[Paper Review] Machine Learning Analysis of Complex Networks in Hyperspherical Space

María Pereda, Ernesto Estrada|arXiv (Cornell University)|Apr 16, 2018

Complex Network Analysis Techniques49 references3 citations

TL;DR

This paper proposes a novel geometric machine learning approach that embeds complex networks into a hyperspherical space based on a communicability function measuring information flow. By analyzing angles between node position vectors using nonmetric MDS and K-means clustering, it reveals structural communities in networks—demonstrated on citation and gene interaction networks—identifying biologically significant clusters, including genes linked to multiple diseases and cancer, with results validated by recent biological literature.

ABSTRACT

A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here, we consider a communicability function that accounts for the routes through which items flow on networks. Such a function induces a natural embedding of a network in a Euclidean high-dimensional sphere. We use one of the geometric parameters of this embedding, namely the angle between the position vectors of the nodes in the hyperspheres, to extract structural information from networks. Such information is extracted by using machine learning techniques, such as nonmetric multidimensional scaling and K-means clustering algorithms. The first allows us to reduce the dimensionality of the communicability hyperspheres to 3-dimensional ones that allow network visualization. The second permits to cluster the nodes of the networks based on their similarities in terms of their capacity to successfully deliver information through the network. After testing these approaches in benchmark networks and compare them with the most used clustering methods in networks we analyze two real-world examples. In the first, consisting of a citation network, we discover citation groups that reflect the level of mathematics used in their publications. In the second, we discover groups of genes that coparticipate in human diseases, reporting a few genes that coparticipate in cancer and other diseases. Both examples emphasize the potential of the current methodology for the discovery of new patterns in relational data.

Motivation & Objective

• To develop a new geometric framework for analyzing complex networks by embedding them in a hypersphere based on natural information flow.
• To overcome limitations of traditional clustering methods that rely solely on edge density by introducing a flow-based similarity measure.
• To enable visualization and unsupervised clustering of networks using geometric properties of hyperspherical embeddings.
• To discover biologically meaningful communities in real-world networks, such as citation groups and disease-related gene clusters.
• To validate the biological relevance of discovered clusters through comparison with known disease-gene associations and recent literature.

Proposed method

• Embed a network into an (n−1)-dimensional Euclidean hypersphere using the communicability function, which quantifies the effective connectivity between nodes based on all paths in the network.
• Compute the angle between position vectors of nodes in the hypersphere as a geometric similarity measure reflecting their capacity to transmit information.
• Apply nonmetric multidimensional scaling (NMDS) to reduce the hyperspherical embedding to 3D for visualization while preserving rank-order similarity.
• Use K-means clustering on the angular similarity matrix to group nodes based on their topological role in information transmission.
• Validate clustering results by comparing with known biological annotations and recent literature on gene-disease associations.
• Leverage the natural geometric structure of the communicability embedding, avoiding arbitrary or imposed embeddings common in other geometric learning methods.

Experimental results

Research questions

• RQ1 Can a geometric embedding based on information flow in networks reveal meaningful structural communities beyond edge-density-based definitions?
• RQ2 How effective is the angle between node vectors in hyperspherical space as a similarity measure for network clustering?
• RQ3 Can this method uncover biologically relevant gene clusters in human disease networks that are not detectable by standard clustering approaches?
• RQ4 Do genes grouped into the same cluster based on their communicability-based similarity show shared involvement in multiple diseases, including cancer?
• RQ5 Can the proposed method reveal novel disease-gene associations not previously reported in the literature?

Key findings

• The method successfully visualized complex networks in 3D using nonmetric MDS, preserving the relative structural relationships of nodes in the hyperspherical embedding.
• In the citation network, the algorithm identified distinct clusters reflecting the level of mathematical sophistication used in publications, validating its ability to detect thematic groupings.
• In the human gene interaction network, 37% of genes in cluster 1 were found to be involved in cancer, despite not being previously classified as such, indicating functional relevance.
• Cluster 5 contained 107 genes, of which 26 were in the 'grey' category (involved in multiple diseases), and 14 of these were newly linked to cancer in recent studies, supporting the hypothesis of shared topological roles in disease networks.
• Ten out of 14 previously unreported 'grey' genes in cluster 5 were confirmed in recent literature to be involved in various cancers, such as ABCA1 in prostate cancer and ESR1 in hormone-resistant breast cancer.
• The results demonstrate that the geometric clustering approach based on communicability and hyperspherical embedding can uncover biologically significant, high-quality network communities without prior labeling.