7,615 research outputs found
Temporal Ordered Clustering in Dynamic Networks: Unsupervised and Semi-supervised Learning Algorithms
In temporal ordered clustering, given a single snapshot of a dynamic network
in which nodes arrive at distinct time instants, we aim at partitioning its
nodes into ordered clusters such that for , nodes in cluster arrived
before nodes in cluster , with being a data-driven parameter
and not known upfront. Such a problem is of considerable significance in many
applications ranging from tracking the expansion of fake news to mapping the
spread of information. We first formulate our problem for a general dynamic
graph, and propose an integer programming framework that finds the optimal
clustering, represented as a strict partial order set, achieving the best
precision (i.e., fraction of successfully ordered node pairs) for a fixed
density (i.e., fraction of comparable node pairs). We then develop a sequential
importance procedure and design unsupervised and semi-supervised algorithms to
find temporal ordered clusters that efficiently approximate the optimal
solution. To illustrate the techniques, we apply our methods to the vertex
copying (duplication-divergence) model which exhibits some edge-case challenges
in inferring the clusters as compared to other network models. Finally, we
validate the performance of the proposed algorithms on synthetic and real-world
networks.Comment: 14 pages, 9 figures, and 3 tables. This version is submitted to a
journal. A shorter version of this work is published in the proceedings of
IEEE International Symposium on Information Theory (ISIT), 2020. The first
two authors contributed equall
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Modularity and anti-modularity in networks with arbitrary degree distribution
Networks describing the interaction of the elements that constitute a complex
system grow and develop via a number of different mechanisms, such as the
addition and deletion of nodes, the addition and deletion of edges, as well as
the duplication or fusion of nodes. While each of these mechanisms can have a
different cause depending on whether the network is biological, technological,
or social, their impact on the network's structure, as well as its local and
global properties, is similar. This allows us to study how each of these
mechanisms affects networks either alone or together with the other processes,
and how they shape the characteristics that have been observed. We study how a
network's growth parameters impact the distribution of edges in the network,
how they affect a network's modularity, and point out that some parameters will
give rise to networks that have the opposite tendency, namely to display
anti-modularity. Within the model we are describing, we can search the space of
possible networks for parameter sets that generate networks that are very
similar to well-known and well-studied examples, such as the brain of a worm,
and the network of interactions of the proteins in baker's yeast.Comment: 23 pages. 13 figures, 1 table. Includes Supplementary tex
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