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vectorsearch's Introduction

VectorSearch

DataSet

Data Source

Hugging Face C4

images/00_01_DataSet_C4.png

images/00_02_DataSet_C4_Embedded.png

Qurey Sample

Query1 : "Bridge Over Trouble Water"
Query2 : "When a man loves a woman"
Query3 : "November Rain"

Azure PostgreSQL Flexible Server

Reference Doc:
How to enable and use pgvector on Azure Database for PostgreSQL - Flexible Server
https://github.com/pgvector/pgvector

Create Table

CREATE TABLE IF NOT EXISTS public.T_IVF_COS
(
    id bigint,
    text_v vector(1536)
)
TABLESPACE pg_default;

Create Indexes

CREATE INDEX IVF_COS_IDX ON T_IVF_COS USING ivfflat (text_v vector_cosine_ops) WITH (lists = 365);
CREATE INDEX IVF_IP_IDX ON T_IVF_IP USING ivfflat (text_v vector_ip_ops) WITH (lists = 365);
CREATE INDEX IVF_L2_IDX ON T_IVF_L2 USING ivfflat (text_v vector_l2_ops) WITH (lists = 365);

SELECT phase, round(100.0 * tuples_done / nullif(tuples_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;
CREATE INDEX HNSW_COS_IDX ON T_HNSW_COS USING hnsw (text_v vector_cosine_ops);
CREATE INDEX HNSW_IP_IDX ON T_HNSW_IP USING hnsw (text_v vector_ip_ops);
CREATE INDEX HNSW_L2_IDX ON T_HNSW_L2 USING hnsw (text_v vector_l2_ops);

SELECT phase, round(100.0 * blocks_done / nullif(blocks_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;

Query Vector

SELECT ID, 1 - (text_v <=> '[Embedding]') AS cosine_similarity 
FROM T_IVF_COS
ORDER BY cosine_similarity DESC
LIMIT 5;

SELECT ID, (text_v <#> '[Embedding]') * -1 AS inner_product 
FROM T_IVF_IP
ORDER BY inner_product DESC
LIMIT 5;

SELECT ID, text_v <-> '[Embedding]' AS distance 
FROM T_IVF_L2
ORDER BY distance
LIMIT 5;
SELECT ID, 1 - (text_v <=> '[Embedding]') AS cosine_similarity 
FROM T_HNSW_COS
ORDER BY cosine_similarity DESC
LIMIT 5;

SELECT ID, (text_v <#> '[Embedding]') * -1 AS inner_product 
FROM T_HNSW_IP
ORDER BY inner_product DESC
LIMIT 5;

SELECT ID, text_v <-> '[Embedding]' AS distance 
FROM T_HNSW_L2
ORDER BY distance
LIMIT 5;

Results

images/01_01_PostgreSQL_Results.png

Azure SQL Database

Reference Doc:
Vector Similarity Search with Azure SQL database and OpenAI
SQL SERVER VECTOR SEARCH
azure-sql-db-openai

Create Table with Column Store Index

images/02_01_SQLDB_01.png

CREATE TABLE [dbo].[dfv_sum](
	[id] [bigint] NULL,
	[pos] [int] NOT NULL,
	[col] [float] NULL
) ON [PRIMARY]
GO

CREATE CLUSTERED COLUMNSTORE INDEX [CCIDX] ON [dbo].[dfv_sum] ORDER ([id])WITH (DROP_EXISTING = OFF, COMPRESSION_DELAY = 0) ON [PRIMARY]
GO

Query Embedding

declare @inputText nvarchar(max) = 'Bridge Over Trouble Water';
declare @retval int, @response nvarchar(max);
declare @payload nvarchar(max) = json_object('input': @inputText);
exec @retval = sp_invoke_external_rest_endpoint
    @url = 'Deployment URL',
    @method = 'POST',
    @headers = '{"api-key":"Your API Key"}',
    @payload = @payload,
    @response = @response output;

select 
    cast([key] as int) as [vector_value_id],
    cast([value] as float) as [vector_value]
into    
    #QRY1
from 
    openjson(@response, '$.result.data[0].embedding');

Calculate Cosine Similarity

SELECT 
    SUM(a.col * b.vector_value) / (  
        SQRT(SUM(a.col * a.col)) * SQRT(SUM(b.vector_value * b.vector_value))   
    ) AS cosine_similarity
FROM
    dbo.dfv_sum a, #QRY1 b
WHERE
	a.id = 1;

Query Cosine Similarity

select top (50)
    v2.id, 
    sum(v1.[vector_value] * v2.col) / 
        (
            sqrt(sum(v1.[vector_value] * v1.[vector_value])) 
            * 
            sqrt(sum(v2.col * v2.col))
        ) as cosine_similarity
from 
    #QRY1 v1
inner join 
    dbo.dfv_sum v2 on v1.vector_value_id = v2.pos
group by
    v2.id
order by
    cosine_similarity desc;

Results

images/02_02_SQLDB_Results.png

Azure Cosmos MongoDB vCore

Reference Doc: Use vector search on embeddings in Azure Cosmos DB for MongoDB vCore

