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