TY - JOUR
T1 - Vector-Valued Graph Trend Filtering with Non-Convex Penalties
AU - Varma, Rohan
AU - Lee, Harlin
AU - Kovacevic, Jelena
AU - Chi, Yuejie
N1 - Funding Information:
Manuscript received May 29, 2019; revised September 1, 2019 and November 17, 2019; accepted November 18, 2019. Date of publication December 6, 2019; date of current version December 30, 2019. This work was supported in part by National Science Foundation under Grants CCF-1563918, CCF-1826519, CCF-1806154 and ECCS-1818571, in part by the Office of Naval Research under Grant N00014-18-1-2142, in part by the ARO under Grant W911NF-18-1-0303, and in part by National Institutes of Health under Grant R01EB025018. This paper was presented in part at the IEEE International Conference on Acoustics, Speech and Signal Processing, Brighton, U.K., May 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. David I Shuman. (Rohan Varma and Harlin Lee contributed equally to this work.) (Corresponding author: Harlin Lee.) R. Varma, H. Lee, and Y. Chi are with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: rohanv@andrew.cmu.edu; harlinl@andrew.cmu.edu; yuejiec@andrew.cmu.edu).
Publisher Copyright:
© 2015 IEEE.
PY - 2020
Y1 - 2020
N2 - This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.
AB - This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.
KW - Graph signal processing
KW - graph trend filtering
KW - non-convex optimization
KW - semi-supervised classification
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U2 - 10.1109/TSIPN.2019.2957717
DO - 10.1109/TSIPN.2019.2957717
M3 - Article
C2 - 33748408
AN - SCOPUS:85078703123
SN - 2373-776X
VL - 6
SP - 48
EP - 62
JO - IEEE Transactions on Signal and Information Processing over Networks
JF - IEEE Transactions on Signal and Information Processing over Networks
M1 - 8926407
ER -