2,299 research outputs found
Batch kernel SOM and related Laplacian methods for social network analysis
Large graphs are natural mathematical models for describing the structure of
the data in a wide variety of fields, such as web mining, social networks,
information retrieval, biological networks, etc. For all these applications,
automatic tools are required to get a synthetic view of the graph and to reach
a good understanding of the underlying problem. In particular, discovering
groups of tightly connected vertices and understanding the relations between
those groups is very important in practice. This paper shows how a kernel
version of the batch Self Organizing Map can be used to achieve these goals via
kernels derived from the Laplacian matrix of the graph, especially when it is
used in conjunction with more classical methods based on the spectral analysis
of the graph. The proposed method is used to explore the structure of a
medieval social network modeled through a weighted graph that has been directly
built from a large corpus of agrarian contracts
Similarities on Graphs: Kernels versus Proximity Measures
We analytically study proximity and distance properties of various kernels
and similarity measures on graphs. This helps to understand the mathematical
nature of such measures and can potentially be useful for recommending the
adoption of specific similarity measures in data analysis.Comment: 16 page
Applications of Structural Balance in Signed Social Networks
We present measures, models and link prediction algorithms based on the
structural balance in signed social networks. Certain social networks contain,
in addition to the usual 'friend' links, 'enemy' links. These networks are
called signed social networks. A classical and major concept for signed social
networks is that of structural balance, i.e., the tendency of triangles to be
'balanced' towards including an even number of negative edges, such as
friend-friend-friend and friend-enemy-enemy triangles. In this article, we
introduce several new signed network analysis methods that exploit structural
balance for measuring partial balance, for finding communities of people based
on balance, for drawing signed social networks, and for solving the problem of
link prediction. Notably, the introduced methods are based on the signed graph
Laplacian and on the concept of signed resistance distances. We evaluate our
methods on a collection of four signed social network datasets.Comment: 37 page
Empirical stationary correlations for semi-supervised learning on graphs
In semi-supervised learning on graphs, response variables observed at one
node are used to estimate missing values at other nodes. The methods exploit
correlations between nearby nodes in the graph. In this paper we prove that
many such proposals are equivalent to kriging predictors based on a fixed
covariance matrix driven by the link structure of the graph. We then propose a
data-driven estimator of the correlation structure that exploits patterns among
the observed response values. By incorporating even a small fraction of
observed covariation into the predictions, we are able to obtain much improved
prediction on two graph data sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS293 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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