22,199 research outputs found

    A Monte Carlo Evaluation of Weighted Community Detection Algorithms

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    The past decade has been marked with a proliferation of community detection algorithms that aim to organize nodes (e.g., individuals, brain regions, variables) into modular structures that indicate subgroups, clusters, or communities. Motivated by the emergence of big data across many fields of inquiry, these methodological developments have primarily focused on the detection of communities of nodes from matrices that are very large. However, it remains unknown if the algorithms can reliably detect communities in smaller graph sizes (i.e., 1000 nodes and fewer) which are commonly used in brain research. More importantly, these algorithms have predominantly been tested only on binary or sparse count matrices and it remains unclear the degree to which the algorithms can recover community structure for different types of matrices, such as the often used cross-correlation matrices representing functional connectivity across predefined brain regions. Of the publicly available approaches for weighted graphs that can detect communities in graph sizes of at least 1000, prior research has demonstrated that Newman's spectral approach (i.e., Leading Eigenvalue), Walktrap, Fast Modularity, the Louvain method (i.e., multilevel community method), Label Propagation, and Infomap all recover communities exceptionally well in certain circumstances. The purpose of the present Monte Carlo simulation study is to test these methods across a large number of conditions, including varied graph sizes and types of matrix (sparse count, correlation, and reflected Euclidean distance), to identify which algorithm is optimal for specific types of data matrices. The results indicate that when the data are in the form of sparse count networks (such as those seen in diffusion tensor imaging), Label Propagation and Walktrap surfaced as the most reliable methods for community detection. For dense, weighted networks such as correlation matrices capturing functional connectivity, Walktrap consistently outperformed the other approaches for recovering communities

    Planetary Detection Efficiency of the Magnification 3000 Microlensing Event OGLE-2004-BLG-343

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    OGLE-2004-BLG-343 was a microlensing event with peak magnification A_{max}=3000+/-1100, by far the highest-magnification event ever analyzed and hence potentially extremely sensitive to planets orbiting the lens star. Due to human error, intensive monitoring did not begin until 43 minutes after peak, at which point the magnification had fallen to A~1200, still by far the highest ever observed. As the light curve does not show significant deviations due to a planet, we place upper limits on the presence of such planets by extending the method of Yoo et al. (2004b), which combines light-curve analysis with priors from a Galactic model of the source and lens populations, to take account of finite-source effects. This is the first event so analyzed for which finite-source effects are important, and hence we develop two new techniques for evaluating these effects. Somewhat surprisingly, we find that OGLE-2004-BLG-343 is no more sensitive to planets than two previously analyzed events with A_{max}~100, despite the fact that it was observed at ~12 times higher magnification. However, we show that had the event been observed over its peak, it would have been sensitive to almost all Neptune-mass planets over a factor of 5 of projected separation and even would have had some sensitivity to Earth-mass planets. This shows that some microlensing events being detected in current experiments are sensitive to very low-mass planets. We also give suggestions on how extremely high-magnification events can be more promptly monitored in the future.Comment: 50 pages, 13 figures, published in The Astrophysical Journa

    Detecting Communities under Differential Privacy

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    Complex networks usually expose community structure with groups of nodes sharing many links with the other nodes in the same group and relatively few with the nodes of the rest. This feature captures valuable information about the organization and even the evolution of the network. Over the last decade, a great number of algorithms for community detection have been proposed to deal with the increasingly complex networks. However, the problem of doing this in a private manner is rarely considered. In this paper, we solve this problem under differential privacy, a prominent privacy concept for releasing private data. We analyze the major challenges behind the problem and propose several schemes to tackle them from two perspectives: input perturbation and algorithm perturbation. We choose Louvain method as the back-end community detection for input perturbation schemes and propose the method LouvainDP which runs Louvain algorithm on a noisy super-graph. For algorithm perturbation, we design ModDivisive using exponential mechanism with the modularity as the score. We have thoroughly evaluated our techniques on real graphs of different sizes and verified their outperformance over the state-of-the-art
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