A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

现在的研究趋势是将数据库索引结构视为机器学习模型，通过训练单个或多个机器学习模型来学习从键到数据集内位置的映射关系，从而实现改进搜索性能和减少空间需求。该调查重点关注学习多维索引结构，介绍了该研究领域的现状，解释了每个方法的核心概念，并根据多个明确定义的标准对这些方法进行分类。我们提供了一个分类法以对每个学习多维索引进行分类和归类，并根据此分类法对现有的学习多维索引文献进行了调查。此外，我们还提供了一个时间线来说明学习索引研究的发展历程，并重点介绍了这个新兴且非常活跃的领域中的几个挑战和未来研究方向。

多维空间的学习索引调查