TY - JOUR A1 - Brill, Markus A1 - Fluschnik, Till A1 - Froese, Vincent A1 - Jain, Brijnesh A1 - Niedermeier, Rolf A1 - Schultz, David T1 - Exact mean computation in dynamic time warping spaces JF - Data Mining and Knowledge Discovery N2 - Averaging time series under dynamic time warping is an important tool for improving nearest-neighbor classifiers and formulating centroid-based clustering. The most promising approach poses time series averaging as the problem of minimizing a Fréchet function. Minimizing the Fréchet function is NP-hard and so far solved by several heuristics and inexact strategies. Our contributions are as follows: we first discuss some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Then we propose an exponential-time dynamic program for computing a global minimum of the Fréchet function. The proposed algorithm is useful for benchmarking and evaluating known heuristics. In addition, we present an exact polynomial-time algorithm for the special case of binary time series. Based on the proposed exponential-time dynamic program, we empirically study properties like uniqueness and length of a mean, which are of interest for devising better heuristics. Experimental evaluations indicate substantial deficits of state-of-the-art heuristics in terms of their output quality. Y1 - 2019 U6 - https://doi.org/10.1007/s10618-018-0604-8 VL - 33 SP - 252 EP - 291 PB - Springer Nature ER - TY - JOUR A1 - Froese, Vincent A1 - Jain, Brijnesh A1 - Niedermeier, Rolf A1 - Renken, Malte T1 - Comparing temporal graphs using dynamic time warping JF - Social Network Analysis and Mining N2 - 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 tem- poral graph warping (dtgw) distance 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-world data, we show that the heuristic performs very well and that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches. Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-38493 VL - 10 SP - 1 EP - 16 PB - Springer Nature ER -