We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

翻译：我们提出了演化图傅里叶变换（Evolving Graph Fourier Transform, EFT），这是首个能够捕捉时序图上演化表示的可逆谱变换。由于现有方法在捕捉演化图谱方面的不足（且因时间维度与图顶点域的结合导致计算代价高昂），我们以此作为研究动机。我们将该问题视为连续时间动态图拉普拉斯矩阵上的优化过程。此外，我们提出了伪谱松弛方法以分解变换过程，从而显著提升计算效率。EFT方法能够精准捕捉演化图的结构与位置特性，使其有效支持演化图的下游任务。为此，我们基于EFT实现了一个简单神经模型作为参考框架，用于捕捉演化图谱。我们在多个大规模标准时序图基准上对理论发现进行了实证验证，结果表明我们的模型达到了最先进的性能水平。