Advancements in Vector Indexing Techniques: KD-Trees, HNSW, and Product Quantization for Vector Databases

Abstract—The growth of high-dimensional data in fields

like computer vision, natural language processing, and

data mining has necessitated the development of efficient

vector indexing techniques. This paper presents a

comparative analysis of three state-of-the-art vector

indexing techniques—KD-Trees, Hierarchical

Navigable Small World (HNSW) graphs, and Product

Quantization (PQ). We provide a detailed exploration of

each method’s algorithmic foundations, mathematical

formulations, advantages, and limitations, followed by a

discussion of recent advancements aimed at optimizing

these methods for large-scale databases. Through my

analysis, I aim to offer a comprehensive understanding

of how these techniques perform and can be adapted for

various real-world applications.

Index Terms—Vector Indexing, KD-Trees, HNSW,

Product

Quantization, High-Dimensional Data, Nearest

Neighbor Search