43,994 research outputs found
Element-centric clustering comparison unifies overlaps and hierarchy
Clustering is one of the most universal approaches for understanding complex
data. A pivotal aspect of clustering analysis is quantitatively comparing
clusterings; clustering comparison is the basis for many tasks such as
clustering evaluation, consensus clustering, and tracking the temporal
evolution of clusters. In particular, the extrinsic evaluation of clustering
methods requires comparing the uncovered clusterings to planted clusterings or
known metadata. Yet, as we demonstrate, existing clustering comparison measures
have critical biases which undermine their usefulness, and no measure
accommodates both overlapping and hierarchical clusterings. Here we unify the
comparison of disjoint, overlapping, and hierarchically structured clusterings
by proposing a new element-centric framework: elements are compared based on
the relationships induced by the cluster structure, as opposed to the
traditional cluster-centric philosophy. We demonstrate that, in contrast to
standard clustering similarity measures, our framework does not suffer from
critical biases and naturally provides unique insights into how the clusterings
differ. We illustrate the strengths of our framework by revealing new insights
into the organization of clusters in two applications: the improved
classification of schizophrenia based on the overlapping and hierarchical
community structure of fMRI brain networks, and the disentanglement of various
social homophily factors in Facebook social networks. The universality of
clustering suggests far-reaching impact of our framework throughout all areas
of science
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
Dynamical affinity in opinion dynamics modelling
We here propose a model to simulate the process of opinion formation, which
accounts for the mutual affinity between interacting agents. Opinion and
affinity evolve self-consistently, manifesting a highly non trivial interplay.
A continuous transition is found between single and multiple opinion states.
Fractal dimension and signature of critical behaviour are also reported. A rich
phenomenology is presented and discussed with reference to corresponding
psychological implications
Extracting the hierarchical organization of complex systems
Extracting understanding from the growing ``sea'' of biological and
socio-economic data is one of the most pressing scientific challenges facing
us. Here, we introduce and validate an unsupervised method that is able to
accurately extract the hierarchical organization of complex biological, social,
and technological networks. We define an ensemble of hierarchically nested
random graphs, which we use to validate the method. We then apply our method to
real-world networks, including the air-transportation network, an electronic
circuit, an email exchange network, and metabolic networks. We find that our
method enables us to obtain an accurate multi-scale descriptions of a complex
system.Comment: Figures in screen resolution. Version with full resolution figures
available at
http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd
Modeling Social Networks with Node Attributes using the Multiplicative Attribute Graph Model
Networks arising from social, technological and natural domains exhibit rich
connectivity patterns and nodes in such networks are often labeled with
attributes or features. We address the question of modeling the structure of
networks where nodes have attribute information. We present a Multiplicative
Attribute Graph (MAG) model that considers nodes with categorical attributes
and models the probability of an edge as the product of individual attribute
link formation affinities. We develop a scalable variational expectation
maximization parameter estimation method. Experiments show that MAG model
reliably captures network connectivity as well as provides insights into how
different attributes shape the network structure.Comment: 15 pages, 7 figures, 7 table
Opinion Dynamics in an Open Community
We here discuss the process of opinion formation in an open community where
agents are made to interact and consequently update their beliefs. New actors
(birth) are assumed to replace individuals that abandon the community (deaths).
This dynamics is simulated in the framework of a simplified model that accounts
for mutual affinity between agents. A rich phenomenology is presented and
discussed with reference to the original (closed group) setting. Numerical
findings are supported by analytical calculations
- …