14 research outputs found
Higher-Order Spectral Clustering for Geometric Graphs
The present paper is devoted to clustering geometric graphs. While the
standard spectral clustering is often not effective for geometric graphs, we
present an effective generalization, which we call higher-order spectral
clustering. It resembles in concept the classical spectral clustering method
but uses for partitioning the eigenvector associated with a higher-order
eigenvalue. We establish the weak consistency of this algorithm for a wide
class of geometric graphs which we call Soft Geometric Block Model. A small
adjustment of the algorithm provides strong consistency. We also show that our
method is effective in numerical experiments even for graphs of modest size.Comment: 23 pages, 6 figure
Improved bounds for noisy group testing with constant tests per item
The group testing problem is concerned with identifying a small set of
infected individuals in a large population. At our disposal is a testing
procedure that allows us to test several individuals together. In an idealized
setting, a test is positive if and only if at least one infected individual is
included and negative otherwise. Significant progress was made in recent years
towards understanding the information-theoretic and algorithmic properties in
this noiseless setting. In this paper, we consider a noisy variant of group
testing where test results are flipped with certain probability, including the
realistic scenario where sensitivity and specificity can take arbitrary values.
Using a test design where each individual is assigned to a fixed number of
tests, we derive explicit algorithmic bounds for two commonly considered
inference algorithms and thereby naturally extend the results of Scarlett \&
Cevher (2016) and Scarlett \& Johnson (2020). We provide improved performance
guarantees for the efficient algorithms in these noisy group testing models --
indeed, for a large set of parameter choices the bounds provided in the paper
are the strongest currently proved
Improved bounds for noisy group testing with constant tests per item
The group testing problem is concerned with identifying a small set of
infected individuals in a large population. At our disposal is a testing
procedure that allows us to test several individuals together. In an idealized
setting, a test is positive if and only if at least one infected individual is
included and negative otherwise. Significant progress was made in recent years
towards understanding the information-theoretic and algorithmic properties in
this noiseless setting. In this paper, we consider a noisy variant of group
testing where test results are flipped with certain probability, including the
realistic scenario where sensitivity and specificity can take arbitrary values.
Using a test design where each individual is assigned to a fixed number of
tests, we derive explicit algorithmic bounds for two commonly considered
inference algorithms and thereby naturally extend the results of Scarlett \&
Cevher (2016) and Scarlett \& Johnson (2020). We provide improved performance
guarantees for the efficient algorithms in these noisy group testing models --
indeed, for a large set of parameter choices the bounds provided in the paper
are the strongest currently proved