Working with Vector Data

Vector Data

Vector data consists of arrays of numbers. Vector data can be stored in SingleStoreDB as blobs. Vector embeddings, which are vectors describing the meaning of objects, can be obtained from many sources. For example, OpenAI has APIs that will give vector embeddings for text, and facenet is an open-source software package with a pre-trained neural network that can provide embeddings for face images.

Many large language models (LLMs) are now available, and can be used to provide vector embeddings for language to help implement semantic search, chatbots, and other applications. Some of the more well-known LLMs are:

• GPT models from OpenAI

• BERT by Google

• LaMDA by Google

• PaLM by Google

• LLaMA by Meta AI

LLM technology is evolving quickly, and new sources of embeddings for language are rapidly becoming available. Moreover, it is possible to train your own models that produce embeddings for database information. Regardless of the embedding source, these embeddings can be used for vector similarity search in SingleStoreDB.

Vector embeddings can be stored as vector data in SingleStoreDB. Vector embeddings are typically high-dimensional, with anywhere from a hundred to a few thousand dimensions.

Vector Similarity Search

A similarity search is the most common vector data operation. A vector similarity search in SingleStoreDB uses SELECT…ORDER BY…LIMIT… queries that use vector similarity functions, including DOT_PRODUCT and EUCLIDEAN_DISTANCE. DOT_PRODUCT is the most commonly used similarity metric.

If the vectors are normalized to length one before saving to a database, and the query vector is also normalized to length one, then DOT_PRODUCT gives the cosine of the angle between the two vectors. DOT_PRODUCT will produce what is known as the cosine similarity metric for its two arguments. If the cosine is close to one, then the angle between the vectors is close to zero. A cosine value closer to one shows that the vectors are pointing in almost the same direction, so the objects they represent are similar.

The figure below illustrates when vectors are similar (cosine close to 1) and dissimilar (cosine close to 0):

Many vector models that produce vector embeddings will already have the vectors normalized to length one. In this case, when using DOT_PRODUCT, it is not necessary to normalized the vectors again.

Loading, Inserting, and Updating Vectors

Vector data can be added to a database as blob data containing packed arrays of numbers. For example using this table format:

CREATE TABLE comments(id INT not null PRIMARY KEY,
  comment TEXT,   
  vector blob,   
  category VARCHAR(256));

Consider the following information, where @jv is a JSON array of numbers representing the vector embedding for the phrase "The cafeteria in building 35 has a great salad bar." Fictional vectors are used here to keep the examples small enough to read easily.

SET @_id = 1;
SET @jv = '[0.2, 0.11, 0.37, 0.05]';
SET @cmt = "The cafeteria in building 35 has a great salad bar";
SET @cat = "Food"; 

This data can be inserted into the comments table with a standard INSERT, using JSON_ARRAY_PACK:

INSERT INTO comments VALUES  (@_id, @cmt, json_array_pack(@jv), @cat);

It is important to convert vectors into an internal binary vector format before inserting them into a database. In this example, the conversion is done by calling JSON_ARRAY_PACK in the INSERT statement. Storing vectors as strings and converting them to binary during query will deliver much slower performance and is not recommended.

Binary data may be inserted in hexadecimal string format and converted using UNHEX before inserting it in a table. For example, suppose that client application software produces this hex string 00000000CDCC4C3F9A99193E00000000 for the vector [0, 0.8, 0.15, 0].

UNHEX can be used to convert a string into a blob that works with DOT_PRODUCT. For example:

SET @_id = 2;
SET @hs = "00000000CDCC4C3F9A99193E00000000";
SET @cmt = "I love the taco bar in the B16 cafeteria.";
SET @cat = "Food";

Insert the values into the table.

INSERT INTO comments VALUES (@_id, @cmt, unhex(@hs), @cat);

View the contents of the comments table using this query:

SELECT id, comment, json_array_unpack(vector), category FROM comments\G

*** 1. row ***
                       id: 1
                  comment: The cafeteria in building 35 has a great salad bar
json_array_unpack(vector): [0.200000003,0.109999999,0.370000005,0.0500000007]
                 category: Food
*** 2. row ***
                       id: 2
                  comment: I love the taco bar in the B16 cafeteria.
json_array_unpack(vector): [0,0.800000012,0.150000006,0]
                 category: Food

Another way to insert binary vectors is to convert them to a packed binary format in the client application and submit them through a standard client API. Consult the corresponding API documentation for details on how to do this.

