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Introduction to HNSW Index on Azure Cosmos DB for PostgreSQL

When it comes to performing efficient and accurate vector similarity search, the HNSW (Hierarchical Navigable Small World) index is a popular choice. This indexing algorithm is widely used for its high performance and ability to handle large-scale datasets. In this article, we will explore the implementation of the HNSW index with Azure Cosmos DB for PostgreSQL.

What is the HNSW index?

The HNSW index is a data structure used for approximate nearest neighbor search. It is based on a multi-layered graph structure, where each node represents a datapoint and edges connect nodes to their neighboring datapoints. The index is built in a way that preserves the locality of datapoints, allowing for faster and more efficient similarity search operations.

Why is it popular for vector similarity search?

The HNSW index has gained popularity among researchers and developers due to its ability to handle high-dimensional data and provide fast search results. It is particularly effective in scenarios where the dimensionality of the data is high, such as image and text similarity search. Additionally, the HNSW index can be easily integrated with various database systems, including Azure Cosmos DB for PostgreSQL.

Overview of Azure Cosmos DB for PostgreSQL

Azure Cosmos DB is a globally distributed, multi-model database service provided by Microsoft. It provides support for various data models, including document, key-value, columnar, and graph, making it suitable for a wide range of applications. With the PostgreSQL API in Azure Cosmos DB, developers can leverage the power of PostgreSQL query language and tools while benefiting from the scalability and global distribution capabilities of Azure Cosmos DB.

Now that we have an understanding of the HNSW index and Azure Cosmos DB for PostgreSQL, let’s explore the steps required to implement the HNSW index with Azure Cosmos DB for PostgreSQL.

Prerequisites for using the HNSW index with Azure Cosmos DB for PostgreSQL

Before we dive into the implementation details, let’s ensure that we have all the necessary prerequisites in place.

• Azure subscription: To use Azure Cosmos DB for PostgreSQL, you will need an active Azure subscription. You can sign up for a free trial if you don’t already have an account.
• Installing Python 3.10: The implementation of the HNSW index will require Python, and it is recommended to have the latest version installed. You can download Python 3.10 from the official Python website and follow the installation instructions for your operating system.
• Setting up Visual Studio Code: Visual Studio Code is a popular code editor that provides a rich development environment. Install Visual Studio Code from the official website and set it up according to your preferences.
• Configuring Jupyter Notebook: Jupyter Notebook is an interactive development environment that allows you to create and share documents containing live code, equations, visualizations, and narrative text. You can install Jupyter Notebook by running the following command in your terminal or command prompt:

pip install jupyter

• Installing Jupyter Extension for Visual Studio Code: To enhance your development experience, install the Jupyter extension for Visual Studio Code. This extension provides features such as code completion, interactive plots, and markdown support within the Visual Studio Code environment.

With these prerequisites in place, we can now move on to setting up the working environment with the Faiss Python API.

Setting up the working environment with the Faiss Python API

To implement the HNSW index with Azure Cosmos DB for PostgreSQL, we will be using the Faiss Python API. Faiss is a library for efficient similarity search and clustering of dense vectors. In this section, we will walk through the steps to set up the necessary environment and install the required packages.

• Cloning the GitHub repository: Start by cloning the Faiss GitHub repository to your local machine. You can do this by running the following command in your terminal or command prompt:

git clone https://github.com/facebookresearch/faiss.git

This will create a local copy of the Faiss repository on your machine.

• Installing required Python packages: Navigate to the cloned Faiss repository and install the required Python packages by running the following command:

pip install -r tests/requirements.txt

This command will install all the dependencies needed for the Faiss Python API.

• Overview of the Faiss Python API: The Faiss Python API provides a set of functions and classes that allow you to create and manipulate indexes for efficient similarity search. It offers various index structures, including the HNSW index, that can be used for different types of data and similarity search requirements.
• Potential challenges and troubleshooting: Setting up the Faiss Python API and configuring the working environment might involve some challenges and troubleshooting. Make sure to refer to the official Faiss documentation and community forums for guidance in case you encounter any issues.

With the working environment set up and the Faiss Python API installed, we can now proceed to understand the HNSW index and its search process.

Understanding the HNSW index and its search process

The HNSW index is based on a multi-layered graph structure where each layer represents a different level of resolution. The search process in the HNSW index involves navigating this graph to find approximate nearest neighbors.

