16,308 research outputs found
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes
We investigate approximating joint distributions of random processes with
causal dependence tree distributions. Such distributions are particularly
useful in providing parsimonious representation when there exists causal
dynamics among processes. By extending the results by Chow and Liu on
dependence tree approximations, we show that the best causal dependence tree
approximation is the one which maximizes the sum of directed informations on
its edges, where best is defined in terms of minimizing the KL-divergence
between the original and the approximate distribution. Moreover, we describe a
low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure
Multiplexity and multireciprocity in directed multiplexes
Real-world multi-layer networks feature nontrivial dependencies among links
of different layers. Here we argue that, if links are directed, dependencies
are twofold. Besides the ordinary tendency of links of different layers to
align as the result of `multiplexity', there is also a tendency to anti-align
as the result of what we call `multireciprocity', i.e. the fact that links in
one layer can be reciprocated by \emph{opposite} links in a different layer.
Multireciprocity generalizes the scalar definition of single-layer reciprocity
to that of a square matrix involving all pairs of layers. We introduce
multiplexity and multireciprocity matrices for both binary and weighted
multiplexes and validate their statistical significance against maximum-entropy
null models that filter out the effects of node heterogeneity. We then perform
a detailed empirical analysis of the World Trade Multiplex (WTM), representing
the import-export relationships between world countries in different
commodities. We show that the WTM exhibits strong multiplexity and
multireciprocity, an effect which is however largely encoded into the degree or
strength sequences of individual layers. The residual effects are still
significant and allow to classify pairs of commodities according to their
tendency to be traded together in the same direction and/or in opposite ones.
We also find that the multireciprocity of the WTM is significantly lower than
the usual reciprocity measured on the aggregate network. Moreover, layers with
low (high) internal reciprocity are embedded within sets of layers with
comparably low (high) mutual multireciprocity. This suggests that, in the WTM,
reciprocity is inherent to groups of related commodities rather than to
individual commodities. We discuss the implications for international trade
research focusing on product taxonomies, the product space, and
fitness/complexity metrics.Comment: 20 pages, 8 figure
Ranking and clustering of nodes in networks with smart teleportation
Random teleportation is a necessary evil for ranking and clustering directed
networks based on random walks. Teleportation enables ergodic solutions, but
the solutions must necessarily depend on the exact implementation and
parametrization of the teleportation. For example, in the commonly used
PageRank algorithm, the teleportation rate must trade off a heavily biased
solution with a uniform solution. Here we show that teleportation to links
rather than nodes enables a much smoother trade-off and effectively more robust
results. We also show that, by not recording the teleportation steps of the
random walker, we can further reduce the effect of teleportation with dramatic
effects on clustering.Comment: 10 pages, 7 figure
A similarity-based community detection method with multiple prototype representation
Communities are of great importance for understanding graph structures in
social networks. Some existing community detection algorithms use a single
prototype to represent each group. In real applications, this may not
adequately model the different types of communities and hence limits the
clustering performance on social networks. To address this problem, a
Similarity-based Multi-Prototype (SMP) community detection approach is proposed
in this paper. In SMP, vertices in each community carry various weights to
describe their degree of representativeness. This mechanism enables each
community to be represented by more than one node. The centrality of nodes is
used to calculate prototype weights, while similarity is utilized to guide us
to partitioning the graph. Experimental results on computer generated and
real-world networks clearly show that SMP performs well for detecting
communities. Moreover, the method could provide richer information for the
inner structure of the detected communities with the help of prototype weights
compared with the existing community detection models
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