236 research outputs found
Multimodal Network Alignment
A multimodal network encodes relationships between the same set of nodes in
multiple settings, and network alignment is a powerful tool for transferring
information and insight between a pair of networks. We propose a method for
multimodal network alignment that computes a matrix which indicates the
alignment, but produces the result as a low-rank factorization directly. We
then propose new methods to compute approximate maximum weight matchings of
low-rank matrices to produce an alignment. We evaluate our approach by applying
it on synthetic networks and use it to de-anonymize a multimodal transportation
network.Comment: 14 pages, 6 figures, Siam Data Mining 201
Unifying Sparsest Cut, Cluster Deletion, and Modularity Clustering Objectives with Correlation Clustering
Graph clustering, or community detection, is the task of identifying groups
of closely related objects in a large network. In this paper we introduce a new
community-detection framework called LambdaCC that is based on a specially
weighted version of correlation clustering. A key component in our methodology
is a clustering resolution parameter, , which implicitly controls the
size and structure of clusters formed by our framework. We show that, by
increasing this parameter, our objective effectively interpolates between two
different strategies in graph clustering: finding a sparse cut and forming
dense subgraphs. Our methodology unifies and generalizes a number of other
important clustering quality functions including modularity, sparsest cut, and
cluster deletion, and places them all within the context of an optimization
problem that has been well studied from the perspective of approximation
algorithms. Our approach is particularly relevant in the regime of finding
dense clusters, as it leads to a 2-approximation for the cluster deletion
problem. We use our approach to cluster several graphs, including large
collaboration networks and social networks
Using Triangles to Improve Community Detection in Directed Networks
In a graph, a community may be loosely defined as a group of nodes that are
more closely connected to one another than to the rest of the graph. While
there are a variety of metrics that can be used to specify the quality of a
given community, one common theme is that flows tend to stay within
communities. Hence, we expect cycles to play an important role in community
detection. For undirected graphs, the importance of triangles -- an undirected
3-cycle -- has been known for a long time and can be used to improve community
detection. In directed graphs, the situation is more nuanced. The smallest
cycle is simply two nodes with a reciprocal connection, and using information
about reciprocation has proven to improve community detection. Our new idea is
based on the four types of directed triangles that contain cycles. To identify
communities in directed networks, then, we propose an undirected edge-weighting
scheme based on the type of the directed triangles in which edges are involved.
We also propose a new metric on quality of the communities that is based on the
number of 3-cycles that are split across communities. To demonstrate the impact
of our new weighting, we use the standard METIS graph partitioning tool to
determine communities and show experimentally that the resulting communities
result in fewer 3-cycles being cut. The magnitude of the effect varies between
a 10 and 50% reduction, and we also find evidence that this weighting scheme
improves a task where plausible ground-truth communities are known.Comment: 10 pages, 3 figure
- …