An alternate way to insert vector data is using the SingleStoreDBLoad Data with Pipelines and Load Data from a Data Source features. Vector data has to be converted into packed binary before inserting in a column in the target table. Use JSON_ARRAY_PACK, HEX, or convert the vector data to binary before inserting.

Example Search Based on Vector Similarity

To find the most similar vectors in a query vector, use an ORDER BY… LIMIT… query. ORDER BY will arrange the vectors by their similarity score produced by a vector similarity function, with the highest scores at the top. To demonstrate, another vector will be added to the comments table.

SET @_id = 3;
SET @jv = '[0.1, 0.15, 0.37, 0.05]';
SET @cmt = "The B24 restaurant salad bar is quite good.";
SET @cat = "Food";

Insert the values into the table.

INSERT INTO comments VALUES (@_id, @cmt, json_array_pack(@jv), @cat);

Suppose that the query is "restaurants with good salad," and for this query, the vector embedding API returned this vector:

SET @query_vec = json_array_pack('[0.09, 0.14, 0.5, 0.05]');

To find the top two matches for this query vector use this query:

SELECT id, comment, category, dot_product(vector, @query_vec) AS score
    FROM comments
    ORDER BY score DESC
    LIMIT 2
    \G

*** 1. row ***
      id: 1
 comment: The cafeteria in building 35 has a great salad bar
category: Food
   score: 0.22089999914169312
*** 2. row ***
      id: 3
 comment: The B24 restaurant salad bar is quite good.
category: Food
   score: 0.2175000011920929

Hybrid Filtering or Metadata Filtering

When building vector search applications, you may wish to filter on the fields of a record, with simple filters or via joins, in addition to applying vector similarity operations. Filtering on fields of a record using simple filters or joins along with applying vector similarity operations is often referred to as hybrid filtering or metadata filtering. SingleStoreDB can handle this filtering using standard SQL operations.

For example, given the comments table, you can get the top three matches for a query vector that is in the category "Food" using this SQL:

SET @query_vec = json_array_pack('[ a query vector from your application ]');

SELECT id, comment, category, dot_product(vector, @query_vec) AS score
    FROM comments
    WHERE category = "Food"
    ORDER BY score DESC
    LIMIT 3;

Any SQL feature can be used along with vector similarity calculation using DOT_PRODUCT() and EUCLIDEAN_DISTANCE(). These include filtering, ordering, grouping, aggregation, window functions, full-text search, and more.

How to Bulk Load Vectors into SingleStoreDB

Vector data can be inserted into SingleStoreDB from your application by using standard INSERT statements. For larger datasets, you can bulk load vectors and associated data with LOAD DATA or CREATE PIPELINE.

Use this format for the table:

CREATE TABLE vec_test(id INT, vec blob, shard(id));

Use a text file formatted using tabs (or some other character besides commas) between the columns. This is so the loader does not interpret the commas in the JSON array as column separators. Below is the sample data that has been cut and pasted into a text file (/tmp/vec_data.text in the examples below):

1    [0.18,0.36,0.54,0.73]
2    [0.62,0.70,0.15,0.31]

LOAD DATA infile '/tmp/vec_data.txt'
INTO TABLE vec_test
fields terminated by '\t'
(id, @vec_text)
SET vec = json_array_pack(@vec_text);

SELECT id, json_array_unpack(vec)
FROM vec_test;

+------+---------------------------------------------------+
| id   | json_array_unpack(vec)                            |
+------+---------------------------------------------------+
|    1 | [0.180000007,0.360000014,0.540000021,0.730000019] |
|    2 | [0.620000005,0.699999988,0.150000006,0.310000002] |
+------+---------------------------------------------------+

TRUNCATE TABLE vec_test;

CREATE PIPELINE vec_pipeline AS
LOAD DATA fs '/tmp/vec_data.txt'
INTO TABLE vec_test fields terminated BY '\t'
(id, @vec_text)
SET vec = json_array_pack(@vec_text);

START PIPELINE vec_pipeline;

SELECT id, json_array_unpack(vec)
FROM vec_test;

+------+---------------------------------------------------+
| id   | json_array_unpack(vec)                            |
+------+---------------------------------------------------+
|    1 | [0.180000007,0.360000014,0.540000021,0.730000019] |
|    2 | [0.620000005,0.699999988,0.150000006,0.310000002] |
+------+---------------------------------------------------+

STOP PIPELINE vec_pipeline;

DROP PIPELINE vec_pipeline;

Related Topics

• Why Your Vector Database Should Not Be a Vector Database