GRAPH

Authors: Fenia Christopoulou, Makoto Miwa, Sophia Ananiadou

Fourier Transform Virtually everything in the world can be described via a waveform - a function of time, space or some other variable. For instance, sound waves, the price of a stock, etc. The Fourier Transform gives us a unique and powerful way of viewing these waveforms: All waveforms, no matter what you scribble or observe in the universe, are actually just the sum of simple sinusoids of different frequencies....

Note This is the second post of the Graph Neural Networks (GNNs) series. Convolutional graph neural networks (ConvGNNs) Convolutional graph neural networks (ConvGNNs) generalize the operation of convolution from grid data to graph data. The main idea is to generate a node $v$’s representation by aggregating its own features $\mathbf{x}_{v}$ and neighbors’ features $\mathbf{x}_{u}$, where $u \in N(v)$. Different from RecGNNs, ConvGNNs stack fixed number of multiple graph convolutional layers with different weights to extract high-level node representations....

Note This is the first post of the Graph Neural Networks (GNNs) series. Background and Intuition There is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. For examples, in e-commence, a graph-based learning system can exploit the interactions between users and products to make highly accurate recommendations. In chemistry, molecules are modeled as graphs....