Joint Network Topology Inference via Structured Fusion Regularization

03/05/2021
by   Yanli Yuan, et al.
0

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component shared among multiple networks. However, in practice, a more intricate topological pattern, comprising simultaneously of sparse, homogeneity and heterogeneity components, would exhibit in multiple networks. In this paper, we propose a general graph estimator based on a novel structured fusion regularization that enables us to jointly learn multiple graph Laplacian matrices with such complex topological patterns, and enjoys both high computational efficiency and rigorous theoretical guarantee. Moreover, in the proposed regularization term, the topological pattern among networks is characterized by a Gram matrix, endowing our graph estimator with the ability of flexible modelling different types of topological patterns by different choices of the Gram matrix. Computationally, the regularization term, coupling the parameters together, makes the formulated optimization problem intractable and thus, we develop a computationally-scalable algorithm based on the alternating direction method of multipliers (ADMM) to solve it efficiently. Theoretically, we provide a theoretical analysis of the proposed graph estimator, which establishes a non-asymptotic bound of the estimation error under the high-dimensional setting and reflects the effect of several key factors on the convergence rate of our algorithm. Finally, the superior performance of the proposed method is illustrated through simulated and real data examples.

READ FULL TEXT
research
02/11/2019

Error Analysis on Graph Laplacian Regularized Estimator

We provide a theoretical analysis of the representation learning problem...
research
02/20/2021

Graph Laplacian for image deblurring

Image deblurring is relevant in many fields of science and engineering. ...
research
10/14/2014

A graph Laplacian regularization for hyperspectral data unmixing

This paper introduces a graph Laplacian regularization in the hyperspect...
research
05/31/2017

Learning Graphs with Monotone Topology Properties and Multiple Connected Components

Learning graphs with topology properties is a non-convex optimization pr...
research
07/28/2020

Superpixel Based Graph Laplacian Regularization for Sparse Hyperspectral Unmixing

An efficient spatial regularization method using superpixel segmentation...
research
10/31/2021

Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency

This paper considers the problem of estimating high dimensional Laplacia...
research
02/20/2020

A General Pairwise Comparison Model for Extremely Sparse Networks

Statistical inference using pairwise comparison data has been an effecti...

Please sign up or login with your details

Forgot password? Click here to reset