Multi-Relational Algebra for Multi-Granular Data Analytics

In modern data analytics, analysts frequently face the challenge of searching for desirable entities by evaluating, for each entity, a collection of its feature relations to derive key analytical properties. This search is challenging because the definitions of both entities and their feature relations may span multiple, varying granularities. Existing constructs such as GROUP BY CUBE, GROUP BY GROUPING SETS, ARRAY AGGREGATE, WINDOW functions, OLAP cube, and various data explanation paradigms aim to facilitate such analyses, but all exhibit limitations in terms of composability, clear specifications, and performance. To address these challenges, we introduce Multi-Relational Algebra (MRA), which generalizes relational algebra with two core data abstractions: RelationSpace, for managing collections of relations, and SliceRelation, which structures data around entities with corresponding relation-valued features. MRA introduces a rich set of operators for transforming data between these representations, enabling complex multi-granular analysis in a modular and declarative way. An early version of MRA is in production at Google, supporting diverse data insight applications. This paper describes the motivation for MRA, its formalism, implementation, and future opportunities.