Simplex2Vec embeddings for community detection in simplicial complexes
arXiv:1906.09068
Abstract
Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and computational social science, in representing both descriptive features of data and inference models. While intense research has focused on the connectivity and homological features of topological representations, surprisingly scarce attention has been given to the investigation of the community structures of simplicial complexes. To this end, we adopt recent advances in symbolic embeddings to compute and visualize the community structures of simplicial complexes. We first investigate the stability properties of embedding obtained for synthetic simplicial complexes to the presence of higher order interactions. We then focus on complexes arising from social and brain functional data and show how higher order interactions can be leveraged to improve clustering detection and assess the effect of higher order interaction on individual nodes. We conclude delineating limitations and directions for extension of this work.
References in corpus (25)
- Fast unfolding of communities in large networks
- Statistical mechanics of complex networks
- Distributed Representations of Words and Phrases and their Compositionality
- Modularity and community structure in networks
- Community detection in graphs
- Maps of random walks on complex networks reveal community structure
- The architecture of complex weighted networks
- Graph Embedding Techniques, Applications, and Performance: A Survey
- word2vec Explained: deriving Mikolov et al.'s negative-sampling word-embedding method
- Finding statistically significant communities in networks
- Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys
- Simplicial Closure and higher-order link prediction
- Spectral methods for network community detection and graph partitioning
- Clique topology reveals intrinsic geometric structure in neural correlations
- Fundamental structures of dynamic social networks
- Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
- Self-organization of collaboration networks
- Mitigation of infectious disease at school: targeted class closure vs school closure
- Topological strata of weighted complex networks
- Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
- Simplicial Activity Driven Model
- Emergent Hyperbolic Network Geometry
- Maximal-entropy random walks in complex networks with limited information
- Topological Percolation on Hyperbolic Simplicial Complexes
- Complex Quantum Network Manifolds in Dimension are Scale-Free