12,237 research outputs found
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
Graph Variogram: A novel tool to measure spatial stationarity
Irregularly sampling a spatially stationary random field does not yield a
graph stationary signal in general. Based on this observation, we build a
definition of graph stationarity based on intrinsic stationarity, a less
restrictive definition of classical stationarity. We introduce the concept of
graph variogram, a novel tool for measuring spatial intrinsic stationarity at
local and global scales for irregularly sampled signals by selecting subgraphs
of local neighborhoods. Graph variograms are extensions of variograms used for
signals defined on continuous Euclidean space. Our experiments with
intrinsically stationary signals sampled on a graph, demonstrate that graph
variograms yield estimates with small bias of true theoretical models, while
being robust to sampling variation of the space.Comment: Submitted to IEEE Global Conference on Signal and Information
Processing 2018 (IEEE GlobalSIP 2018), Nov 2018, Anaheim, CA, United States.
(https://2018.ieeeglobalsip.org/
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks
In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud
and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm
Random Forests and Networks Analysis
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient
algorithm based on loop-erased random walks to sample uniform spanning trees
and more generally weighted trees or forests spanning a given graph. This
algorithm provides a powerful tool in analyzing structures on networks and
along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we
focused on applications of spanning rooted forests on finite graphs. The
resulting main conclusions are reviewed in this paper by collecting related
theorems, algorithms, heuristics and numerical experiments. A first
foundational part on determinantal structures and efficient sampling procedures
is followed by four main applications: 1) a random-walk-based notion of
well-distributed points in a graph 2) how to describe metastable dynamics in
finite settings by means of Markov intertwining dualities 3) coarse graining
schemes for networks and associated processes 4) wavelets-like pyramidal
algorithms for graph signals.Comment: Survey pape
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