80,428 research outputs found
Robustness of large-scale stochastic matrices to localized perturbations
Upper bounds are derived on the total variation distance between the
invariant distributions of two stochastic matrices differing on a subset W of
rows. Such bounds depend on three parameters: the mixing time and the minimal
expected hitting time on W for the Markov chain associated to one of the
matrices; and the escape time from W for the Markov chain associated to the
other matrix. These results, obtained through coupling techniques, prove
particularly useful in scenarios where W is a small subset of the state space,
even if the difference between the two matrices is not small in any norm.
Several applications to large-scale network problems are discussed, including
robustness of Google's PageRank algorithm, distributed averaging and consensus
algorithms, and interacting particle systems.Comment: 12 pages, 4 figure
Fourier-based Rotation-invariant Feature Boosting: An Efficient Framework for Geospatial Object Detection
Geospatial object detection of remote sensing imagery has been attracting an
increasing interest in recent years, due to the rapid development in spaceborne
imaging. Most of previously proposed object detectors are very sensitive to
object deformations, such as scaling and rotation. To this end, we propose a
novel and efficient framework for geospatial object detection in this letter,
called Fourier-based rotation-invariant feature boosting (FRIFB). A
Fourier-based rotation-invariant feature is first generated in polar
coordinate. Then, the extracted features can be further structurally refined
using aggregate channel features. This leads to a faster feature computation
and more robust feature representation, which is good fitting for the coming
boosting learning. Finally, in the test phase, we achieve a fast pyramid
feature extraction by estimating a scale factor instead of directly collecting
all features from image pyramid. Extensive experiments are conducted on two
subsets of NWPU VHR-10 dataset, demonstrating the superiority and effectiveness
of the FRIFB compared to previous state-of-the-art methods
Quantitative Measure of Memory Loss in Complex Spatio-Temporal Systems
To make progress in understanding the issue of memory loss and history
dependence in evolving complex systems, we consider the mixing rate that
specifies how fast the future states become independent of the initial
condition. We propose a simple measure for assessing the mixing rate that can
be directly applied to experimental data observed in any metric space . For
a compact phase space , we prove the following statement. If the
underlying dynamical system has a unique physical measure and its dynamics is
strongly mixing with respect to this measure, then our method provides an upper
bound of the mixing rate. We employ our method to analyze memory loss for the
system of slowly sheared granular particles with a small inertial number .
The shear is induced by the moving walls as well as by the linear motion of the
support surface that ensures approximately linear shear throughout the sample.
We show that even if is kept fixed, the rate of memory loss (considered at
the time scale given by the inverse shear rate) depends erratically on the
shear rate. Our study suggests a presence of bifurcations at which the rate of
memory loss increases with the shear rate while it decreases away from these
points. We also find that the memory loss is not a smooth process. Its rate is
closely related to frequency of the sudden transitions of the force network.
The loss of memory, quantified by observing evolution of force networks, is
found to be correlated with the loss of correlation of shear stress measured on
the system scale. Thus, we have established a direct link between the evolution
of force networks and macroscopic properties of the considered system
Particle filtering in high-dimensional chaotic systems
We present an efficient particle filtering algorithm for multiscale systems,
that is adapted for simple atmospheric dynamics models which are inherently
chaotic. Particle filters represent the posterior conditional distribution of
the state variables by a collection of particles, which evolves and adapts
recursively as new information becomes available. The difference between the
estimated state and the true state of the system constitutes the error in
specifying or forecasting the state, which is amplified in chaotic systems that
have a number of positive Lyapunov exponents. The purpose of the present paper
is to show that the homogenization method developed in Imkeller et al. (2011),
which is applicable to high dimensional multi-scale filtering problems, along
with important sampling and control methods can be used as a basic and flexible
tool for the construction of the proposal density inherent in particle
filtering. Finally, we apply the general homogenized particle filtering
algorithm developed here to the Lorenz'96 atmospheric model that mimics
mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure
Probabilistic Modeling Paradigms for Audio Source Separation
This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems
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