87,209 research outputs found
Average mixing matrix of trees
We investigate the rank of the average mixing matrix of trees, with all
eigenvalues distinct. The rank of the average mixing matrix of a tree on
vertices with distinct eigenvalues is upper-bounded by .
Computations on trees up to vertices suggest that the rank attains this
upper bound most of the times. We give an infinite family of trees whose
average mixing matrices have ranks which are bounded away from this upper
bound. We also give a lower bound on the rank of the average mixing matrix of a
tree.Comment: 18 pages, 2 figures, 3 table
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Preserving Link Privacy in Social Network Based Systems
A growing body of research leverages social network based trust relationships
to improve the functionality of the system. However, these systems expose
users' trust relationships, which is considered sensitive information in
today's society, to an adversary.
In this work, we make the following contributions. First, we propose an
algorithm that perturbs the structure of a social graph in order to provide
link privacy, at the cost of slight reduction in the utility of the social
graph. Second we define general metrics for characterizing the utility and
privacy of perturbed graphs. Third, we evaluate the utility and privacy of our
proposed algorithm using real world social graphs. Finally, we demonstrate the
applicability of our perturbation algorithm on a broad range of secure systems,
including Sybil defenses and secure routing.Comment: 16 pages, 15 figure
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