3,957 research outputs found
Stochastic blockmodels and community structure in networks
Stochastic blockmodels have been proposed as a tool for detecting community
structure in networks as well as for generating synthetic networks for use as
benchmarks. Most blockmodels, however, ignore variation in vertex degree,
making them unsuitable for applications to real-world networks, which typically
display broad degree distributions that can significantly distort the results.
Here we demonstrate how the generalization of blockmodels to incorporate this
missing element leads to an improved objective function for community detection
in complex networks. We also propose a heuristic algorithm for community
detection using this objective function or its non-degree-corrected counterpart
and show that the degree-corrected version dramatically outperforms the
uncorrected one in both real-world and synthetic networks.Comment: 11 pages, 3 figure
Serial position effects in 2-alternative forced choice recognition: Functional equivalence across visual and auditory modalities
Two experiments examined Ward, Avons and Melling’s (2005) proposition that the serial position function is task, rather than modality, dependent. Specifically, they proposed that for backward testing the 2-alternative forced choice (2AFC) recognition paradigm is characterised by single-item recency irrespective of the modality of the stimulus presentation. In Experiment 1 the same nonwords sequences, presented both visually or auditorially, produced qualitatively equivalent serial position functions with 2AFC testing. Forward testing produced a flat serial position function, whilst backward testing produced two-item recency in the absence of primacy. In order to rule out the possibility that the serial position functions for visual stimuli were the product of sub-vocal rehearsal, Experiment 2 employed articulatory suppression during the presentation phase. Serial position function equivalence was again observed together with a modest impairment in overall recognition rates. Taken together, these data are consistent with the Ward et al. proposition and further support the existence of a visual memory that can facilitate storage of visual-verbal material e.g. Logie, Della Sella, Wynn, and Baddeley (2000). However, the observation of two-item recency contradicts the original Duplex account of single-item recency traditionally observed for backwards recognition testing of visual stimuli (Phillips and Christie, 1977)
Searching for network modules
When analyzing complex networks a key target is to uncover their modular
structure, which means searching for a family of modules, namely node subsets
spanning each a subnetwork more densely connected than the average. This work
proposes a novel type of objective function for graph clustering, in the form
of a multilinear polynomial whose coefficients are determined by network
topology. It may be thought of as a potential function, to be maximized, taking
its values on fuzzy clusterings or families of fuzzy subsets of nodes over
which every node distributes a unit membership. When suitably parametrized,
this potential is shown to attain its maximum when every node concentrates its
all unit membership on some module. The output thus is a partition, while the
original discrete optimization problem is turned into a continuous version
allowing to conceive alternative search strategies. The instance of the problem
being a pseudo-Boolean function assigning real-valued cluster scores to node
subsets, modularity maximization is employed to exemplify a so-called quadratic
form, in that the scores of singletons and pairs also fully determine the
scores of larger clusters, while the resulting multilinear polynomial potential
function has degree 2. After considering further quadratic instances, different
from modularity and obtained by interpreting network topology in alternative
manners, a greedy local-search strategy for the continuous framework is
analytically compared with an existing greedy agglomerative procedure for the
discrete case. Overlapping is finally discussed in terms of multiple runs, i.e.
several local searches with different initializations.Comment: 10 page
Overlapping modularity at the critical point of k-clique percolation
One of the most remarkable social phenomena is the formation of communities
in social networks corresponding to families, friendship circles, work teams,
etc. Since people usually belong to several different communities at the same
time, the induced overlaps result in an extremely complicated web of the
communities themselves. Thus, uncovering the intricate community structure of
social networks is a non-trivial task with great potential for practical
applications, gaining a notable interest in the recent years. The Clique
Percolation Method (CPM) is one of the earliest overlapping community finding
methods, which was already used in the analysis of several different social
networks. In this approach the communities correspond to k-clique percolation
clusters, and the general heuristic for setting the parameters of the method is
to tune the system just below the critical point of k-clique percolation.
However, this rule is based on simple physical principles and its validity was
never subject to quantitative analysis. Here we examine the quality of the
partitioning in the vicinity of the critical point using recently introduced
overlapping modularity measures. According to our results on real social- and
other networks, the overlapping modularities show a maximum close to the
critical point, justifying the original criteria for the optimal parameter
settings.Comment: 20 pages, 6 figure
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