Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved clustering algorithms for the Bipartite Stochastic Block Model   We establish sufficient conditions of exact and almost full recovery of the
node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time
algorithms. First, we improve upon the known conditions of almost full recovery
by spectral clustering algorithms in BSBM. Next, we propose a new
computationally simple and fast procedure achieving exact recovery under milder
conditions than the state of the art. Namely, if the vertex sets $V_1$ and
$V_2$ in BSBM have sizes $n_1$ and $n_2$, we show that the condition $p =
\Omega\left(\max\left(\sqrt{\frac{\log{n_1}}{n_1n_2}},\frac{\log{n_1}}{n_2}\right)\right)$
on the edge intensity $p$ is sufficient for exact recovery witin $V_1$. This
condition exhibits an elbow at $n_{2} \asymp n_1\log{n_1}$ between the
low-dimensional and high-dimensional regimes. The suggested procedure is a
variant of Lloyd's iterations initialized with a well-chosen spectral estimator
leading to what we expect to be the optimal condition for exact recovery in
BSBM. {The optimality conjecture is supported by showing that, for a supervised
oracle procedure, such a condition is necessary to achieve exact recovery.} The
key elements of the proof techniques are different from classical community
detection tools on random graphs. Numerical studies confirm our theory, and
show that the suggested algorithm is both very fast and achieves {almost the
same} performance as the supervised oracle. Finally, using the connection
between planted satisfiability problems and the BSBM, we improve upon the
sufficient number of clauses to completely recover the planted assignment.

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin