Visibility Graph Based Community Detection for Biological Time Series

Abstract Motivation Temporal behavior is an essential aspect of all biological systems. Time series have been previously represented as networks. Such representations must address two fundamental problems: (i) How to create the appropriate network to reflect the characteristics of biological time series. (ii) How to detect characteristic temporal patterns or events as network communities. General methods to detect communities have used metrics to compare the connectivity within a community to the connectivity one would expect in a random model, or assumed a known number of communities, or are based on the betweenness centrality of edges or nodes. However, such methods were not specifically designed for network representations of time series. We introduce a visibility-graph-based method to build networks from different kinds of biological time series and detect temporal communities within these networks. Results To characterize the uneven sampling of typical experimentally obtained biological time series, and simultaneously capture events associated to peaks and troughs, we introduce the Weighted Dual-Perspective Visibility Graph (WDPVG) for time series. To detect communities, we first find the shortest path of the network between start and end nodes to identify nodes which have high intensities. This identifies the main stem of our community detection algorithm. Then, we aggregate nodes outside the shortest path to the nodes found on the main stem based on the closest path length. Through simulation, we demonstrate the validity of our method in detecting community structures on various networks derived from simulated time series. We also confirm its effectiveness in revealing temporal communities in experimental biological time series. Our results suggest our method of visibility graph based community detection can be effective in detecting temporal biological patterns. Availability The methods of building WDPVG and visibility graph based community detection are available as a module of the open source Python package PyIOmica ( https://doi.org/10.5281/zenodo.3691912 ) with documentation at https://pyiomica.readthedocs.io/en/latest/ . The dataset and codes we used in this manuscript are publicly available at https://doi.org/10.5281/zenodo.3693984 . Contact gmias@msu.edu