Connecting the Dots

被引:271
作者
Mateos, Gonzalo [1 ,2 ]
Segarra, Santiago [3 ,4 ]
Marques, Antonio G. [5 ]
Ribeiro, Alejandro [6 ]
机构
[1] Univ Rochester, Dept Elect & Comp Engn, Rochester, NY 14627 USA
[2] Univ Rochester, Goergen Inst Data Sci, Rochester, NY 14627 USA
[3] MIT, Inst Data Syst & Soc, 77 Massachusetts Ave, Cambridge, MA 02139 USA
[4] Rice Univ, Dept Elect & Comp Engn, Houston, TX 77251 USA
[5] King Juan Carlos Univ, Dept Signal Theory & Commun, Madrid, Spain
[6] Univ Minnesota, Dept Elect & Comp Engn, Minneapolis, MN USA
基金
美国国家科学基金会;
关键词
COVARIANCE ESTIMATION; MODEL SELECTION; INFERENCE; GRAPHS;
D O I
10.1109/MSP.2018.2890143
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Network topology inference is a significant problem in network science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with, e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This article offers an overview of graph-learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks and nonlinear models of pairwise interaction, as well as extensions to directed (di) graphs and their relation to causal inference. All in all, this article introduces readers to challenges and opportunities for SP research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.
引用
收藏
页码:16 / 43
页数:28
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