322,666 research outputs found
Metric clusters in evolutionary games on scale-free networks
The evolution of cooperation in social dilemmas in structured populations has
been studied extensively in recent years. Whereas many theoretical studies have
found that a heterogeneous network of contacts favors cooperation, the impact
of spatial effects in scale-free networks is still not well understood. In
addition to being heterogeneous, real contact networks exhibit a high mean
local clustering coefficient, which implies the existence of an underlying
metric space. Here, we show that evolutionary dynamics in scale-free networks
self-organize into spatial patterns in the underlying metric space. The
resulting metric clusters of cooperators are able to survive in social dilemmas
as their spatial organization shields them from surrounding defectors, similar
to spatial selection in Euclidean space. We show that under certain conditions
these metric clusters are more efficient than the most connected nodes at
sustaining cooperation and that heterogeneity does not always favor--but can
even hinder--cooperation in social dilemmas. Our findings provide a new
perspective to understand the emergence of cooperation in evolutionary games in
realistic structured populations
The Metric Space of Networks
We study the question of reconstructing a weighted, directed network up to
isomorphism from its motifs. In order to tackle this question we first relax
the usual (strong) notion of graph isomorphism to obtain a relaxation that we
call weak isomorphism. Then we identify a definition of distance on the space
of all networks that is compatible with weak isomorphism. This global approach
comes equipped with notions such as completeness, compactness, curves, and
geodesics, which we explore throughout this paper. Furthermore, it admits
global-to-local inference in the following sense: we prove that two networks
are weakly isomorphic if and only if all their motif sets are identical, thus
answering the network reconstruction question. Further exploiting the
additional structure imposed by our network distance, we prove that two
networks are weakly isomorphic if and only if certain essential associated
structures---the skeleta of the respective networks---are strongly isomorphic
Self-organized Emergence of Navigability on Small-World Networks
This paper mainly investigates why small-world networks are navigable and how
to navigate small-world networks. We find that the navigability can naturally
emerge from self-organization in the absence of prior knowledge about
underlying reference frames of networks. Through a process of information
exchange and accumulation on networks, a hidden metric space for navigation on
networks is constructed. Navigation based on distances between vertices in the
hidden metric space can efficiently deliver messages on small-world networks,
in which long range connections play an important role. Numerical simulations
further suggest that high cluster coefficient and low diameter are both
necessary for navigability. These interesting results provide profound insights
into scalable routing on the Internet due to its distributed and localized
requirements.Comment: 3 figure
Geometric Graph Properties of the Spatial Preferred Attachment model
The spatial preferred attachment (SPA) model is a model for networked
information spaces such as domains of the World Wide Web, citation graphs, and
on-line social networks. It uses a metric space to model the hidden attributes
of the vertices. Thus, vertices are elements of a metric space, and link
formation depends on the metric distance between vertices. We show, through
theoretical analysis and simulation, that for graphs formed according to the
SPA model it is possible to infer the metric distance between vertices from the
link structure of the graph. Precisely, the estimate is based on the number of
common neighbours of a pair of vertices, a measure known as {\sl co-citation}.
To be able to calculate this estimate, we derive a precise relation between the
number of common neighbours and metric distance. We also analyze the
distribution of {\sl edge lengths}, where the length of an edge is the metric
distance between its end points. We show that this distribution has three
different regimes, and that the tail of this distribution follows a power law
Deep Metric Learning via Facility Location
Learning the representation and the similarity metric in an end-to-end
fashion with deep networks have demonstrated outstanding results for clustering
and retrieval. However, these recent approaches still suffer from the
performance degradation stemming from the local metric training procedure which
is unaware of the global structure of the embedding space.
We propose a global metric learning scheme for optimizing the deep metric
embedding with the learnable clustering function and the clustering metric
(NMI) in a novel structured prediction framework.
Our experiments on CUB200-2011, Cars196, and Stanford online products
datasets show state of the art performance both on the clustering and retrieval
tasks measured in the NMI and Recall@K evaluation metrics.Comment: Submission accepted at CVPR 201
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