From data to concepts via wiring diagrams

TL;DR

This paper introduces a new graph-based framework called quasi-skeleton wiring diagrams, proves their correspondence to Hasse diagrams, and develops algorithms to extract these diagrams from sequential data, demonstrating their effectiveness in analyzing autonomous agent behavior.

Contribution

It presents the concept of quasi-skeleton wiring diagram graphs, proves their relation to Hasse diagrams, and designs algorithms for extracting wiring diagrams from sequential data.

Findings

Algorithms accurately identified winning strategies in a computer game.

The proposed algorithms outperform standard clustering methods in perturbed data scenarios.

The approach integrates category theory, graph theory, clustering, reinforcement learning, and data engineering.

Abstract

A wiring diagram is a labeled directed graph that represents an abstract concept such as a temporal process. In this article, we introduce the notion of a quasi-skeleton wiring diagram graph, and prove that quasi-skeleton wiring diagram graphs correspond to Hasse diagrams. Using this result, we designed algorithms that extract wiring diagrams from sequential data. We used our algorithms in analyzing the behavior of an autonomous agent playing a computer game, and the algorithms correctly identified the winning strategies. We compared the performance of our main algorithm with two other algorithms based on standard clustering techniques (DBSCAN and agglomerative hierarchical), including when some of the data was perturbed. Overall, this article brings together techniques in category theory, graph theory, clustering, reinforcement learning, and data engineering.