6 research outputs found
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Graph-based learning under perturbations via total least-squares
Graphs are pervasive in different fields unveiling complex relationships between data. Two major graph-based learning tasks are topology identification and inference of signals over graphs. Among the possible models to explain data interdependencies, structural equation models (SEMs) accommodate a gamut of applications involving topology identification. Obtaining conventional SEMs though requires measurements across nodes. On the other hand, typical signal inference approaches “blindly trust” a given nominal topology. In practice however, signal or topology perturbations may be present in both tasks, due to model mismatch, outliers, outages or adversarial behavior. To cope with such perturbations, this work introduces a regularized total least-squares (TLS) approach and iterative algorithms with convergence guarantees to solve both tasks. Further generalizations are also considered relying on structured and/or weighted TLS when extra prior information on the perturbation is available. Analyses with simulated and real data corroborate the effectiveness of the novel TLS-based approaches
Blind Deconvolution of Sparse Graph Signals in the Presence of Perturbations
Blind deconvolution over graphs involves using (observed) output graph
signals to obtain both the inputs (sources) as well as the filter that drives
(models) the graph diffusion process. This is an ill-posed problem that
requires additional assumptions, such as the sources being sparse, to be
solvable. This paper addresses the blind deconvolution problem in the presence
of imperfect graph information, where the observed graph is a perturbed version
of the (unknown) true graph. While not having perfect knowledge of the graph is
arguably more the norm than the exception, the body of literature on this topic
is relatively small. This is partly due to the fact that translating the
uncertainty about the graph topology to standard graph signal processing tools
(e.g. eigenvectors or polynomials of the graph) is a challenging endeavor. To
address this limitation, we propose an optimization-based estimator that solves
the blind identification in the vertex domain, aims at estimating the inverse
of the generating filter, and accounts explicitly for additive graph
perturbations. Preliminary numerical experiments showcase the effectiveness and
potential of the proposed algorithm.Comment: Submitted to the 2024 IEEE International Conference on Acoustics,
Speech, and Signal Processing (ICASSP 2024
Compressive Recovery of Signals Defined on Perturbed Graphs
Recovery of signals with elements defined on the nodes of a graph, from
compressive measurements is an important problem, which can arise in various
domains such as sensor networks, image reconstruction and group testing. In
some scenarios, the graph may not be accurately known, and there may exist a
few edge additions or deletions relative to a ground truth graph. Such
perturbations, even if small in number, significantly affect the Graph Fourier
Transform (GFT). This impedes recovery of signals which may have sparse
representations in the GFT bases of the ground truth graph. We present an
algorithm which simultaneously recovers the signal from the compressive
measurements and also corrects the graph perturbations. We analyze some
important theoretical properties of the algorithm. Our approach to correction
for graph perturbations is based on model selection techniques such as
cross-validation in compressed sensing. We validate our algorithm on signals
which have a sparse representation in the GFT bases of many commonly used
graphs in the network science literature. An application to compressive image
reconstruction is also presented, where graph perturbations are modeled as
undesirable graph edges linking pixels with significant intensity difference.
In all experiments, our algorithm clearly outperforms baseline techniques which
either ignore the perturbations or use first order approximations to the
perturbations in the GFT bases.Comment: 18 pages, 15 figures. v2: Minor correction in ref [32