Vector Indexes

db.runCommand({
  "createIndexes": "C4_IVF_COS",
  "indexes": [
    {
      "name": "IVF_COS_IDX",
      "key": {
        "text_v": "cosmosSearch"
      },
      "cosmosSearchOptions": {
        "kind": "vector-ivf",
        "numLists": 365,
        "similarity": "COS",
        "dimensions": 1536
      }
    }
  ]
});

images/03_01_Cosmos_IVF.png

db.runCommand({ 
    "createIndexes": "C4_HNSW_COS",
    "indexes": [
        {
            "name": "HNSW_COS_IDX",
            "key": {
                "text_v": "cosmosSearch"
            },
            "cosmosSearchOptions": { 
                "kind": "vector-hnsw", 
                "m": 16, 
                "efConstruction": 64, 
                "similarity": "COS", 
                "dimensions": 1536 
            } 
        } 
    ] 
});

images/03_02_Cosmos_HNSW.png

Vector Query

const queryVector1 = 
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Query1 : "Bridge Over Trouble Water"
Query2 : "When a man loves a woman"
Query3 : "November Rain"

db.C4_IVF_COS.aggregate([
  {
    $search: {
      "cosmosSearch": {
        "vector": queryVector3,
        "path": "text_v",
		    "nProbes":100,
        "k": 5
      },
    "returnStoredSource": true }},
  {
    "$project": { "similarityScore": {
           "$meta": "searchScore" },
            "document" : "$$ROOT.id"
        }
  }
]);

images/03_03_Cosmos_Search_IVF.png

db.C4_HNSW_COS.aggregate([
  {
    $search: {
      "cosmosSearch": {
        "vector": queryVector3,
        "path": "text_v",
        "k": 5,
		"efSearch": 64
      },
    "returnStoredSource": true }},
  {
    "$project": { "similarityScore": {
           "$meta": "searchScore" },
            "document" : "$$ROOT.id"
        }
  }
]);

images/03_04_Cosmos_Search_HNSW.png

Results

1st Try

HNSW Index Created with following parameters:
m: 64
efConstruction: 256
images/03_05_Cosmos_Result_1st.png

2nd Try

HNSW Index Created with following parameters:
M: 16
efConstruction: 64

Put the following parameters in the search query for IVFFLAT:
nProbes:100
images/03_06_Cosmos_Result_2nd.png


Azure AI Search

Reference Doc:
Vectors in Azure AI Search
Create a vector store
Create a vector query in Azure AI Search
azure-search-vector-samples

Index and Vector Profile

images/04_01_AISearch_Indexes.png
images/04_02_AISearch_Fields.png
images/04_03_AISearch_Vector_Profile.png

Query Vector

{
    "count": true,
    "select": "id, text",
    "vectorQueries": [
        {
            "kind": "vector",
            "vector": 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            "exhaustive": true,
            "fields": "text_v",
            "k": 5
        }
    ]
}

Results

images/04_04_AISearch_Results.png


Summary

What are your options when choosing a vector search in Azure?

A vector database is a type of database that stores and retrieves data in the form of vectors, which are arrays of numbers that represent features or attributes of objects. Vector databases are often used for applications that require fast and accurate similarity search, such as image retrieval, natural language processing, recommendation systems, and machine learning. In Azure, there are several options for choosing a vector database, depending on your needs and preferences. Some of the most common options are:

Traditional Relational Database

  • Azure Database for PostgreSQL: This is a fully managed relational database service that offers high availability, security, and scalability. You can use Azure Database for PostgreSQL to store and query vector data using PostgreSQL extensions such as pgvector, which enables vector indexing and similarity search using various distance metrics.
  • Azure SQL Database: This is a fully managed relational database service that offers high performance, security, and scalability. You can use Azure SQL Database to store and query vector data using features such as columnstore index, which enables columnar storage and compression for large vector data.

Distributed Relational Database

  • Azure Cosmos DB for PostgreSQL: This is a fully managed and scalable service that provides compatibility with the PostgreSQL wire protocol and supports JSON and geospatial data types. You can use Azure Cosmos DB for PostgreSQL to store and query vector data using PostgreSQL extensions such as pgvector, which enables vector indexing and similarity search using various distance metrics.

NoSQL Database

  • Azure Cosmos DB for MongoDB (vCore): This is another fully managed and scalable service that provides compatibility with the MongoDB wire protocol and supports BSON and geospatial data types. You can use Azure Cosmos DB for MongoDB to store and query vector data using MongoDB features such as vector field, which allows you to perform text search and cosine similarity on vector data.

Search Engine

  • Azure AI Search (formally Azure Cognitive Search): This is a cloud-based search service that allows you to easily add sophisticated search capabilities to your applications. You can use Azure AI Search to store and query vector data using features such as semantic search, which leverages natural language processing and deep learning to perform semantic similarity and ranking on vector

Vector Search Algorithm, Indexing and Similarity/Distance Calculation

images/05_01_Algorithm_Index.png

  • Azure Database for PostgreSQL & Azure Cosmos DB for PostgreSQL
    By default, pgvector performs exact nearest neighbor search, which provides perfect recall. You can query or add indexes with different distance functions you want to use.

    • IVFFLAT (Approximate Nearest Neighbor) and HNSW (Hierarchical Navigable Small Worlds)
    • L2 Distance, Inner Product and Cosine Distance are available with index.
  • Azure SQL Database
    SQL Database doesn't have vector data type. However, you can pivot vector array into clustered columnstore indexed table. images/02_01_SQLDB_01.png
    Cosign Similarity calculation is available with query.
    images/05_02_Summary_SQL_Query.png

  • Azure Cosmos DB for MongoDB (vCore)

    • IVFFLAT and HNSW (Preview)
    • L2 Distance, Inner Product and Cosine Distance are available with index.
    • HNSW is in preview and value m and efConstruction is adjustable. (need a guide for m and efConstruction)
    • nProbe is set to 1 by default. in future release, automatic nProbe will be available.
    • Index must create first with empty collection before large data loading.
  • Azure AI Search

    • HNSW and Exhaustive KNN (K-Nearest Neighbors)
    • L2 Distance, Inner Product and Cosine Distance are available.

Overall Results

images/05_03_Overall_Results.png

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