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Abstract:
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We consider an undirected, simple graph with signals on the vertices. The signals on the vertices have two types: response signals and predictor signals. This study is motivated by the fact that the signals on the graph can be related to the graph topology, and associated with other predictors. For example, the temperatures in nearby locations without significant terrain variations will be similar, and temperature has a linear relationship with pressure. Our model assumes that the signals on the vertices are representations of the combinations of the smoothness of the part of response signals that are agnostic to the predictors and linear relationships with other predictors. In this study, we developed a method to infer a graph topology from smooth signals on the network along with other covariates. We demonstrated our graph learning framework using simulated and real data. The results of our study provide new insight into graph learning models, and can be widely applied in the analysis of geographical, biomedical, and social networks.
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