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Graph Signal Processing

Weak Law of Large Numbers for Stationary Graph Processes


The ability to obtain accurate estimators from a set of measurements is a key factor in science and engineering. Typically, there is an inherent assumption that the measurements were taken in a sequential order, be it in space or time. However, data is increasingly irregular so this assumption of sequentially obtained measurements no longer holds. By leveraging notions of graph signal processing to account for these irregular domains, we propose an unbiased estimator for the mean of a wide sense stationary graph process based on the diffusion of a single realization.

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Authors:
Fernando Gama, Alejandro Ribeiro
Submitted On:
2 March 2017 - 9:47am
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[1] Fernando Gama, Alejandro Ribeiro, "Weak Law of Large Numbers for Stationary Graph Processes", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/1585. Accessed: Oct. 15, 2019.
@article{1585-17,
url = {http://sigport.org/1585},
author = {Fernando Gama; Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Weak Law of Large Numbers for Stationary Graph Processes},
year = {2017} }
TY - EJOUR
T1 - Weak Law of Large Numbers for Stationary Graph Processes
AU - Fernando Gama; Alejandro Ribeiro
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/1585
ER -
Fernando Gama, Alejandro Ribeiro. (2017). Weak Law of Large Numbers for Stationary Graph Processes. IEEE SigPort. http://sigport.org/1585
Fernando Gama, Alejandro Ribeiro, 2017. Weak Law of Large Numbers for Stationary Graph Processes. Available at: http://sigport.org/1585.
Fernando Gama, Alejandro Ribeiro. (2017). "Weak Law of Large Numbers for Stationary Graph Processes." Web.
1. Fernando Gama, Alejandro Ribeiro. Weak Law of Large Numbers for Stationary Graph Processes [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/1585

Tracking Time-Vertex Propagation using Dynamic Graph Wavelets


Graph Signal Processing generalizes classical signal processing to signal or data indexed by the vertices of a weighted graph. So far, the research efforts have been focused on static graph signals. However numerous applications involve graph signals evolving in time, such as spreading or propagation of waves on a network. The analysis of this type of data requires a new set of methods that takes into account the time and graph dimensions. We propose a novel class of wavelet frames named Dynamic Graph Wavelets, whose time-vertex evolution follows a dynamic process.

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Authors:
Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud
Submitted On:
8 December 2016 - 5:01pm
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[1] Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud, "Tracking Time-Vertex Propagation using Dynamic Graph Wavelets", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1428. Accessed: Oct. 15, 2019.
@article{1428-16,
url = {http://sigport.org/1428},
author = {Francesco Grassi; Nathanael Perraudin; Benjamin Ricaud },
publisher = {IEEE SigPort},
title = {Tracking Time-Vertex Propagation using Dynamic Graph Wavelets},
year = {2016} }
TY - EJOUR
T1 - Tracking Time-Vertex Propagation using Dynamic Graph Wavelets
AU - Francesco Grassi; Nathanael Perraudin; Benjamin Ricaud
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1428
ER -
Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud. (2016). Tracking Time-Vertex Propagation using Dynamic Graph Wavelets. IEEE SigPort. http://sigport.org/1428
Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud, 2016. Tracking Time-Vertex Propagation using Dynamic Graph Wavelets. Available at: http://sigport.org/1428.
Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud. (2016). "Tracking Time-Vertex Propagation using Dynamic Graph Wavelets." Web.
1. Francesco Grassi, Nathanael Perraudin, Benjamin Ricaud. Tracking Time-Vertex Propagation using Dynamic Graph Wavelets [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1428

Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems


Sampling and reconstruction of bandlimited graph signals have well-appreciated merits for dimensionality reduction, affordable storage, and online processing of streaming network data. However, these parsimonious signals are oftentimes encountered with high-dimensional linear inverse problems. Hence, interest shifts from reconstructing the signal itself towards instead approximating the input to a prescribed linear operator efficiently.

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Authors:
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro
Submitted On:
8 December 2016 - 12:32am
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[1] Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1420. Accessed: Oct. 15, 2019.
@article{1420-16,
url = {http://sigport.org/1420},
author = {Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems},
year = {2016} }
TY - EJOUR
T1 - Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems
AU - Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1420
ER -
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. IEEE SigPort. http://sigport.org/1420
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, 2016. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. Available at: http://sigport.org/1420.
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems." Web.
1. Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1420

Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems


Sampling and reconstruction of bandlimited graph signals have well-appreciated merits for dimensionality reduction, affordable storage, and online processing of streaming network data. However, these parsimonious signals are oftentimes encountered with high-dimensional linear inverse problems. Hence, interest shifts from reconstructing the signal itself towards instead approximating the input to a prescribed linear operator efficiently.

