75,361 research outputs found
Gravitational Clustering: A Simple, Robust and Adaptive Approach for Distributed Networks
Distributed signal processing for wireless sensor networks enables that
different devices cooperate to solve different signal processing tasks. A
crucial first step is to answer the question: who observes what? Recently,
several distributed algorithms have been proposed, which frame the
signal/object labelling problem in terms of cluster analysis after extracting
source-specific features, however, the number of clusters is assumed to be
known. We propose a new method called Gravitational Clustering (GC) to
adaptively estimate the time-varying number of clusters based on a set of
feature vectors. The key idea is to exploit the physical principle of
gravitational force between mass units: streaming-in feature vectors are
considered as mass units of fixed position in the feature space, around which
mobile mass units are injected at each time instant. The cluster enumeration
exploits the fact that the highest attraction on the mobile mass units is
exerted by regions with a high density of feature vectors, i.e., gravitational
clusters. By sharing estimates among neighboring nodes via a
diffusion-adaptation scheme, cooperative and distributed cluster enumeration is
achieved. Numerical experiments concerning robustness against outliers,
convergence and computational complexity are conducted. The application in a
distributed cooperative multi-view camera network illustrates the applicability
to real-world problems.Comment: 12 pages, 9 figure
Mapping Topographic Structure in White Matter Pathways with Level Set Trees
Fiber tractography on diffusion imaging data offers rich potential for
describing white matter pathways in the human brain, but characterizing the
spatial organization in these large and complex data sets remains a challenge.
We show that level set trees---which provide a concise representation of the
hierarchical mode structure of probability density functions---offer a
statistically-principled framework for visualizing and analyzing topography in
fiber streamlines. Using diffusion spectrum imaging data collected on
neurologically healthy controls (N=30), we mapped white matter pathways from
the cortex into the striatum using a deterministic tractography algorithm that
estimates fiber bundles as dimensionless streamlines. Level set trees were used
for interactive exploration of patterns in the endpoint distributions of the
mapped fiber tracks and an efficient segmentation of the tracks that has
empirical accuracy comparable to standard nonparametric clustering methods. We
show that level set trees can also be generalized to model pseudo-density
functions in order to analyze a broader array of data types, including entire
fiber streamlines. Finally, resampling methods show the reliability of the
level set tree as a descriptive measure of topographic structure, illustrating
its potential as a statistical descriptor in brain imaging analysis. These
results highlight the broad applicability of level set trees for visualizing
and analyzing high-dimensional data like fiber tractography output
Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
In this work, we propose a novel method for quantifying distances between
Toeplitz structured covariance matrices. By exploiting the spectral
representation of Toeplitz matrices, the proposed distance measure is defined
based on an optimal mass transport problem in the spectral domain. This may
then be interpreted in the covariance domain, suggesting a natural way of
interpolating and extrapolating Toeplitz matrices, such that the positive
semi-definiteness and the Toeplitz structure of these matrices are preserved.
The proposed distance measure is also shown to be contractive with respect to
both additive and multiplicative noise, and thereby allows for a quantification
of the decreased distance between signals when these are corrupted by noise.
Finally, we illustrate how this approach can be used for several applications
in signal processing. In particular, we consider interpolation and
extrapolation of Toeplitz matrices, as well as clustering problems and tracking
of slowly varying stochastic processes
DIAMONDS: a new Bayesian Nested Sampling tool. Application to Peak Bagging of solar-like oscillations
To exploit the full potential of Kepler light curves, sophisticated and
robust analysis tools are now required more than ever. Characterizing single
stars with an unprecedented level of accuracy and subsequently analyzing
stellar populations in detail are fundamental to further constrain stellar
structure and evolutionary models. We developed a new code, termed Diamonds,
for Bayesian parameter estimation and model comparison by means of the nested
sampling Monte Carlo (NSMC) algorithm, an efficient and powerful method very
suitable for high-dimensional and multi-modal problems. A detailed description
of the features implemented in the code is given with a focus on the novelties
and differences with respect to other existing methods based on NSMC. Diamonds
is then tested on the bright F8 V star KIC~9139163, a challenging target for
peak-bagging analysis due to its large number of oscillation peaks observed,
which are coupled to the blending that occurs between peaks, and the
strong stellar background signal. We further strain the performance of the
approach by adopting a 1147.5 days-long Kepler light curve. The Diamonds code
is able to provide robust results for the peak-bagging analysis of KIC~9139163.
We test the detection of different astrophysical backgrounds in the star and
provide a criterion based on the Bayesian evidence for assessing the peak
significance of the detected oscillations in detail. We present results for 59
individual oscillation frequencies, amplitudes and linewidths and provide a
detailed comparison to the existing values in the literature. Lastly, we
successfully demonstrate an innovative approach to peak bagging that exploits
the capability of Diamonds to sample multi-modal distributions, which is of
great potential for possible future automatization of the analysis technique.Comment: 22 pages, 14 figures, 3 tables. Accepted for publication in A&
- …