What Is Vector Quantization?

Today’s world is driven by data and artificial intelligence (AI) innovations. However, managing large datasets has created challenges. AI and machine learning (ML) use high-dimensional data, which can be difficult to store, transmit, and retrieve. To mitigate the risk, developers have turned to data compression to reduce the size of this essential data. 

Vector quantization (VQ) compresses data by mapping high-dimensional vectors to a finite set of representative points called code words or centroids. VQ minimizes a dataset’s size without sacrificing functionality, making it easier to process and store. This approach is ideal for image compression, audio processing, machine learning, and approximate nearest neighbor search. 

In this guide, we’ll help you understand vector quantization and its types. We’ll also discuss its benefits, use cases, and VQ techniques for efficient data retrieval. Finally, we’ll provide an overview of its limitations with ways to mitigate these barriers for effective implementation. 

Understanding vector quantization

Modern AI and ML systems rely on large datasets to function. Vector quantization helps make these immense sets of information easier to work with and more cost-effective to store. This data compression technique uses a small set of vectors, called code words or centroids, to represent a large set of similar data points or input vectors. 

VQ groups these input vectors into clusters and assigns each cluster a representative code word. This collection of code words is known as a codebook. By dividing a high-dimensional space into discrete regions and representing each region with a central vector, indexes are optimized for faster search and retrieval. 

Instead of needing to store each vector or item of data individually, a vector index stores only the centroids or data approximations. These data approximations serve as representatives of the whole dataset, each centroid standing for a small cluster of data points. This reduces the amount of storage you need for each dataset while keeping the data functional and readable. 

There are a few common techniques used within vector quantization and vector databases, including:

Scalar quantization

One of the simplest forms of quantization is scalar quantization. This straightforward approach treats each dimension independently. Scalar quantization converts floating-point values to integers, as in converting 32-bit floats to 8-bit integers. This compression saves storage space and speeds up computation during signal processing. However, when dealing with high-dimensional vectors, it can lead to less accurate data. 

Product quantization

Product quantization (PQ) is a more advanced compression technique. This process splits high-dimensional vectors into smaller sub-vectors, and each sub-vector represents a different segment of the original vector. A codebook is created for each sub-vector that represents data regions that share common patterns or characteristics. 

PQ reduces search complexity and memory use because each codebook serves as a representative that summarizes similar sub-vectors. This significantly reduces memory usage and can offer up to 64x compression, depending on the configuration. However, it can also lead to a drop in quality, especially if the application requires high precision or real-time performance. 

PQ also reduces the search complexity of the approximate nearest neighbor (ANN) search in high-dimensional vector spaces. It divides immense datasets into equally sized sub-vectors. Each sub-vector is then quantized separately, which reduces the dimensionality of the vectors by mapping them to shorter representations. This process assigns each sub-vector the ID of the nearest centroid and then uses these IDs to form a compact code representing the original vector.

Binary quantization

Binary quantization compresses data by converting vector dimensions into a binary representation. Each dimension of the original vector is assigned a binary value. If the value is positive, it’s represented by a 1. If it’s negative, it’s represented by 0. This binary encoding reduces the amount of storage needed because each dimension is represented by a single bit.

This approach reduces the memory footprint significantly, sometimes up to 32x, while increasing the search speed. It is commonly used in hashing-based searches because it offers fast Hamming distance computation.

What does vector quantization do?

Vector quantization reduces the memory footprint of 32-bit floating-point number vector embeddings. This technique reduces their size by representing them as 8-bit integers or binary numbers and may also reduce the number of dimensions within the vector embeddings. VQ speeds data processing and helps you save money on storage because you don’t have to maintain large datasets.

Benefits

VQ offers several key benefits, especially regarding data representation and processing of high-dimensional data. The technique allows data compression, faster searches, and reduced memory usage, which makes it valuable for image and voice compression, autonomous systems, and pattern recognition. 

The positive impacts of VQ include: 

• Reduced memory footprint: By compressing vectors, VQ enables you to store more data within your existing systems.
• Faster similarity search: VQ enables faster searches because it reduces the amount of data a system needs to process during similarity searches. Instead of comparing original vectors directly, your system can sort through the representations.
• Lower bandwidth in transmission: VQ represents vectors with fewer bits compared to the original datasets. These smaller sub-vectors are easier to process and transmit and require less bandwidth and processing power.
• Efficiency in training large-scale machine-learning models: ML models rely on data to function. Vector quantization allows you to train these models faster by providing rapid access to similar, smaller vectors that focus on the relevant features. 

Use cases

Vector quantization is a powerful data compression technique, which makes it useful across a variety of industries and applications. Common use cases include: 

• Image compression (e.g., JPEG): Vector quantization reduces the size of image files while maintaining their quality. This is essential for media-heavy applications that utilize and store many photos and video assets.
• Speech recognition: VQ represents speech frames with codebook indices. These indices speed up the comparison process, enabling real-time translation and speech capabilities.
• Large-scale retrieval systems (e.g., recommender systems, search engines): VQ reduces large datasets into smaller subsets. These subsets make it easier for search engines to resolve queries faster and allow systems to make real-time recommendations based on user preferences.
• Vector databases: Vector databases such as FAISS, Milvus, or Pinecone use VQ to reduce storage requirements. VQ groups related items and represents each group with a single identifier, making it easier to quickly find items in a large dataset. 

Example

There are numerous instances of vector quantization. Here we’ll use image compression, one of the most common applications, as an example. 

