Cardinality Estimation for High Dimensional Similarity Queries with Adaptive Bucket Probing

In this work, we address the problem of cardinality estimation for similarity search in high-dimensional spaces. Our goal is to design a framework that is lightweight, easy to construct, and capable of providing accurate estimates with satisfying online efficiency. We leverage locality-sensitive hashing (LSH) to partition the vector space while preserving distance proximity. Building on this, we adopt the principles of classical multi-probe LSH to adaptively explore neighboring buckets, accounting for distance thresholds of varying magnitudes. To improve online efficiency, we employ progressive sampling to reduce the number of distance computations and utilize asymmetric distance computation in product quantization to accelerate distance calculations in high-dimensional spaces. In addition to handling static datasets, our framework includes updating algorithm designed to efficiently support large-scale dynamic scenarios of data updates.Experiments demonstrate that our methods can accurately estimate the cardinality of similarity queries, yielding satisfying efficiency.

Exploring the Meaningfulness of Nearest Neighbor Search in High-Dimensional Space

Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these vector can exceed several thousands easily. Despite the nearest neighbor search (NNS) over these dense high dimensional vectors have been widely used for retrieval augmented generation (RAG) and many other applications, the effectiveness of NNS in such a high-dimensional space remains uncertain, given the possible challenge caused by the "curse of dimensionality." To address above question, in this paper, we conduct extensive NNS studies with different distance functions, such as $L_1$ distance, $L_2$ distance and angular-distance, across diverse embedding datasets, of varied types, dimensionality and modality. Our aim is to investigate factors influencing the meaningfulness of NNS. Our experiments reveal that high-dimensional text embeddings exhibit increased resilience as dimensionality rises to higher levels when compared to random vectors. This resilience suggests that text embeddings are less affected to the "curse of dimensionality," resulting in more meaningful NNS outcomes for practical use. Additionally, the choice of distance function has minimal impact on the relevance of NNS. Our study shows the effectiveness of the embedding-based data representation method and can offer opportunity for further optimization of dense vector-related applications.