Identification of co-evolving temporal networks

Abstract

Motivation:Biological networks describes the mechanisms which govern cellular functions. Temporal networks show how these networks evolve over time. Studying the temporal progression of network topologies is of utmost importance since it uncovers how a network evolves and how it resists to external stimuli and internal variations. Two temporal networks have co-evolving subnetworks if the topologies of these subnetworks remain similar to each other as the network topology evolves over a period of time. In this paper, we consider the problem of identifying co-evolving pair of temporal networks, which aim to capture the evolution of molecules and their interactions over time. Although this problem shares some characteristics of the well-known network alignment problems, it differs from existing network alignment formulations as it seeks a mapping of the two network topologies that is invariant to temporal evolution of the given networks. This is a computationally challenging problem as it requires capturing not only similar topologies between two networks but also their similar evolution patterns. Results: We present an efficient algorithm, Tempo, for solving identifying coevolving subnetworks with two given temporal networks. We formally prove the correctness of our method. We experimentally demonstrate that Tempo scales efficiently with the size of network as well as the number of time points, and generates statistically significant alignments-even when evolution rates of given networks are high. Our results on a human aging dataset demonstrate that Tempo identifies novel genes contributing to the progression of Alzheimer's, Huntington's and Type II diabetes, while existing methods fail to do so.

Comparing Temporal Graphs Using Dynamic Time Warping

“…The vertex coloring indicates an optimal vertex mapping M . The connections between the boxes indicate an optimal warping path p = {(1, 1), (2, 1), (3,2), (3,3), (4,4), (5,5), (6,5)}. The labels correspond to the costs C(G i , H j , M ) where the vertex signatures are their degrees and the metric is the absolute value of the difference.…”

“…For example, one approach is based on network embeddings where nodes are mapped into a feature space [1,19,26]. Another approach is based on network alignments [5,23] where a vertex mapping that optimizes some criteria is computed. However, dynamic time warping has not been used in this context so far.…”

“…Source code available at www.akt.tu-berlin.de/menue/software 5. This code is available as a Python module at github.com/src-d/lapjv.…”