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    Graph Sampling for Covariance Estimation

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    Type
    Article
    Authors
    Chepuri, Sundeep Prabhakar
    Leus, Geert
    KAUST Grant Number
    OSR-2015-Sensors-2700
    Date
    2017-07-24
    Permanent link to this record
    http://hdl.handle.net/10754/626703
    
    Metadata
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    Abstract
    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.
    Citation
    Chepuri, S. P., & Leus, G. (2017). Graph Sampling for Covariance Estimation. IEEE Transactions on Signal and Information Processing over Networks, 3(3), 451–466. doi:10.1109/tsipn.2017.2731161
    Sponsors
    KAUST-MIT-TUD consortium
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Signal and Information Processing over Networks
    DOI
    10.1109/tsipn.2017.2731161
    arXiv
    arXiv:1704.07661
    Additional Links
    http://ieeexplore.ieee.org/document/7990050/
    ae974a485f413a2113503eed53cd6c53
    10.1109/tsipn.2017.2731161
    Scopus Count
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