convolutional filter bank

Data

subject:: Data Science Methods for Large Scale Graphs parent:: Graph Signals and Graph Signal Processing theme:: math notes

Convolutional Filter Bank

Let $X\in {\mathbb{R}}^{n\times d}$, $H_k\in {\mathbb{R}}^{d\times d^{\prime }}$ for $k=0,\dots ,K-1$. Then a convolutional filter bank (or multiple input multiple output graph convolution) is a multi-dimensional graph convolutiongiven by $Y={\sum }_{k=0}^{K-1}{S}^{k}X{H}_k$

• $S^k\in {\mathbb{R}}^{n\times n}$ is still a graph diffusion/shift
• $H_k$ is a linear transformation mapping $d$ features to $d^{\prime }$ features

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