Yoshiharu Ishikawa

Kejing Lu, Chuan Xiao, Yoshiharu Ishikawa

Approximate nearest neighbor search (ANNS) in high-dimensional spaces is a pivotal challenge in the field of machine learning. In recent years, graph-based methods have emerged as the superior approach to ANNS, establishing a new state of the art. Although various optimizations for graph-based ANNS have been introduced, they predominantly rely on heuristic methods that lack formal theoretical backing. This paper aims to enhance routing within graph-based ANNS by introducing a method that offers a probabilistic guarantee when exploring a node's neighbors in the graph. We formulate the problem as probabilistic routing and develop two baseline strategies by incorporating locality-sensitive techniques. Subsequently, we introduce PEOs, a novel approach that efficiently identifies which neighbors in the graph should be considered for exact distance calculation, thus significantly improving efficiency in practice. Our experiments demonstrate that equipping PEOs can increase throughput on commonly utilized graph indexes (HNSW and NSSG) by a factor of 1.6 to 2.5, and its efficiency consistently outperforms the leading-edge routing technique by 1.1 to 1.4 times.

Yaoshu Wang, Chuan Xiao, Jianbin Qin et al.

Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection, query optimization, and data integration. The estimation problem is especially challenging for large-scale high-dimensional data due to the curse of dimensionality, the large variance of selectivity across different queries, and the need to make the estimator consistent (i.e., the selectivity is non-decreasing in the threshold). We propose a new deep learning-based model that learns a query-dependent piecewise linear function as selectivity estimator, which is flexible to fit the selectivity curve of any distance function and query object, while guaranteeing that the output is non-decreasing in the threshold. To improve the accuracy for large datasets, we propose to partition the dataset into multiple disjoint subsets and build a local model on each of them. We perform experiments on real datasets and show that the proposed model consistently outperforms state-of-the-art models in accuracy in an efficient way and is useful for real applications.