Representing higher-order dependencies in networks

TL;DR

This paper introduces Higher-Order Networks (HON), a novel method for representing complex sequential data with dependencies beyond the first order, improving accuracy in network analysis tasks like clustering and ranking.

Contribution

The paper proposes HON, a new network representation that captures variable-order dependencies, addressing limitations of traditional first-order network models.

Findings

HON improves accuracy in network analysis tasks.

HON is scalable and compatible with existing methods.

Empirical evaluation confirms HON's effectiveness.

Abstract

To ensure the correctness of network analysis methods, the network (as the input) has to be a sufficiently accurate representation of the underlying data. However, when representing sequential data from complex systems such as global shipping traffic or web clickstream traffic as networks, conventional network representations that implicitly assume the Markov property (first-order dependency) can quickly become limiting. This assumption holds that when movements are simulated on the network, the next movement depends only on the current node, discounting the fact that the movement may depend on several previous steps. However, we show that data derived from many complex systems can show up to fifth-order dependencies. In these cases, the oversimplifying assumption of the first-order network representation can lead to inaccurate network analysis results. To address this problem, we propose the Higher-Order Network (HON) representation that can discover and embed variable orders of dependencies in a network representation. Through a comprehensive empirical evaluation and analysis, we establish several desirable characteristics of HON, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods. We illustrate how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking, and we demonstrate that by using it as input, HON yields more accurate results without any modification to these tasks.