Imagine looking for similar things based on deeper insights than just keywords. Vector databases and similarity searches help with this. Vector databases enable vector similarity searches. Find data points in a search query using distances between vectors.
However, similarity search for high-dimensional data can be time-consuming and resource-intensive. Introduce quantization techniques! They play an important role in optimizing data storage and speeding up data retrieval in vector databases.
This article describes various quantization techniques, their types, and practical use cases.
What is quantization and how does it work?
Quantization is the process of converting continuous data into discrete data points. Quantization is essential for management and processing, especially when dealing with billions of parameters. In vector databases, quantization transforms high-dimensional data into a compressed space while preserving important features and vector distances.
Quantization significantly reduces memory bottlenecks and improves storage efficiency.
The quantization process involves three main processes:
1. Compression of high-dimensional vectors
Quantization uses techniques such as codebook generation, feature engineering, and encoding. These techniques compress high-dimensional vector embeddings into low-dimensional subspaces. In other words, the vector is divided into many subvectors. Vector embeddings are numerical representations of audio, image, video, text, or signal data that are easier to process.
2. Mapping to discrete values
This step involves mapping low-dimensional subvectors to discrete values. Mapping further reduces the number of bits in each subvector.
3. Compressed vector storage
Finally, the mapped discrete values of the subvectors are placed into the database of the original vectors. Compressed data represents the same information in fewer bits, optimizing storage.
Advantages of quantization for vector databases
Quantization has various benefits, resulting in improved computational processing and reduced memory usage.
1. Efficient scalable vector search
Quantization reduces comparison computational costs and optimizes vector searches. Therefore, fewer resources are required for vector search, increasing overall efficiency.
2. Memory optimization
Quantization vectors allow you to store more data in the same space. Additionally, data indexing and searching are optimized.
3. Speed
Efficient storage and retrieval speeds up calculations. Reducing dimensions can speed up data operations, queries, predictions, and more.
Some popular vector databases include: quadrant, pine coneand milvus It offers different quantization techniques for different use cases.
Example of use
Quantization capabilities that can reduce data size while preserving important information make data a valuable asset.
Let’s take a closer look at some of its applications.
1. Image and video processing
Image and video data have a wide range of parameters, which significantly increases computational complexity and memory footprint. Quantization It compresses data without losing important details, allowing for efficient storage and processing. This speeds up image and video searches.
2. Compression of machine learning models
Training AI models on large datasets is an intensive task. Quantization is Model size and complexity without compromising efficiency.
3. Signal processing
Signal data represents continuous data points, such as GPS or surveillance video. Quantization maps data into discrete values for faster storage and analysis. Additionally, efficient storage and analysis speeds up search operations and enables faster signal comparisons.
Various quantization techniques
Quantization allows seamless processing of billions of parameters, but at the risk of irreversible information loss. However, finding the right balance between acceptable information loss and compression can improve efficiency.
Each quantization method has advantages and disadvantages. Before choosing, you should understand your compression requirements and the strengths and limitations of each technology.
1. Binary quantization
Binary quantization is a method that converts all vector embeddings to 0 or 1. If the value is greater than 0, it is mapped to 1, otherwise it is marked as 0. Therefore, it transforms high-dimensional data into significantly lower-dimensional data. Speeding up similarity searches.
formula
The formula is:
Binary quantization formula. Image by author.
Below is an example showing how binary quantization works for vectors.
Graphical representation of binary quantization. Image by author.
Strengths
- Fastest search that outperforms both scalar and product quantization techniques.
- Reduce memory usage by one coefficient of 32.
Limitations
- The rate of information loss is high.
- The vector components must have a mean approximately equal to zero.
- Low-dimensional data performs poorly due to high information loss.
- Re-scoring is required for best results.
like a vector database quadrant and Weaviate Provides binary quantization.
2. Scalar quantization
Scalar quantization converts floating point or decimal numbers to integers. This starts by identifying the minimum and maximum values for each dimension. The identified range is then divided into several bins. Finally, each value in each dimension is assigned to a bin.
The precision or level of detail of the quantization vector depends on the number of bins. A larger number of bins captures more detailed information, which increases accuracy. Therefore, the accuracy of vector search also depends on the number of bins.
formula
The formula is:
Formula for scalar quantization. Image by author.
Here is an example showing how scalar quantization works for vectors.
Graphical representation of scalar quantization. Image by author.
Strengths
- important memory optimization.
- Small information loss.
- Partially reversible process.
- Fast compression.
- Efficient and scalable search is possible because there is little information loss.
Limitations
- Search quality will be slightly reduced.
- Low-dimensional vectors are more susceptible to information loss because each data point carries important information.
vector database etc. quadrant and milvus Provides scalar quantization.
3. Quantization of the product
Product quantization divides a vector into subvectors. For each section, a center point, or centroid, is calculated using a clustering algorithm. Their nearest centroid represents all subvectors.
Similarity search in product quantization works by dividing the search vector into an equal number of subvectors. A list of similar results is then created in increasing order of the distance from each subvector’s centroid to each query subvector. Because the vector search process compares the distance from the query subvector to the centroid of the quantized vector, the search results are less accurate. However, product quantization speeds up the similarity search process, and higher accuracy can be achieved by increasing the number of subvectors.
formula
Searching for centroids is an iterative process. A recalculation of the Euclidean distance between each data point and its centroid is used until convergence. The formula for Euclidean distance in n-dimensional space is:
Product quantization formula. Image by author.
Below is an example of how product quantization works with vectors.
Graphical representation of product quantization. Image by author.
Strengths
- Highest compression ratio.
- Better storage efficiency than other technologies.
Limitations
- Not suitable for low-dimensional vectors.
- Resource-intensive compression.
like a vector database quadrant and Weaviate provide product quantization.
Choosing an appropriate quantization method
Each quantization method has advantages and disadvantages. Choosing the appropriate method depends on factors such as, but not limited to:
- data dimensions
- Compression accuracy trade-off
- efficiency requirements
- Resource constraints.
To better understand which quantization technique is suitable for your use case, consider the comparison table below. This graph shows the accuracy, speed, and compression ratio of each quantization method.
Image by Qdrant
From optimizing storage to speeding up retrieval, quantization eases the challenges of storing billions of parameters. However, understanding the requirements and tradeoffs upfront is important for successful implementation.
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