Multi-Relational Algebra and Its Applications to Data Insights

A range of data insight analytical tasks involves analyzing a large set of tables of different schemas, possibly induced by various groupings, to find salient patterns. This paper presents Multi-Relational Algebra, an extension of the classic Relational Algebra, to facilitate such transformations and their compositions. Multi-Relational Algebra has two main characteristics: (1) Information Unit. The information unit is a slice $(r, X)$, where $r$ is a (region) tuple, and $X$ is a (feature) table. Specifically, a slice can encompass multiple columns, which surpasses the information unit of "a single tuple" or "a group of tuples of one column" in the classic relational algebra, (2) Schema Flexibility. Slices can have varying schemas, not constrained to a single schema. This flexibility further expands the expressive power of the algebra. Through various examples, we show that multi-relational algebra can effortlessly express many complex analytic problems, some of which are beyond the scope of traditional relational analytics. We have implemented and deployed a service for multi-relational analytics. Due to a unified logical design, we are able to conduct systematic optimization for a variety of seemingly different tasks. Our service has garnered interest from numerous internal teams who have developed data-insight applications using it, and serves millions of operators daily.