"_index": "my-index-000002","_id": "3","_score": 1,"_source": {"my_dense_vector": [0,0,1],"status": "published"}}]}
}

4、L1方法查询数据

GET my-index-000002/_search
{"query": {"script_score": {"query" : {"bool" : {"filter" : {"term" : {"status" : "published"}}}},"script": {"source": "1 / (1 + l1norm(params.queryVector, 'my_dense_vector'))","params": {"queryVector": [0, 0, 1]}}}}
}

{"took": 2,"timed_out": false,"_shards": {"total": 1,"successful": 1,"skipped": 0,"failed": 0},"hits": {"total": {"value": 3,"relation": "eq"},"max_score": 1,"hits": [{"_index": "my-index-000002","_id": "3","_score": 1,"_source": {"my_dense_vector": [0,0,1],"status": "published"}},{"_index": "my-index-000002","_id": "1","_score": 0.33333334,"_source": {"my_dense_vector": [1,0,0],"status": "published"}},{"_index": "my-index-000002","_id": "2","_score": 0.33333334,"_source": {"my_dense_vector": [0,1,0],"status": "published"}}]}
}

结果中，id1和id2得分相同，但在文本向量空间中他们不同。

5、使用l2查询

GET my-index-000002/_search
{"query": {"script_score": {"query" : {"bool" : {"filter" : {"term" : {"status" : "published"}}}},"script": {"source": "1 / (1 + l2norm(params.queryVector, 'my_dense_vector'))","params": {"queryVector": [0, 0, 1]}}}}
}

{"took": 2,"timed_out": false,"_shards": {"total": 1,"successful": 1,"skipped": 0,"failed": 0},"hits": {"total": {"value": 3,"relation": "eq"},"max_score": 1,"hits": [{"_index": "my-index-000002","_id": "3","_score": 1,"_source": {"my_dense_vector": [0,0,1],"status": "published"}},{"_index": "my-index-000002","_id": "1","_score": 0.41421357,"_source": {"my_dense_vector": [1,0,0],"status": "published"}},{"_index": "my-index-000002","_id": "2","_score": 0.41421357,"_source": {"my_dense_vector": [0,1,0],"status": "published"}}]}
}

同样出现相同情况，l1和l2计算文本的距离有相同得分

6、cos 查询

GET my-index-000002/_search
{"query": {"script_score": {"query" : {"bool" : {"filter" : {"term" : {"status" : "published"       }}}},"script": {"source": "cosineSimilarity(params.query_vector, 'my_dense_vector') + 1.0",    "params": {"query_vector": [0, 0, 1]      }}}}
}

结果

{"took": 1,"timed_out": false,"_shards": {"total": 1,"successful": 1,"skipped": 0,"failed": 0},"hits": {"total": {"value": 3,"relation": "eq"},"max_score": 2,"hits": [{"_index": "my-index-000002","_id": "3","_score": 2,"_source": {"my_dense_vector": [0,0,1],"status": "published"}},{"_index": "my-index-000002","_id": "1","_score": 1,"_source": {"my_dense_vector": [1,0,0],"status": "published"}},{"_index": "my-index-000002","_id": "2","_score": 1,"_source": {"my_dense_vector": [0,1,0],"status": "published"}}]}
}

三种方法都会产生 不同向量的相同分数情况

GET my-index-000002/_search
{"query": {"script_score": {"query" : {"bool" : {"filter" : {"term" : {"status" : "published"       }}}},"script": {"source": "cosineSimilarity(params.query_vector, 'my_dense_vector') + 1.0",    "params": {"query_vector": [0, 0, 100]      }}}}
}

结果：

{"took": 2,"timed_out": false,"_shards": {"total": 1,"successful": 1,"skipped": 0,"failed": 0},"hits": {"total": {"value": 3,"relation": "eq"},"max_score": 2,"hits": [{"_index": "my-index-000002","_id": "3","_score": 2,"_source": {"my_dense_vector": [0,0,1],"status": "published"}},{"_index": "my-index-000002","_id": "1","_score": 1,"_source": {"my_dense_vector": [1,0,0],"status": "published"}},{"_index": "my-index-000002","_id": "2","_score": 1,"_source": {"my_dense_vector": [0,1,0],"status": "published"}}]}
}

三种方法都会存在 不同空间位置，得到向量距离可能相同的情况