Simultaneous low-rank component and graph estimation for high-dimensional graph signals: Application to brain imaging

Abstract

We propose an algorithm to uncover the intrinsic low-rank component of a high-dimensional, graph-smooth and grossly-corrupted dataset, under the situations that the underlying graph is unknown. Based on a model with a low-rank component plus a sparse perturbation, and an initial graph estimation, our proposed algorithm simultaneously learns the low-rank component and refines the graph. The refined graph improves the effectiveness of the graph smoothness constraint and increases the accuracy of the low-rank estimation. We derive the learning steps using ADMM. Our evaluations using synthetic and real brain imaging data in a supervised classification task demonstrate encouraging performance.

Graph Learning for Spatiotemporal Signals with Long- and Short-Term Characterization

“…The works of [13] and [36] are most related to our work. Different from the method in [13], we focus on the spatiotemporal signals, and hence fully exploit both long and short term correlated property of spatiotemporal signals to facilitate the graph learning.…”

“…Different from the method in [13], we focus on the spatiotemporal signals, and hence fully exploit both long and short term correlated property of spatiotemporal signals to facilitate the graph learning. Rui et al [36] and this work jointly estimate low-rank component and graph structure, while authors in [36] propose a single integrated scheme from [13] and [37] for lack of representation between graph and observed signals. Besides, the formulation and algorithm of [36] are different from this work.…”

Connecting the Dots: Identifying Network Structure via Graph Signal Processing

“…The graph frequency decomposition of neuroimaging data shows promise for analyzing brain signals and connectivity [23]; see also the numerical test in Section IX-C. For supervised classification of brain states (in response to different visual stimuli), GFT-based dimensionality reduction of functional magnetic resonance imaging (fMRI) data has been shown to outperform state-of-the art reduction techniques relying on PCA or independent component analysis (ICA) [37]; see also [47] for related approaches dealing with electroencephalogram (EEG) data. Results in [37] indicate that the smooth signal prior along with the graph learning approach in [25] yield the best performance for the aforementioned classification task.…”

scSGL: Signed Graph Learning for Single-Cell Gene Regulatory Network Inference

“…Kalofolias et al [30] extended this framework by establishing the link between smoothness and sparsity and adding a regularization term on the degree vector to ensure that each vertex has at least one incident edge. Different variations of these frameworks to handle missing values and sparse outliers in the graph signals were considered in [31,32,33,34,35]. All of the previous works learn unsigned graphs with the exception of [36], where a signed graph is learned by employing signed graph Laplacian defined in [37].…”

“…This analysis results in an optimization problem where a graph is learned such that variation of signals over the learned graph is minimized. Di↵erent variations of this framework with constraints on the learned topology and for handling noisy graph signals were considered in (Kalofolias, 2016;Hou et al, 2016;Berger et al, 2020;Kadambari and Chepuri, 2020;Rui et al, 2017). All of the previous works learn unsigned graphs with the exception of (Matz and Dittrich, 2020), where a signed graph is learned by employing signed graph Laplacian defined by Kunegis et al (2010).…”