17 research outputs found
Estimating the number of communities in weighted networks
Community detection in weighted networks has been a popular topic in recent
years. However, while there exist several flexible methods for estimating
communities in weighted networks, these methods usually assume that the number
of communities is known. It is usually unclear how to determine the exact
number of communities one should use. Here, to estimate the number of
communities for weighted networks generated from arbitrary distribution under
the degree-corrected distribution-free model, we propose one approach that
combines weighted modularity with spectral clustering. This approach allows a
weighted network to have negative edge weights and it also works for signed
networks. We compare the proposed method to several existing methods and show
that our method is more accurate for estimating the number of communities both
numerically and empirically
Latent class analysis by regularized spectral clustering
The latent class model is a powerful tool for identifying latent classes
within populations that share common characteristics for categorical data in
social, psychological, and behavioral sciences. In this article, we propose two
new algorithms to estimate a latent class model for categorical data. Our
algorithms are developed by using a newly defined regularized Laplacian matrix
calculated from the response matrix. We provide theoretical convergence rates
of our algorithms by considering a sparsity parameter and show that our
algorithms stably yield consistent latent class analysis under mild conditions.
Additionally, we propose a metric to capture the strength of latent class
analysis and several procedures designed based on this metric to infer how many
latent classes one should use for real-world categorical data. The efficiency
and accuracy of our algorithms are verified by extensive simulated experiments,
and we further apply our algorithms to real-world categorical data with
promising results.Comment: 22 pages, 7 figures, 2 table
Degree-corrected distribution-free model for community detection in weighted networks
A degree-corrected distribution-free model is proposed for weighted social
networks with latent structural information. The model extends the previous
distribution-free models by considering variation in node degree to fit
real-world weighted networks, and it also extends the classical
degree-corrected stochastic block model from un-weighted network to weighted
network. We design an algorithm based on the idea of spectral clustering to fit
the model. Theoretical framework on consistent estimation for the algorithm is
developed under the model. Theoretical results when edge weights are generated
from different distributions are analyzed. We also propose a general modularity
as an extension of Newman's modularity from un-weighted network to weighted
network. Using experiments with simulated and real-world networks, we show that
our method significantly outperforms the uncorrected one, and the general
modularity is effective.Comment: 21 pages, 11 figures, 5 tables, comments are welcom