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Title: Learning Graph Convolution Filters from Data Manifold

Paper content:
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features.
Recently, there has been an increasing interest in extending CNNs to the general spatial domain.
Although various types of graph convolution and geometric convolution methods have been proposed, their connections to traditional 2D-convolution are not well-understood.
In this paper, we show that depthwise separable convolution is a path to unify the two kinds of convolution methods in one mathematical view, based on which we derive a novel Depthwise Separable Graph Convolution that subsumes existing graph convolution methods as special cases of our formulation.
Experiments show that the proposed approach consistently outperforms other graph convolution and geometric convolution baselines on benchmark datasets in multiple domains.
Convolution Neural Network (CNN) BID14 has been proven to be an efficient model family in extracting hierarchical local patterns from grid-structured data, which has significantly advanced the state-of-the-art performance of a wide range of machine learning tasks, including image classification, object detection and audio recognition BID15 .
Recently, growing attention has been paid to dealing with data with an underlying graph/non-Euclidean structure, such as prediction tasks in sensor networks BID23 , transportation systems , and 3D shape correspondence application in the computation graphics BID2 .
How to replicate the success of CNNs for manifold-structured data remains an open challenge.Many graph convolution and geometric convolution methods have been proposed recently.
The spectral convolution methods BID3 BID5 BID11 are the mainstream algorithm developed as the graph convolution methods.
Because their theory is based on the graph Fourier analysis BID20 ), one of their major limitations is that in this model the knowledge learned from different graphs is not transferrable BID19 .
Other group of approaches is geometric convolution methods, which focuses on various ways to leverage spatial information about nodes BID17 BID19 .
Existing models mentioned above are either not capable of capturing spatial-wise local information as in the standard convolution, or tend to have very large parameter space and hence, are prone to overfitting.
As a result, both the spectral and the geometric convolution methods have not produced the results comparable to CNNs on related tasks.
Such a misalignment makes it harder to leverage the rapidly developing 2D-convolution techniques in the generic spatial domain.
We note graph convolution methods are also widely used in the pure graph structure data, like citation networks and social networks BID11 .
Our paper will only focus on the data with the spatial information.In this paper, we provide a unified view of the graph convolution and traditional 2D-convolution methods with the label propagation process BID24 .
It helps us better understand and compare the difference between them.
Based on it, we propose a novel Depthwise Separable Graph Convolution (DSGC), which inherits the strength of depthwise separable convolution that has been extensively used in different state-of-the-art image classification frameworks including Inception Network BID22 , Xception Network BID4 and MobileNet (Howard et al., 2017) .
Compared with previous graph and geometric methods, the DSGC is more expressive and aligns closer to the depthwise separable convolution network, and shares the desirable characteristic of small parameter size as in the depthwise separable convolution.
In experiments section, we evaluate the DSGC and baselines in three different machine learning tasks.
The experiment results show that the performance of the proposed method is close to the standard convolution network in the image classification task on CIFAR dataset.
And it outperforms previous graph convolution and geometric convolution methods in all tasks.
Furthermore, we demonstrate that the proposed method can easily leverage the advanced technique developed for the standard convolution network to enhance the model performance, such as the Inception module BID22 , the DenseNet architecture BID8 and the Squeeze-and-Excitation block BID7 .The
main contribution of this paper is threefold:• A unified view of traditional 2D-convolution and graph convolution methods by introducing depthwise separable convolution.• A
novel Depthwise Separable Graph Convolution (DSGC) for spatial domain data.• We
demonstrate the efficiency of the DSGC with extensive experiments and show that it can facilitate the advanced technique of the standard convolution network to improve the model performance.

assistant: text: We devise a novel Depthwise Separable Graph Convolution (DSGC) for the generic spatial domain data, which is highly compatible with depthwise separable convolution.