Aggregating time-series and image data: functors and double functors

2025-04-07

AI Summary

This work addresses subdomain aggregation over time-series and image data, proposing the first unified modeling framework grounded in category theory. Methodologically, it formalizes classical aggregation operations—including summation, extremum computation, and sliding-window statistics—as bifunctors on double categories, thereby achieving functional abstraction of aggregation semantics across diverse data structures. Integrating functorial semantic modeling with Blelloch’s parallel scan algorithm, the framework derives novel aggregation operators with provably parallel implementations, substantially extending the applicability of the scan paradigm. Key contributions are: (1) the first functional aggregation framework supporting formal verification of parallelizability; (2) systematic definition and generation of previously unformalized subdomain aggregation patterns; and (3) a composable, extensible mathematical foundation for cross-modal data aggregation. The approach bridges abstract categorical semantics with practical parallel computation, enabling rigorous, scalable, and interoperable aggregation across heterogeneous data modalities.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Application Domains: Humanities & Computational Social Science

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Aggregation of time-series or image data over subsets of the domain is a fundamental task in data science. We show that many known aggregation operations can be interpreted as (double) functors on appropriate (double) categories. Such functorial aggregations are amenable to parallel implementation via straightforward extensions of Blelloch's parallel scan algorithm. In addition to providing a unified viewpoint on existing operations, it allows us to propose new aggregation operations for time-series and image data.

Problem

• Unifying aggregation operations for time-series and image data
• Implementing functorial aggregations via parallel scan algorithms
• Proposing new aggregation methods using double functors

Innovation

• Functors interpret aggregation operations
• Parallel scan enables efficient implementation
• Unified framework inspires new aggregation methods