21,595 research outputs found
Crime incidents embedding using restricted Boltzmann machines
We present a new approach for detecting related crime series, by unsupervised
learning of the latent feature embeddings from narratives of crime record via
the Gaussian-Bernoulli Restricted Boltzmann Machines (RBM). This is a
drastically different approach from prior work on crime analysis, which
typically considers only time and location and at most category information.
After the embedding, related cases are closer to each other in the Euclidean
feature space, and the unrelated cases are far apart, which is a good property
can enable subsequent analysis such as detection and clustering of related
cases. Experiments over several series of related crime incidents hand labeled
by the Atlanta Police Department reveal the promise of our embedding methods.Comment: 5 pages, 3 figure
Poisson Matrix Completion
We extend the theory of matrix completion to the case where we make Poisson
observations for a subset of entries of a low-rank matrix. We consider the
(now) usual matrix recovery formulation through maximum likelihood with proper
constraints on the matrix , and establish theoretical upper and lower bounds
on the recovery error. Our bounds are nearly optimal up to a factor on the
order of . These bounds are obtained by adapting
the arguments used for one-bit matrix completion \cite{davenport20121}
(although these two problems are different in nature) and the adaptation
requires new techniques exploiting properties of the Poisson likelihood
function and tackling the difficulties posed by the locally sub-Gaussian
characteristic of the Poisson distribution. Our results highlight a few
important distinctions of Poisson matrix completion compared to the prior work
in matrix completion including having to impose a minimum signal-to-noise
requirement on each observed entry. We also develop an efficient iterative
algorithm and demonstrate its good performance in recovering solar flare
images.Comment: Submitted to IEEE for publicatio
Dynamic change-point detection using similarity networks
From a sequence of similarity networks, with edges representing certain
similarity measures between nodes, we are interested in detecting a
change-point which changes the statistical property of the networks. After the
change, a subset of anomalous nodes which compares dissimilarly with the normal
nodes. We study a simple sequential change detection procedure based on
node-wise average similarity measures, and study its theoretical property.
Simulation and real-data examples demonstrate such a simply stopping procedure
has reasonably good performance. We further discuss the faulty sensor isolation
(estimating anomalous nodes) using community detection.Comment: appeared in Asilomar Conference 201
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