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Abstract:Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on graphs. We convert the original graph to a line graph where its nodes and edges, respectively, represent the original edges and the connections between the edges. We then perform node sampling of the line graph based on the edge smoothness assumption: This process selects the most critical edges in the original graph. We present a general framework of edge sampling based on graph sampling theory and reveal a theoretical relationship between the degree of the original graph and the line graph. We also propose an acceleration method for edge sampling in the proposed framework by using the relationship between two types of Laplacian of the node and edge domains. Experimental results in synthetic and real-world graphs validate the effectiveness of our approach against some alternative edge selection methods.

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Abstract:We propose a task to generate a complex sentence from a simple sentence in order to amplify various kinds of responses in the database. We first divide a complex sentence into a main clause and a subordinate clause to learn a generator model of modifiers, and then use the model to generate a modifier clause to create a complex sentence from a simple sentence. We present an automatic evaluation metric to estimate the quality of the models and show that a pipeline model outperforms an end-to-end model.

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