38,740 research outputs found
Clustering and Community Detection with Imbalanced Clusters
Spectral clustering methods which are frequently used in clustering and
community detection applications are sensitive to the specific graph
constructions particularly when imbalanced clusters are present. We show that
ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to
imbalanced cluster sizes since they tend to emphasize cut sizes over cut
values. We propose a graph partitioning problem that seeks minimum cut
partitions under minimum size constraints on partitions to deal with imbalanced
cluster sizes. Our approach parameterizes a family of graphs by adaptively
modulating node degrees on a fixed node set, yielding a set of parameter
dependent cuts reflecting varying levels of imbalance. The solution to our
problem is then obtained by optimizing over these parameters. We present
rigorous limit cut analysis results to justify our approach and demonstrate the
superiority of our method through experiments on synthetic and real datasets
for data clustering, semi-supervised learning and community detection.Comment: Extended version of arXiv:1309.2303 with new applications. Accepted
to IEEE TSIP
Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions
Genetic regulatory networks (GRNs) have been widely studied, yet there is a
lack of understanding with regards to the final size and properties of these
networks, mainly due to no network currently being complete. In this study, we
analyzed the distribution of GRN structural properties across a large set of
distinct prokaryotic organisms and found a set of constrained characteristics
such as network density and number of regulators. Our results allowed us to
estimate the number of interactions that complete networks would have, a
valuable insight that could aid in the daunting task of network curation,
prediction, and validation. Using state-of-the-art statistical approaches, we
also provided new evidence to settle a previously stated controversy that
raised the possibility of complete biological networks being random and
therefore attributing the observed scale-free properties to an artifact
emerging from the sampling process during network discovery. Furthermore, we
identified a set of properties that enabled us to assess the consistency of the
connectivity distribution for various GRNs against different alternative
statistical distributions. Our results favor the hypothesis that highly
connected nodes (hubs) are not a consequence of network incompleteness.
Finally, an interaction coverage computed for the GRNs as a proxy for
completeness revealed that high-throughput based reconstructions of GRNs could
yield biased networks with a low average clustering coefficient, showing that
classical targeted discovery of interactions is still needed.Comment: 28 pages, 5 figures, 12 pages supplementary informatio
Spectral Clustering with Imbalanced Data
Spectral clustering is sensitive to how graphs are constructed from data
particularly when proximal and imbalanced clusters are present. We show that
Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to
imbalanced data since they tend to emphasize cut sizes over cut values. We
propose a graph partitioning problem that seeks minimum cut partitions under
minimum size constraints on partitions to deal with imbalanced data. Our
approach parameterizes a family of graphs, by adaptively modulating node
degrees on a fixed node set, to yield a set of parameter dependent cuts
reflecting varying levels of imbalance. The solution to our problem is then
obtained by optimizing over these parameters. We present rigorous limit cut
analysis results to justify our approach. We demonstrate the superiority of our
method through unsupervised and semi-supervised experiments on synthetic and
real data sets.Comment: 24 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1302.513
- …