Abstract: Graph convolutional networks learn the convolution kernels through feature propagation to achieve graph convolution. Its core lies in the construction of the convolution operator. When applied to specific graph data, the applications of convolution kernels are often limited due to the difference of scenarios. This paper addresses the convolution kernels from a graph filtering perspective. Under the graph filtering framework, the data features of nodes are regarded as graph signals, and the smooth signals are processed by low-pass filter. The extracted smooth graph signals are placed on topographic map for convolution in spectral domain. In this process, the local graph structure information will be integrated into the similarity representation of the nodes to complete the graph embedding learning. In order to improve the flexibility of the graphics filter and achieve more detailed design, this paper naturally extends the original model and introduces a new balance parameter, which can easily control the smoothness of the filter to meet the filtering requirements of various application scenarios without increasing the number of trainable weights of the neural network, and its mechanism is to control the horizontal displacement of the frequency response function. By setting a variety of parameter values on three citation networks and a knowledge graph to perform the task of graph embedding learning, this paper verifies the effectiveness of introducing the balance parameter and proposes a more comprehensive view from the perspective of graph partition.

Key words: graph signal, graph convolutional network, low-pass filter, smoothness, graph partition, balance parameter