• Explaining the concept of a multi-layered graph structure: In the HNSW index, each layer of the graph represents a different level of resolution. The top layer of the graph holds a small number of highly connected datapoints, while each subsequent layer holds progressively more datapoints with fewer connections. This hierarchical structure allows for efficient and accurate similarity search.
• How approximate nearest neighbor search works: The approximate nearest neighbor search in the HNSW index involves traversing the graph from the top layer to the bottom layer. At each layer, the nearest neighbors are identified based on their distances to the query datapoint. The search process continues until the desired number of nearest neighbors is found or a stopping criterion is met.
• Visualization of the HNSW graph search process: To better understand the search process in the HNSW graph, the Faiss library provides visualization tools. These tools allow you to visualize the graph structure, navigate through the layers, and observe the connections between datapoints.

Now that we have a good understanding of the HNSW index and its search process, let’s move on to creating an HNSW index in Azure Cosmos DB for PostgreSQL.

Creating an HNSW index in Azure Cosmos DB for PostgreSQL

To create an HNSW index in Azure Cosmos DB for PostgreSQL, we need to execute SQL statements that define the index and specify its parameters. The following steps outline the process of creating an HNSW index:

1. Connect to your Azure Cosmos DB for PostgreSQL instance: First, establish a connection to your Azure Cosmos DB for PostgreSQL instance using your preferred PostgreSQL client or the Azure portal.
2. Execute the SQL statement to create the HNSW index: Execute the following SQL statement to create the HNSW index on a specific table:

CREATE INDEX hnsw_index ON table_name USING hnsw (column_name) WITH (distance_method = 'Euclidean', m = 16, ef_construction = 200);

Replace table_name with the name of the table you want to create the index on, and column_name with the name of the column that contains the vectors.

1. Explanation of important parameters: The SQL statement includes three important parameters that need to be specified:

• distance_method: This parameter specifies the distance metric to be used for similarity calculations. The ‘Euclidean’ distance metric is commonly used for vector similarity search.
• m: This parameter specifies the maximum number of connections (edges) that a node can have in the graph. A higher value of m can result in better accuracy but also increases the search time and memory usage.
• ef_construction: This parameter specifies the size of the list that holds the nearest neighbor candidates during index construction. A higher value of ef_construction can improve search accuracy but requires more memory.

1. Considerations for optimizing index creation: When creating an HNSW index, consider the following factors to optimize the index creation process:

• Data distribution: Ensure that the data is evenly distributed across different tables and partitions to achieve better query performance.
• Partitioning: If you have a large dataset, consider using partitioning to distribute the data across multiple servers for parallel query execution.
• Index maintenance: Regularly monitor the performance of your index and consider updating or rebuilding it based on the changing characteristics of your data.

With the HNSW index created in Azure Cosmos DB for PostgreSQL, we can now move on to performing similarity search using the index.

Performing similarity search using the pgvector HNSW index

The pgvector extension for PostgreSQL provides the necessary functions and operators for performing similarity search using the HNSW index. Let’s explore how we can use the pgvector HNSW index to detect similar images using the following steps:

1. Prepare your data: Ensure that your data is stored in a PostgreSQL table and the necessary vectors are stored in a column with the appropriate data type (e.g., pgvector).
2. Perform a similarity search: Use the following SQL SELECT statement to perform a similarity search using the pgvector HNSW index:

SELECT *
FROM table_name
WHERE hnsw_index <-> query_vector < distance_threshold
ORDER BY hnsw_index <-> query_vector;

Replace table_name with the name of the table where your data is stored, hnsw_index with the name of the HNSW index column, query_vector with the vector representing the query image, and distance_threshold with the desired threshold for similarity.

1. Using built-in distance operators: The pgvector extension provides built-in operators for distance calculations. For example, the <-> operator calculates the Euclidean distance between two vectors. You can also use other operators, such as <@> for cosine distance or <<-> for Jaccard similarity.
2. Adjusting the ef_search parameter: The ef_search parameter controls the size of the list of nearest neighbor candidates during query execution. By adjusting this parameter, you can trade off search accuracy for query speed. Increase the value of ef_search for better accuracy, but be aware that it may impact query performance.

In addition to these steps, you can further enhance your similarity search implementation by integrating text-to-image or image-to-image search scenarios. For a complete code sample and a hands-on tutorial, you can refer to the Jupyter Notebook available in the GitHub repository mentioned in the additional resources section.

Code Sample

For a comprehensive code sample and step-by-step instructions on implementing image similarity search using the HNSW index on Azure Cosmos DB for PostgreSQL, refer to the Image Similarity Search with HNSW Index Jupyter Notebook.

Additional Resources

Here are some additional resources for learning more about the HNSW algorithm and the pgvector extension for PostgreSQL:

• Faiss GitHub Repository
• Azure Cosmos DB for PostgreSQL Documentation
• pgvector Extension Documentation

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