Distributed Multi-task Learning Algorithms Based On Graph Signal Processing

In recent years,the processing technology for irregular datasets from large-scale networks such as social networks,energy networks,transportation networks,sensor networks and neural networks has drawn much attention.However,many existing signal processing techniques designed for small datasets might be of only limit applicability due to the large-scale datasets and the complex structure.As an extension of the classical digital signal processing technology,the graph signal processing technology can be utilized to analyze signals,extract signal characteristics,and realize the sampling or filtering operations based on large-scale datasets with complex topology.There is a wide range of applications for the graph signal processing technology.For example,the climate profiles of the whole network can be predicted by using the data from weather stations in irregular geographical locations.By analyzing the data and the underlying graph structure of the power consumption in the smart grid,the security of the power system state estimation can be effectively enhanced.In this thesis,the multi-task learning problem in the graph signal processing field and the application of the graph signal processing technology in smart grid are respectively discussed.Specifically,the main contents can be divided into three parts as follows:Firstly,the multi-task learning problem based on partial observation scenarios is studied,and the diffusion Least-Mean-Square algorithm with cluster-wise sampling strategy（dLMS-CS in short）is proposed based on the minimum mean square error criterion.In the multi-task learning scenarios,nodes on the graph tend to learn different graph filter parameters at the same time.In order to reduce the amount of data collected during the learning process,the cluster-wise sampling strategy is derived in favour of the learning algorithms in multi-task learning scenarios.The simulation results validate that the multiple filter parameters of graphs can be efficiently estimated via the proposed dLMS-CS algorithm.Secondly,the performance of the proposed dLMS-CS is analyzed,with both the convergence conditions and the theoretical steady-state mean-square-deviation of dLMS-CS derived.With the theoretical steady-state network mean-square-deviation utilized,the sampling probability in the cluster-wise sampling strategy are further optimized.The simulation results show that the optimized sampling probability not only slightly improves the steady-state performance of the proposed dLMS-CS algorithm,but also significantly accelerates the convergence rate of dLMS-CS.Finally,the application of graph signal processing technology in smart grid is explored,and the detection of false data injection attacks in smart grid is discussed in the field of graph signal processing.Based on the existing grid-graph signal processing framework,the detection algorithms for false data injection attack are derived both in the graph frequency domain and in the graph vertex domain,respectively,with the corresponding threshold presented.Simulation results show the effectiveness of the proposed detection algorithms and the corresponding thresholds.