18 research outputs found
Partial recovery bounds for clustering with the relaxed means
We investigate the clustering performances of the relaxed means in the
setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM).
After identifying the appropriate signal-to-noise ratio (SNR), we prove that
the misclassification error decay exponentially fast with respect to this SNR.
These partial recovery bounds for the relaxed means improve upon results
currently known in the sGMM setting. In the SBM setting, applying the relaxed
means SDP allows to handle general connection probabilities whereas other
SDPs investigated in the literature are restricted to the assortative case
(where within group probabilities are larger than between group probabilities).
Again, this partial recovery bound complements the state-of-the-art results.
All together, these results put forward the versatility of the relaxed
means.Comment: 39 page
Inference in the Stochastic Block Model with a Markovian assignment of the communities
We tackle the community detection problem in the Stochastic Block Model (SBM)
when the communities of the nodes of the graph are assigned with a Markovian
dynamic. To recover the partition of the nodes, we adapt the relaxed K-means
SDP program presented in [11]. We identify the relevant signal-to-noise ratio
(SNR) in our framework and we prove that the misclassification error decays
exponentially fast with respect to this SNR. We provide infinity norm
consistent estimation of the parameters of our model and we discuss our results
through the prism of classical degree regimes of the SBMs' literature. MSC 2010
subject classifications: Primary 68Q32; secondary 68R10, 90C35
Clustering multilayer graphs with missing nodes
Relationship between agents can be conveniently represented by graphs. When
these relationships have different modalities, they are better modelled by
multilayer graphs where each layer is associated with one modality. Such graphs
arise naturally in many contexts including biological and social networks.
Clustering is a fundamental problem in network analysis where the goal is to
regroup nodes with similar connectivity profiles. In the past decade, various
clustering methods have been extended from the unilayer setting to multilayer
graphs in order to incorporate the information provided by each layer. While
most existing works assume - rather restrictively - that all layers share the
same set of nodes, we propose a new framework that allows for layers to be
defined on different sets of nodes. In particular, the nodes not recorded in a
layer are treated as missing. Within this paradigm, we investigate several
generalizations of well-known clustering methods in the complete setting to the
incomplete one and prove some consistency results under the Multi-Layer
Stochastic Block Model assumption. Our theoretical results are complemented by
thorough numerical comparisons between our proposed algorithms on synthetic
data, and also on real datasets, thus highlighting the promising behaviour of
our methods in various settings.Comment: 27 pages, 7 figures, accepted to AISTATS 202