Research Of Key Technology For Graph Learning Based On Incomplete Signals

Booming of information technology leads to geometrically increase of data.such data is with large amount,various types,complex spatio structures.Classic DSP techniques have their own limitations in dealing with structured data above though DSP has been well developed and widely applied for a long time.Therefore,requirements of processing methods for data above bring about graph signal processing(GSP).GSP characterizes spatio structure of data as graph composed of vertices and edges,in which edge weights measure the relationships between nodes,and a scalar mapping value of each vertex is element of graph signal.Obviously graph signal carries structure information.Obtaining spatio structure of data,which is graph learning problem,is the first step of GSP processing.Nevertheless,graph learning problems at present are mainly built on complete graph signals and rarely on incomplete ones.Hence learning graph from missing data remains an important and valuable issue to be urgently researched.Many papers have proved that the properties of signals in the spatial and temporal domain are separable,and it is easy to obtain the properties of signals in the temporal domain.Therefore,this paper increases the temporal constraint of signal to improve graph learning performance indirectly by reducing the reconstruction error of signal.The main contents of this paper are as follows:1)A graph learning model for incomplete static smooth graph signals,which are smooth in vertex domain or spatio domain and have no need to take into account takes into account space-time interactions in signal representation.Starting from graph signal representation,this paper constructs graph learning model for incomplete static smooth graph signals in detail based on the one for complete static smooth signals,add additional penalty term of temporal variation for graph signal,and prove that this model belongs to gaussian graph model.An interactive optimization method is taken advantage to solve the model.And it is easily to find that solutions of the model correspond to a local minimum when analyzing convergence of the model.Synthetic data and real-world temperature data are both used to verify the effectiveness of this model.Experiments show that if original complete smooth signals are just smooth in spatio domain,the temporal variation is useless.But if they are smooth in both spatio and time domain,the time variation is helpful in improve performance of graph and signal reconstruction.2)A graph learning model for incomplete time-varying graph signals.Static smooth graph signal is band limited,but it is difficult to acquire strict band limited signal in realworld applications.Actually,time-varying signals are more common in real-world applications.Space-time interactions must be considered in representation of time-varying graph signals,temporal differential signals of which are smoother on graph rather than original version.Then a graph learning model for incomplete time-varying graph signals is built in detail based on the one for complete signals,add additional penalty term of temporal variation for differential signals,and also prove this model to be gaussian graph model.This model is solved in iterative optimization method.Synthetic dataset and real-world evapotranspiration dataset are both used to verify the effectiveness of this model.Numeric experiments show that better graph learning and graph signal recovery can be obtained with the help of time variation of differential signals.