Comparing Temporal Graphs Using Dynamic Time Warping
This work addresses the need for proximity measures to recognize patterns in temporal graphs, which is incremental as it adapts dynamic time warping to a new domain.
The paper tackles the problem of comparing temporal graphs by proposing a dynamic temporal graph warping distance (dtgw) measure, showing it is NP-hard in general but identifying polynomial-time solvable cases and developing an efficient heuristic that performs well in experiments, such as de-anonymizing networks with favorable results compared to other approaches.
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different temporal graphs. To this end, we propose to study dynamic time warping on temporal graphs. We define the dynamic temporal graph warping distance (dtgw) to determine the dissimilarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general) NP-hard optimization problem and identify some polynomial-time solvable special cases. Moreover, we develop a quadratic programming formulation and an efficient heuristic. In experiments on real-word data we show that the heuristic performs very well and that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.