59,406 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks
Recent advances in electronics are enabling substantial processing to be
performed at each node (robots, sensors) of a networked system. Local
processing enables data compression and may mitigate measurement noise, but it
is still slower compared to a central computer (it entails a larger
computational delay). However, while nodes can process the data in parallel,
the centralized computational is sequential in nature. On the other hand, if a
node sends raw data to a central computer for processing, it incurs
communication delay. This leads to a fundamental communication-computation
trade-off, where each node has to decide on the optimal amount of preprocessing
in order to maximize the network performance. We consider a network in charge
of estimating the state of a dynamical system and provide three contributions.
First, we provide a rigorous problem formulation for optimal real-time
estimation in processing networks in the presence of delays. Second, we show
that, in the case of a homogeneous network (where all sensors have the same
computation) that monitors a continuous-time scalar linear system, the optimal
amount of local preprocessing maximizing the network estimation performance can
be computed analytically. Third, we consider the realistic case of a
heterogeneous network monitoring a discrete-time multi-variate linear system
and provide algorithms to decide on suitable preprocessing at each node, and to
select a sensor subset when computational constraints make using all sensors
suboptimal. Numerical simulations show that selecting the sensors is crucial.
Moreover, we show that if the nodes apply the preprocessing policy suggested by
our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio
Holographic particle localization under multiple scattering
We introduce a novel framework that incorporates multiple scattering for
large-scale 3D particle-localization using single-shot in-line holography.
Traditional holographic techniques rely on single-scattering models which
become inaccurate under high particle-density. We demonstrate that by
exploiting multiple-scattering, localization is significantly improved. Both
forward and back-scattering are computed by our method under a tractable
recursive framework, in which each recursion estimates the next higher-order
field within the volume. The inverse scattering is presented as a nonlinear
optimization that promotes sparsity, and can be implemented efficiently. We
experimentally reconstruct 100 million object voxels from a single 1-megapixel
hologram. Our work promises utilization of multiple scattering for versatile
large-scale applications
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