Research On Graph Learning Method From Data On The Irregular Domain

Graph learning is a key technology in mining natural associations of data,which plays an important role in various fields including financial decision-making,social analysis,and weather forecasting.With the increasing diver-sity of application services,the description of data has expanded from regular Euclidean spaces to irregular and topologically complicated domains,and it makes traditional signal processing methods hard to handle.Fortunately,graph signal processing is an emerging field to deal with signals on the irregular do-main.It utilizes graph to describe the geometric structures of data,and pro-vides a new perspective for representing data and identifying their hidden struc-ture.Based on the theory of graph signal processing,this thesis focuses on the development of effective methods for graph learning consisting of spatiotem-poral smoothness-based graph learning method,low rank and spatiotemporal smoothness-based graph learning method,and distributed time-varying graph learning method.Once an appropriate graph is constructed,it will greatly pro-mote subsequent data analysis and processing,thereby guiding future decision-making.The main content and contribution of this thesis are summarized as follows:1.The graph learning problem of time-varying graph signals is studied.First,a space-time signal model is presented for time-varying graph signals,which takes into account correlation properties from both spatial and tempo-ral directions.Based on this model,a spatiotemporal smoothness-based graph learning method(STSGL)is then proposed,which novelly introduces spa-tiotemporal smoothness to describe the local space-time characteristics of time-varying graph signals.By promoting such smoothness in the graph learning procedure,the proposed method leads to a meaningful graph.For the two cases that temporal correlation structure is known and unknown,the proposed method solves them through alternating minimization and block coordinate descent,re-spectively.Experiments on both synthetic and real-world datasets demonstrate the improvement of the proposed STSGL over current state-of-the-art graph learning methods.2.To solve the performance bottleneck of graph learning caused by the mismatch between signal model and signal features,a novel signal model based on the long-and short-term characterization is first proposed.It utilizes the space-time correlation and the low-rank property of real-world spatiotempo-ral signals to provide a comprehensive signal representation.Then,the graph learning problem is formulated as a joint low-rank component estimation and graph Laplacian inference.Accordingly,we propose a low rank and spatiotem-poral smoothness-based graph learning method(GL-LRSS),which introduces both local correlation and global correlation of spatiotemporal signal for graph learning procedures.By jointly exploiting the low rank of long-time observa-tions and the smoothness of short-time observations,the overall learning per-formance can be effectively improved.Experiments on both synthetic and real-world datasets verify the effectiveness of the proposed model and substantial improvements in the learning accuracy of the proposed method over the state-of-the-art graph learning methods.3.A novel framework based on space-time signal representation is pro-posed to solve the time-varying graph learning problem.First,considering the temporal evolution behaviors of the graph,a dynamic graph-based signal model is presented.Particularly,it involves two typical graph evolutions in-cluding smoothly varying edges over time and single node perturbation.By in-troducing a penalty function to constrain the graph evolution,the time-varying graph learning problem is formulated as a convex optimization problem,which is then solved by the proposed distributed time-varying graph learning method(DTVGL).Benefit from the alternating direction method of multipliers(ADMM),the proposed method splits the problem into a series of subproblems that can be efficiently addressed in parallel.Experimental results on several datasets demonstrate the effectiveness of the proposed method in time-varying graph learning and the superiority of the proposed method compared to static graph learning methods.