A Survey of Learned Indexes for the Multi-dimensional Space

A Comprehensive Survey of Learned Multi-dimensional Indexes

Introduction

Recent advancements in ML have significantly impacted various fields, including database systems. A notable trend is the integration of ML models to enhance or replace traditional database index structures, leading to the emergence of "Learned Indexes." These indexes leverage ML models to learn the key-to-position mapping within a dataset, offering improved search performance and reduced space requirements compared to conventional index structures.

The concept of learned indexes was initially applied to one-dimensional data, demonstrating promising results. This success has inspired the extension of learned indexes to multi-dimensional data, such as spatial data, leading to the development of "Learned Multi-dimensional Indexes." Multi-dimensional data presents unique challenges, such as the lack of an obvious total sort order, which complicates error correction and data layout. Addressing these challenges requires innovative approaches to extend the benefits of learned indexes to multi-dimensional contexts.

This survey aims to provide an in-depth analysis of recent advances in learned multi-dimensional indexes. We present a taxonomy for classifying these indexes, review existing literature, and discuss the core concepts of prominent research works. Additionally, we touch upon the practical implications, theoretical aspects, and future research directions in the realm of learned multi-dimensional indexes.

Taxonomy of Learned Indexes

The proposed taxonomy categorizes learned indexes based on several criteria, including their applicability to static or dynamic datasets, their data layout (fixed or dynamic), the dimensionality of the data they handle (one-dimensional or multi-dimensional), and whether they are pure learned indexes or hybrid structures that combine traditional indexes with ML models. This taxonomy not only organizes existing literature but also highlights research gaps and potential areas for future work.

Evolution of Learned Indexes

Tracing the evolution of learned indexes reveals a pathway from basic one-dimensional structures to sophisticated multi-dimensional systems. This evolution reflects the growing complexity and diversity in data types and query patterns encountered in modern applications, necessitating more advanced indexing solutions.

Learned Multi-dimensional Indexes

In exploring learned multi-dimensional indexes, we delve into a range of innovative structures designed for different types of multi-dimensional data and query requirements. These indexes employ various ML techniques, including neural networks, reinforcement learning, and clustering algorithms, to efficiently organize and query multi-dimensional datasets.

Open Challenges and Future Research Directions

Despite the significant progress, several challenges remain in the field of learned multi-dimensional indexes. Key areas requiring further research include developing methodologies for total ordering and error bound definition in multi-dimensional spaces, optimizing the choice and training of ML models, supporting dynamic updates efficiently, ensuring concurrency, and compressing index structures for space efficiency. Moreover, theoretical analyses that provide deeper insights into the principles underpinning learned indexes are needed to guide the design of future systems.

Conclusion

The intersection of machine learning and database indexing has opened up new horizons for managing and querying multi-dimensional data. Learned multi-dimensional indexes represent a promising approach that combines the predictive power of ML models with the structural advantages of traditional index mechanisms. This survey highlights the state-of-the-art in this rapidly evolving field, emphasizing both the achievements and the challenges that lie ahead. As research in learned multi-dimensional indexes continues to advance, it holds the potential to revolutionize data storage and retrieval in a wide range of applications.