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We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of modeling contexts, especially when coarse-graining the detailed graph information is of interest. One of the main challenges in mining graph data is the definition of a suitable pairwise similarity metric in the space of graphs. We explore two practical solutions to solving this problem: one based on finding subgraph densities, and one using spectral information. The approach is illustrated on three test data sets (ensembles of graphs); two of these are obtained from standard graph generating algorithms, while the graphs in the third example are sampled as dynamic snapshots from an evolving network simulation.
Recent empirical observations suggest a heterogeneous nature of human activities. The heavy-tailed inter-event time distribution at population level is well accepted, while whether the individual acts in a heterogeneous way is still under debate. Mot
We introduce a contrarian opinion (CO) model in which a fraction p of contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, A and B exist. Then
Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of dependent nodes
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. In
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most trustworthy.