graph perceptron

Data

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

Graph Perceptron

Let $\sigma :\mathbb{R}\to \mathbb{R}$. The graph perceptron is defined as

&\to_{u} y \cdot \sigma(u) \;\;\text{pointwise nonlinearity} \to_{y}

\end{aligned}$$

ie a graph convolution followed by a pointwise nonlinear function $y_i=\sigma (u_i)$

Examples

• $\sigma (x)=max(0,x)$ ReLU
• $\sigma (x)=\frac{1}{1+e^{-x}}$ Sigmoid
• $\sigma (x)=\tanh (x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$ hypertangent

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