Mathematics of Digital Hyperspace

TL;DR

This paper introduces the mathematical concept of semilinks, which combine semirings to enhance graph analytics, databases, and machine learning within the GraphBLAS framework, enabling better navigation of unstructured digital data.

Contribution

It presents the novel concept of semilinks and demonstrates how they can extend GraphBLAS to support richer data operations and analysis of unstructured digital hyperspace.

Findings

Semilinks enable combined semiring operations for complex data analysis.

GraphBLAS can be extended with key-based indices and semilinks.

Enhanced GraphBLAS supports more versatile graph and database operations.

Abstract

Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data supported by continuous streams that stretch standard concepts of type and dimension. The unstructured data of digital hyperspace can be elegantly represented, traversed, and transformed via the mathematics of hypergraphs, hypersparse matrices, and associative array algebra. This paper explores a novel mathematical concept, the semilink, that combines pairs of semirings to provide the essential operations for graph analytics, database operations, and machine learning. The GraphBLAS standard currently supports hypergraphs, hypersparse matrices, the mathematics required for semilinks, and seamlessly performs graph, network, and matrix operations. With the addition of key based indices (such as pointers to strings) and semilinks, GraphBLAS can become a richer associative array algebra and be a plug-in replacement for spreadsheets, database tables, and data centric operating systems, enhancing the navigation of unstructured data found in digital hyperspace.