43,416 research outputs found
Fine-grained Graph Learning for Multi-view Subspace Clustering
Multi-view subspace clustering (MSC) is a popular unsupervised method by
integrating heterogeneous information to reveal the intrinsic clustering
structure hidden across views. Usually, MSC methods use graphs (or affinity
matrices) fusion to learn a common structure, and further apply graph-based
approaches to clustering. Despite progress, most of the methods do not
establish the connection between graph learning and clustering. Meanwhile,
conventional graph fusion strategies assign coarse-grained weights to combine
multi-graph, ignoring the importance of local structure. In this paper, we
propose a fine-grained graph learning framework for multi-view subspace
clustering (FGL-MSC) to address these issues. To utilize the multi-view
information sufficiently, we design a specific graph learning method by
introducing graph regularization and local structure fusion pattern. The main
challenge is how to optimize the fine-grained fusion weights while generating
the learned graph that fits the clustering task, thus making the clustering
representation meaningful and competitive. Accordingly, an iterative algorithm
is proposed to solve the above joint optimization problem, which obtains the
learned graph, the clustering representation, and the fusion weights
simultaneously. Extensive experiments on eight real-world datasets show that
the proposed framework has comparable performance to the state-of-the-art
methods
Parallel Graph Partitioning for Complex Networks
Processing large complex networks like social networks or web graphs has
recently attracted considerable interest. In order to do this in parallel, we
need to partition them into pieces of about equal size. Unfortunately, previous
parallel graph partitioners originally developed for more regular mesh-like
networks do not work well for these networks. This paper addresses this problem
by parallelizing and adapting the label propagation technique originally
developed for graph clustering. By introducing size constraints, label
propagation becomes applicable for both the coarsening and the refinement phase
of multilevel graph partitioning. We obtain very high quality by applying a
highly parallel evolutionary algorithm to the coarsened graph. The resulting
system is both more scalable and achieves higher quality than state-of-the-art
systems like ParMetis or PT-Scotch. For large complex networks the performance
differences are very big. For example, our algorithm can partition a web graph
with 3.3 billion edges in less than sixteen seconds using 512 cores of a high
performance cluster while producing a high quality partition -- none of the
competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach
arXiv:1402.328
Partitioning Complex Networks via Size-constrained Clustering
The most commonly used method to tackle the graph partitioning problem in
practice is the multilevel approach. During a coarsening phase, a multilevel
graph partitioning algorithm reduces the graph size by iteratively contracting
nodes and edges until the graph is small enough to be partitioned by some other
algorithm. A partition of the input graph is then constructed by successively
transferring the solution to the next finer graph and applying a local search
algorithm to improve the current solution.
In this paper, we describe a novel approach to partition graphs effectively
especially if the networks have a highly irregular structure. More precisely,
our algorithm provides graph coarsening by iteratively contracting
size-constrained clusterings that are computed using a label propagation
algorithm. The same algorithm that provides the size-constrained clusterings
can also be used during uncoarsening as a fast and simple local search
algorithm.
Depending on the algorithm's configuration, we are able to compute partitions
of very high quality outperforming all competitors, or partitions that are
comparable to the best competitor in terms of quality, hMetis, while being
nearly an order of magnitude faster on average. The fastest configuration
partitions the largest graph available to us with 3.3 billion edges using a
single machine in about ten minutes while cutting less than half of the edges
than the fastest competitor, kMetis
Hearing the clusters in a graph: A distributed algorithm
We propose a novel distributed algorithm to cluster graphs. The algorithm
recovers the solution obtained from spectral clustering without the need for
expensive eigenvalue/vector computations. We prove that, by propagating waves
through the graph, a local fast Fourier transform yields the local component of
every eigenvector of the Laplacian matrix, thus providing clustering
information. For large graphs, the proposed algorithm is orders of magnitude
faster than random walk based approaches. We prove the equivalence of the
proposed algorithm to spectral clustering and derive convergence rates. We
demonstrate the benefit of using this decentralized clustering algorithm for
community detection in social graphs, accelerating distributed estimation in
sensor networks and efficient computation of distributed multi-agent search
strategies
Distance-Dependent Kronecker Graphs for Modeling Social Networks
This paper focuses on a generalization of stochastic
Kronecker graphs, introducing a Kronecker-like operator and
defining a family of generator matrices H dependent on distances
between nodes in a specified graph embedding. We prove
that any lattice-based network model with sufficiently small
distance-dependent connection probability will have a Poisson
degree distribution and provide a general framework to prove
searchability for such a network. Using this framework, we focus
on a specific example of an expanding hypercube and discuss
the similarities and differences of such a model with recently
proposed network models based on a hidden metric space. We
also prove that a greedy forwarding algorithm can find very short
paths of length O((log log n)^2) on the hypercube with n nodes,
demonstrating that distance-dependent Kronecker graphs can
generate searchable network models
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