Research On Graph Learning Algorithm Based On Signal Smoothness

With the rapid development of information technology,social networks,road traffic networks and other actual complex network systems are flooded with a large amount of irregular data information.These irregular data usually have high-dimensional characteristics and complex data structures,which makes it difficult for traditional signal processing methods to fully explore the useful information in the data.In order to learn effective signal representation structures from data for better data analysis and processing,graph topology learning,as an important part of graph signal processing,has received extensive attention.Similar to classical signals,graph signals usually have the smoothness and sparsity of vertex domains.The smoothness of the vertex domain means that the graph signals of neighboring nodes have similar values,while the sparsity means that the graph signal can be represented as a vector with most elements being zero.However,during the observation process,the graph signal may have problems such as Gaussian noise,missing and outliers.Therefore,how to reduce the error impact and learn a meaningful graph topology is the goal of this thesis.The main work of this thesis is summarized as follows:(1)The observed signal is represented as a stationary signal approximately diffused by a graph filter,and an algorithm for learning graph topology from the observed signal is proposed.It assumes that the graph signal is smooth,and on this basis,a corresponding optimization problem is proposed,and the problem is solved by using an iterative method of alternating optimization variables,so as to learn the relationship between entity data,that is,the graph topology.Experimental results show that the proposed scheme is better than other existing schemes in terms of weight error and position recovery of edges.(2)For the case of large graphs,a graph learning algorithm for graph signals in a damaged state is proposed.In practical applications,large graphs are prone to problems such as missing signals,outliers,and Gaussian noise.Therefore,a joint graph learning and signal recovery method is adopted to deal with the damaged data,so as to learn the topology of the graph.The proposed optimization problem extends traditional graph learning schemes with broader applicability.Experimental results show that the graph learning algorithm can achieve satisfactory performance when dealing with different degrees of damaged graph signals.