Decimated Framelet System on Graphs and Fast G-Framelet Transforms
Authors: Xuebin Zheng, Bingxin Zhou, Yu Guang Wang, Xiaosheng Zhuang
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The effectiveness for constructing the decimated framelet system and the FGT is demonstrated by a simulated example of random graphs and real-world applications, including multiresolution analysis for traffic network and representation learning of graph neural networks for graph classification tasks. In this section, we present three experiments for the FGT algorithm. We show the computational complexity analysis of FGT in Section 8.2 and the multiscale analysis by decimated framelets for the real-world traffic network in Section 8.3. Also, we use FGT to define a spectral graph convolution in Section 8.4, which shows good performance in graph-level classification. |
| Researcher Affiliation | Academia | Xuebin Zheng EMAIL University of Sydney Business School University of Sydney Bingxin Zhou EMAIL University of Sydney Business School University of Sydney Yu Guang Wang EMAIL Institute of Natural Sciences and School of Mathematical Sciences Shanghai Jiao Tong University & Max Planck Institute for Mathematics in Sciences & School of Mathematics and Statistics University of New South Wales Xiaosheng Zhuang EMAIL Department of Mathematics City University of Hong Kong |
| Pseudocode | Yes | Algorithm 1: Coarse-Grained Chain Algorithm (CGC) ... Algorithm 2: Chain-based Graph Laplacian Basis ... Algorithm 3: Haar-Like Orthonormal Basis on the Coarse-Grained Chain (HONBC) ... Algorithm 4: Discrete Fourier Transform on G (DFT) ... Algorithm 5: Adjoint Discrete Fourier Transform on G (ADFT) ... Algorithm 6: Decomposition for FGT ... Algorithm 7: Reconstruction for FGT |
| Open Source Code | Yes | The Python and Matlab codes for FGT can be downloaded from Github1. 1. https://github.com/Yu Guang Wang/FGT |
| Open Datasets | Yes | In this section, we present an application of multiscale analysis by FGTs for a real-world traffic network of Minnesota (Rossi and Ahmed, 2015). The dataset represents the roads of Minnesota by edges of a graph and the intersections and towns by 2,642 graph vertices. ... We evaluate the performance of the proposed FGConv on three graph classification benchmarks. The selected datasets are described as follows. D&D (Dobson and Doig, 2003; Shervashidze et al., 2011) is a graph dataset ... PROTEINS (Dobson and Doig, 2003; Borgwardt et al., 2005) is another protein structure dataset ... MUTAG (Debnath et al., 1991; Kriege and Mutzel, 2012) is a mutagen dataset which contains 188 chemical compounds. |
| Dataset Splits | Yes | We split the dataset into training, validation and test sets with portions 80%, 10% and 10% respectively. |
| Hardware Specification | Yes | The computing environment of this experiment is MATLAB R2019b installed on a mac OS Catalina machine with 2.3GHz 8-Core Intel Core i9 processor and 16GB RAM. ... we run the experiments on NVIDIA Tesla V100 GPU with 5,120 CUDA cores and 16GB HBM2 mounted on a high performance computing cluster. |
| Software Dependencies | Yes | The computing environment of this experiment is MATLAB R2019b installed on a mac OS Catalina machine with 2.3GHz 8-Core Intel Core i9 processor and 16GB RAM. ... All the programs used in this section are written in Py Torch and the library Py Torch Geometric (Fey and Lenssen, 2019) |
| Experiment Setup | Yes | We use the Adam optimizer (Kingma and Ba, 2015) with an early stopping strategy suggested in Shchur et al. (2018) to train our model. Specifically, we stop the training if the validation loss does not improve for continuous 10 epochs with a maximum of 50 epochs. We use a simple grid search to tune the hyperparameters. We show a list of the hyperparameters in the model along with their search spaces in Table 6. |