TY - JOUR

T1 - Graph Sampling for Covariance Estimation

AU - Chepuri, Sundeep Prabhakar

AU - Leus, Geert

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2015-Sensors-2700
Acknowledgements: KAUST-MIT-TUD consortium
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2017/7/24

Y1 - 2017/7/24

N2 - In this paper, the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the nonparametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

AB - In this paper, the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the nonparametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

UR - http://hdl.handle.net/10754/626703

UR - http://ieeexplore.ieee.org/document/7990050/

UR - http://www.scopus.com/inward/record.url?scp=85049518198&partnerID=8YFLogxK

U2 - 10.1109/tsipn.2017.2731161

DO - 10.1109/tsipn.2017.2731161

M3 - Article

VL - 3

SP - 451

EP - 466

JO - IEEE Transactions on Signal and Information Processing over Networks

JF - IEEE Transactions on Signal and Information Processing over Networks

SN - 2373-7778

IS - 3

ER -