3,470 research outputs found
Filtering Random Graph Processes Over Random Time-Varying Graphs
Graph filters play a key role in processing the graph spectra of signals
supported on the vertices of a graph. However, despite their widespread use,
graph filters have been analyzed only in the deterministic setting, ignoring
the impact of stochastic- ity in both the graph topology as well as the signal
itself. To bridge this gap, we examine the statistical behavior of the two key
filter types, finite impulse response (FIR) and autoregressive moving average
(ARMA) graph filters, when operating on random time- varying graph signals (or
random graph processes) over random time-varying graphs. Our analysis shows
that (i) in expectation, the filters behave as the same deterministic filters
operating on a deterministic graph, being the expected graph, having as input
signal a deterministic signal, being the expected signal, and (ii) there are
meaningful upper bounds for the variance of the filter output. We conclude the
paper by proposing two novel ways of exploiting randomness to improve (joint
graph-time) noise cancellation, as well as to reduce the computational
complexity of graph filtering. As demonstrated by numerical results, these
methods outperform the disjoint average and denoise algorithm, and yield a (up
to) four times complexity redution, with very little difference from the
optimal solution
Nonlinear denoising of transient signals with application to event related potentials
We present a new wavelet based method for the denoising of {\it event related
potentials} ERPs), employing techniques recently developed for the paradigm of
deterministic chaotic systems. The denoising scheme has been constructed to be
appropriate for short and transient time sequences using circular state space
embedding. Its effectiveness was successfully tested on simulated signals as
well as on ERPs recorded from within a human brain. The method enables the
study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres
Forecasting Time Series with VARMA Recursions on Graphs
Graph-based techniques emerged as a choice to deal with the dimensionality
issues in modeling multivariate time series. However, there is yet no complete
understanding of how the underlying structure could be exploited to ease this
task. This work provides contributions in this direction by considering the
forecasting of a process evolving over a graph. We make use of the
(approximate) time-vertex stationarity assumption, i.e., timevarying graph
signals whose first and second order statistical moments are invariant over
time and correlated to a known graph topology. The latter is combined with VAR
and VARMA models to tackle the dimensionality issues present in predicting the
temporal evolution of multivariate time series. We find out that by projecting
the data to the graph spectral domain: (i) the multivariate model estimation
reduces to that of fitting a number of uncorrelated univariate ARMA models and
(ii) an optimal low-rank data representation can be exploited so as to further
reduce the estimation costs. In the case that the multivariate process can be
observed at a subset of nodes, the proposed models extend naturally to Kalman
filtering on graphs allowing for optimal tracking. Numerical experiments with
both synthetic and real data validate the proposed approach and highlight its
benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin
How random is your heart beat?
We measure the content of random uncorrelated noise in heart rate variability
using a general method of noise level estimation using a coarse grained
entropy. We show that usually - except for atrial fibrillation - the level of
such noise is within 5 - 15% of the variance of the data and that the
variability due to the linearly correlated processes is dominant in all cases
analysed but atrial fibrillation. The nonlinear deterministic content of heart
rate variability remains significant and may not be ignored.Comment: see http://urbanowicz.org.p
Bibliographic Review on Distributed Kalman Filtering
In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud
The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area
- …