Efficient Graph Learning From Noisy and Incomplete Data

Berger, Peter M.; Hannák, Gábor; Matz, Gerald

doi:10.1109/tsipn.2020.2964249

Cited by 33 publications

(23 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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].…”

Section: Graph Learningmentioning

confidence: 99%

“…A graph signal defined on an unsigned graph is said to be smooth if the signal values on connected nodes are similar to each other. There are various measures proposed in GSP literature to quantify the smoothness of a graph signal x [28,32]. One common measure is the quadratic form of the graph Laplacian:…”

Section: Unsigned Graph Learningmentioning

confidence: 99%

“…This modification also allows the usage of other distance metrics when constructing Z, e.g. Manhattan distance as done in [32].…”

Section: Unsigned Graph Learningmentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Karaaslanli

Saha

Aviyente

et al. 2021

Preprint

View full text Add to dashboard Cite

Elucidating the topology of gene regulatory networks (GRN) from large single-cell RNA sequencing (scRNAseq) datasets, while effectively capturing its inherent cell-cycle heterogeneity, is currently one of the most pressing problems in computational systems biology. Recently, graph learning (GL) approaches based on graph signal processing (GSP) have been developed to infer graph topology from signals defined on graphs. However, existing GL methods are not suitable for learning signed graphs, which represent a characteristic feature of GRNs, as they account for both activating and inhibitory relationships between genes. To this end, we propose a novel signed GL approach, scSGL, that incorporates the similarity and dissimilarity between observed gene expression data to construct gene networks. The proposed approach is formulated as a non-convex optimization problem and solved using an efficient ADMM framework. In our experiments on simulated and real single cell datasets, scSGL compares favorably with other single cell gene regulatory network reconstruction algorithms.

show abstract

Section: Graph Learningmentioning

confidence: 99%

Section: Unsigned Graph Learningmentioning

confidence: 99%

“…This modification also allows the usage of other distance metrics when constructing Z, e.g. Manhattan distance as done in [32].…”

Section: Unsigned Graph Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Karaaslanli

Saha

Aviyente

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Different from [22,24,[26][27][28][29] that infer structure from signals assumed to be smooth over the sought undirected graph, here the measurements are assumed related to the graph via filtering (cf. (1) and the opening discussion in Section 2.1).…”

Section: Contributions In Context Of Prior Related Workmentioning

confidence: 99%

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Shafipour

Mateos

2020

Algorithms

View full text Add to dashboard Cite

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

show abstract