Modern video games often offer two image settings: fidelity and performance. In fidelity mode, the graphics remain in their original form, often high resolution with detailed textures. However, because these graphics take longer to load, the frame rate is lower. Performance mode reduces the textures of images, resulting in faster load times and smoother gameplay. While you may sacrifice some graphic quality, your console won’t use as much power to play the game. 

Vector quantization challenges

While vector quantization offers significant advantages in terms of data compression, efficiency, and scalability, it also comes with a few notable challenges. 

1. Initial quantized search

When you use quantized vectors, or compressed representations, to perform searches, you’re not comparing with the original data. This can lead to approximate matches rather than exact ones, depending on how broad your codebook is. 

For example, an e-commerce platform might recommend the same product to two users who seem similar but have different needs. This can happen if the platform’s codebook uses broad, location-based codes (e.g., “likes hiking in Colorado”) instead of specific, product-based codes (e.g., “needs waterproof hiking boots with ankle support”). As a result, a user looking for casual hiking gear might get an irrelevant recommendation for technical equipment, because their profile was grouped with that of a serious backpacker.

To mitigate these accuracy issues, ensure that your codebook utilizes more specific language. You can also apply multistage quantization, such as product quantization, to preserve more of your data’s original structure.

2. Oversampling

Oversampling is a technique to improve search accuracy during vector quantization. However, it can also be risky, especially when dealing with imbalanced datasets. If your dataset is too small, using too many code words could result in centroids being representative of just a few data points, or none. This imbalance can lead to inefficient encoding or poor generalization.

When working with small or imbalanced datasets, focus on high-quality, relevant data. Cleaning and preprocessing this data can help you remove redundancies and irrelevancies. You must also optimize your code book. Start with a small set of vectors and iteratively refine them. Use algorithms that focus on most of the data points while ignoring outliers. 

3. Rescoring with original vectors

A common practice when using quantized vectors is rescoring. When performing a query, your database will use the quantized vectors for coarse filtering. After this initial search, you can re-rank the top results using the non-quantized vectors to improve the accuracy. 

This rescoring does come with a risk. If tincorrect code words are applied to your dataset, the best result may not make it into your top results. To lower this risk, you want to recalculate distances to ensure accurate results. For example, a nearest-neighbor search might find 100 close items. Rescoring these items using the original data allows you to rank them better. Additionally, by keeping the rescoring set small, you can preserve speed. 

4. Re-ranking

Even after rescoring, the order of results may not be ideal. Relevant results are always captured by vector similarity, especially in search or recommendation tasks. For example, you’re listening to a song on a streaming site, such as Spotify. It recommends a similar song to you based on the tempo and genre of the current song. However, the recommendation may not match your current mood or the vibe you’re looking for. 

To mitigate this risk, apply custom re-ranking models. Try filtering based on metadata, context, or user feedback. You can also refine results by utilizing features such as popularity, recent searches, or click-through rate alongside vector similarity to refine results. 

Other techniques in vector quantization

Vector quantization encompasses a broad set of advanced techniques and algorithms. These tools can be used alongside scalar, product, and binary quantization to improve accuracy and optimize storage. 

Lloyd’s algorithm

Lloyd’s algorithm, also known as the k-means algorithm, is a basic iterative method used for clustering data points into groups or clusters. This technique iteratively assigns data points to the nearest cluster center. Next, it recalculates the cluster centers based on the average position of the points within each group. This process then repeats until the cluster assignments are stable, indicating convergence. 

Lloyd’s algorithm is often used in initial VQ setups. It is also used in the fields of data analysis, image processing, and machine learning and can be used to detect anomalies, compress images, and segment customers. 

Linde-Buzo-Gray (LBG) algorithm

The LBG algorithm is a refinement of Lloyd’s algorithm used specifically for vector quantizer design. The process starts with a single centroid that progressively splits to create sub-vectors, optimizing for minimum distortion. This technique iteratively refines a codebook and allows better convergence for VQ applications. The goal of LBG is to minimize the distortion between the original data and its codebook representation. 

This method utilizes the following steps:

1. Initialization: Start with a single code word.
2. Splitting: Each code ord in the codebook is split in two.
3. Classification: Each sub-vector in the resulting code words is assigned to the closest centroid.
4. Update: Each sub-vector is recalculated to ensure that it fits within the assigned code word.
5. Convergence check: Your system compares the current errors to the previous errors. If the difference is below a certain threshold, your algorithm has converged. 

Residual quantization (RQ)

Residual quantization is a multistage approach that quantizes the difference between the original vector and its approximation. This technique utilizes multiple codebooks to achieve higher accuracy and efficiency, especially in audio and speech processing. In the first stage, a codebook is used to quantize the input vector. The difference between the input and quantized vector is calculated.

This difference is then quantized using a second codebook. The process repeats for multiple stages. The final representation of your original dataset is the sum of the values from each stage. By progressively quantizing the residual errors, RQ achieves a more accurate representation of the original data compared to a single vector quantization. 

Vector quantization with Pgvector

Pgvector provides the foundational capability for PostgreSQL to natively store, query, and index high-dimensional vector embeddings, enabling direct vector similarity searches alongside your traditional relational data. Building upon this, EDB Postgres® AI Factory transforms your database into a high-performance engine designed for production-grade generative AI and semantic search applications. By leveraging advanced vector indexing and efficient underlying techniques such as quantization, AI Factory delivers intelligent retrieval and automated semantic search calculations that result in highly performant semantic search at scale. The platform also includes re-ranking capabilities to further enhance the precision of your results for improved accuracy, all within your trusted Postgres environment.

To learn more about how AI Factory can help you build highly performant, reliable GenAI applications and agents, contact us today.