A Power Series Development of the Convolution Theorem

Barrett, Louis C.; Wilde, Carroll O.

doi:10.2307/2309465

Cited by 2 publications

(2 citation statements)

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“…Convolution theorem tells us that convolution in the time domain is equivalent to multiplication in the frequency domain (Barrett and Wilde 1960). Hence, to perform graph convolution on embeddings with the convolution kernel, we only need to transform them into frequency domain by graph Fourier transform, multiply them, and transform the result back to time domain: e * g k = F −1 g F g (e) ⊙ k , where * g represents graph convolution; column vector k ∈ R M +N is convolution kernel and k = F g (k) is the corresponding frequency-domain waveform.…”

Section: Graph Convolutionmentioning

confidence: 99%

Low-Pass Graph Convolutional Network for Recommendation

Zhang

Qin

2022

AAAI

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Spectral graph convolution is extremely time-consuming for large graphs, thus existing Graph Convolutional Networks (GCNs) reconstruct the kernel by a polynomial, which is (almost) fixed. To extract features from the graph data by learning kernels, Low-pass Collaborative Filter Network (LCFN) was proposed as a new paradigm with trainable kernels. However, there are two demerits of LCFN: (1) The hypergraphs in LCFN are constructed by mining 2-hop connections of the user-item bipartite graph, thus 1-hop connections are not used, resulting in serious information loss. (2) LCFN follows the general network structure of GCNs, which is suboptimal. To address these issues, we utilize the bipartite graph to define the graph space directly and explore the best network structure based on experiments. Comprehensive experiments on two real-world datasets demonstrate the effectiveness of the proposed model. Codes are available on https://github.com/Wenhui-Yu/LCFN.

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Section: Graph Convolutionmentioning

confidence: 99%

Low-Pass Graph Convolutional Network for Recommendation

Zhang

Qin

2022

AAAI

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“…We also introduce a widely-used property of convolution, which is crucial in graph convolution design: Convolution Theorem (Barrett & Wilde, 1960) tells us that convolution in the time domain is equivalent to the product in the frequency domain, i.e., f (t) * g(t) = F −1 (F(f (t))F(g(t))). For graph data, convolution is hard to define directly due to the irregular structure of graphs, thus is defined in this way.…”

Section: Convolutionmentioning

confidence: 99%

Graph Convolutional Network for Recommendation with Low-pass Collaborative Filters

Yu,

Qin

2020

Preprint

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Graph Convolutional Network (GCN) is widely used in graph data learning tasks such as recommendation. However, when facing a large graph, the graph convolution is very computationally expensive thus is simplified in all existing GCNs, yet is seriously impaired due to the oversimplification. To address this gap, we leverage the original graph convolution in GCN and propose a Low-pass Collaborative Filter (LCF) to make it applicable to the large graph. LCF is designed to remove the noise caused by exposure and quantization in the observed data, and it also reduces the complexity of graph convolution in an unscathed way. Experiments show that LCF improves the effectiveness and efficiency of graph convolution and our GCN outperforms existing GCNs significantly. Codes are available on https: //github.com/Wenhui-Yu/LCFN.

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A Power Series Development of the Convolution Theorem

Cited by 2 publications

References 0 publications

Low-Pass Graph Convolutional Network for Recommendation

Low-Pass Graph Convolutional Network for Recommendation

Graph Convolutional Network for Recommendation with Low-pass Collaborative Filters

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