4,916 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
SVD, discrepancy, and regular structure of contingency tables
We will use the factors obtained by correspondence analysis to find
biclustering of a contingency table such that the row-column cluster pairs are
regular, i.e., they have small discrepancy. In our main theorem, the constant
of the so-called volume-regularity is related to the SVD of the normalized
contingency table. Our result is applicable to two-way cuts when both the rows
and columns are divided into the same number of clusters, thus extending partly
the result of Butler estimating the discrepancy of a contingency table by the
second largest singular value of the normalized table (one-cluster, rectangular
case), and partly a former result of the author for estimating the constant of
volume-regularity by the structural eigenvalues and the distances of the
corresponding eigen-subspaces of the normalized modularity matrix of an
edge-weighted graph (several clusters, symmetric case)
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
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