Simplifying complex machine learning by linearly separable network embedding spaces

TL;DR

This paper reveals that network data with high homophily can be embedded into linearly separable spaces, simplifying analysis and enabling efficient, explainable network mining using novel graphlet-based methods.

Contribution

It introduces a theoretical link between network homophily and linear separability of embeddings, along with new graphlet-based embedding techniques for better network analysis.

Findings

Higher homophily correlates with more linearly separable embeddings.

Graphlet-based methods improve the linear separability of network embeddings.

Enhanced linear separability leads to more efficient and explainable network mining.

Abstract

Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate downstream tasks. In the field of NLP, word embedding spaces capture semantic relationships \textit{linearly}, allowing for information retrieval using \textit{simple linear operations} on word embedding vectors. Here, we demonstrate that there are structural properties of network data that yields this linearity. We show that the more homophilic the network representation, the more linearly separable the corresponding network embedding space, yielding better downstream analysis results. Hence, we introduce novel graphlet-based methods enabling embedding of networks into more linearly separable spaces, allowing for their better mining. Our fundamental insights into the structure of network data that enable their \textit{\textbf{linear}} mining and exploitation enable the ML community to build upon, towards efficiently and explainably mining of the complex network data.