Metrics and Data Structures in Vector Databases

Vector databases are designed to efficiently store and retrieve high-dimensional data. To achieve this, they employ various metrics and data structures. In this comprehensive guide, we will explore the key metrics and data structures used in vector databases.

Metrics

• Euclidean Distance: Measures the straight-line distance between two points in Euclidean space. It is often used for numerical data.
• Cosine Similarity: Measures the cosine of the angle between two vectors. It is commonly used for text and image data, as it is less sensitive to differences in magnitude.
• Hamming Distance: Measures the number of positions at which two vectors differ. It is often used for binary data.
• Jaccard Similarity: Measures the similarity between two sets. It is often used for categorical data.

Data Structures

• Inverted Indexes: Similar to traditional inverted indexes used in text search, inverted indexes in vector databases map each dimension of a vector to a list of documents that contain that value.
• Tree-Based Indexes: Trees like KD-trees and Annoy (Approximate Nearest Neighbors Oh Yeah) are used to partition the vector space and efficiently search for similar vectors.
• Hashing: Hashing techniques like Locality-Sensitive Hashing (LSH) can be used to group similar vectors together, reducing the search space.
• Product Quantization (PQ): PQ decomposes vectors into smaller sub-vectors and quantizes them to reduce storage requirements and improve search efficiency.

Choosing the Right Metric and Data Structure

The choice of metric and data structure depends on the specific characteristics of your data and the nature of your queries. Consider the following factors:

• Data Type: The type of data (e.g., numerical, categorical, text) will influence the appropriate metric.
• Query Type: The type of queries you will be performing (e.g., exact match, nearest neighbor) will determine the most suitable data structure.
• Performance Requirements: The desired search speed and accuracy will influence the choice of metric and data structure.