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Abstract:
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Recently, techniques based on simplicial complexes and persistence homology have been successful in characterizing the complex relationships seen in systems biology. The extension of protein-protein interaction (PPI) and co-expression networks using simplicial complexes has shown to provide nuanced insights when compared to a purely graph-theoretic analysis. Initial network extensions based on the Vietoris-Rips complex, while capturing much of the relevant topological information, are artificially imposed and fail to reflect underlying geometry. We propose a natural simplicial complex extension for correlation networks based on the Cech complex, providing a topological summary that more accurately reflects the inherent geometry within the space of correlations. An application is made to the protein co-expression networks of three-spined sticklebacks (Gasterosteus aculeatus).
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