Paper Details

Authors:
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro
Submitted On:
8 December 2016 - 3:51pm
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sketching-globalsip16-presentation.pdf

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[1] Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1415. Accessed: Oct. 15, 2019.
@article{1415-16,
url = {http://sigport.org/1415},
author = {Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems},
year = {2016} }
TY - EJOUR
T1 - Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems
AU - Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1415
ER -
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. IEEE SigPort. http://sigport.org/1415
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, 2016. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. Available at: http://sigport.org/1415.
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems." Web.
1. Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1415

Graph Frequency Analysis of Brain Signals


This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations.

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Authors:
Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro
Submitted On:
19 July 2016 - 1:47pm
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[1] Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro, "Graph Frequency Analysis of Brain Signals", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1134. Accessed: Oct. 15, 2019.
@article{1134-16,
url = {http://sigport.org/1134},
author = {Weiyu Huang; Leah Goldsberry; Nicholas F. Wymbs; Scott T. Grafton; Danielle S. Bassett; and Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Graph Frequency Analysis of Brain Signals},
year = {2016} }
TY - EJOUR
T1 - Graph Frequency Analysis of Brain Signals
AU - Weiyu Huang; Leah Goldsberry; Nicholas F. Wymbs; Scott T. Grafton; Danielle S. Bassett; and Alejandro Ribeiro
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1134
ER -
Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro. (2016). Graph Frequency Analysis of Brain Signals. IEEE SigPort. http://sigport.org/1134
Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro, 2016. Graph Frequency Analysis of Brain Signals. Available at: http://sigport.org/1134.
Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro. (2016). "Graph Frequency Analysis of Brain Signals." Web.
1. Weiyu Huang, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro. Graph Frequency Analysis of Brain Signals [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1134

Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction


Signal processing on graphs finds applications in many areas. Motivated by recent developments, this paper studies the concept of spectrum folding (aliasing) for graph signals under the downsample-then-upsample operation. In this development, we use a special eigenvector structure that is unique to the adjacency matrix of M-block cyclic matrices. We then introduce M-channel maximally decimated filter banks. Manipulating the characteristics of the aliasing effect, we construct polynomial filter banks with perfect reconstruction property.

Paper Details

Authors:
Oguzhan Teke, Palghat P. Vaidyanathan
Submitted On:
31 March 2016 - 6:00pm
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[1] Oguzhan Teke, Palghat P. Vaidyanathan, "Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1077. Accessed: Oct. 15, 2019.
@article{1077-16,
url = {http://sigport.org/1077},
author = {Oguzhan Teke; Palghat P. Vaidyanathan },
publisher = {IEEE SigPort},
title = {Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction},
year = {2016} }
TY - EJOUR
T1 - Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction
AU - Oguzhan Teke; Palghat P. Vaidyanathan
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1077
ER -
Oguzhan Teke, Palghat P. Vaidyanathan. (2016). Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction. IEEE SigPort. http://sigport.org/1077
Oguzhan Teke, Palghat P. Vaidyanathan, 2016. Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction. Available at: http://sigport.org/1077.
Oguzhan Teke, Palghat P. Vaidyanathan. (2016). "Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction." Web.
1. Oguzhan Teke, Palghat P. Vaidyanathan. Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1077

Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction


Signal processing on graphs finds applications in many areas. Motivated by recent developments, this paper studies the concept of spectrum folding (aliasing) for graph signals under the downsample-then-upsample operation. In this development, we use a special eigenvector structure that is unique to the adjacency matrix of M-block cyclic matrices. We then introduce M-channel maximally decimated filter banks. Manipulating the characteristics of the aliasing effect, we construct polynomial filter banks with perfect reconstruction property.

Paper Details

Authors:
Oguzhan Teke, Palghat P. Vaidyanathan
Submitted On:
31 March 2016 - 6:00pm
Short Link:
Type:
Event:
Presenter's Name:
Paper Code:
Document Year:
Cite

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mchannel_graph_icassp_presentation_noTime.pdf

(489)

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[1] Oguzhan Teke, Palghat P. Vaidyanathan, "Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1068. Accessed: Oct. 15, 2019.
@article{1068-16,
url = {http://sigport.org/1068},
author = {Oguzhan Teke; Palghat P. Vaidyanathan },
publisher = {IEEE SigPort},
title = {Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction},
year = {2016} }
TY - EJOUR
T1 - Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction
AU - Oguzhan Teke; Palghat P. Vaidyanathan
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1068
ER -
Oguzhan Teke, Palghat P. Vaidyanathan. (2016). Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction. IEEE SigPort. http://sigport.org/1068
Oguzhan Teke, Palghat P. Vaidyanathan, 2016. Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction. Available at: http://sigport.org/1068.
Oguzhan Teke, Palghat P. Vaidyanathan. (2016). "Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction." Web.
1. Oguzhan Teke, Palghat P. Vaidyanathan. Graph Filter Banks With M-Channels, Maximal Decimation, and Perfect Reconstruction [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1068

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