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Graph Neural Network

Deep learning architecture designed to process structured graph data, enabling learning of representations from relationships between nodes and edges.

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Spatial GNN

GNN approach that performs convolution directly on the neighborhood space by aggregating features of adjacent nodes according to predefined schemes.

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Spectral GNN

Family of GNNs based on spectral graph theory, using graph Fourier transform to define convolution operations.

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Graph Fourier Transform

Generalization of the classical Fourier transform to signals defined on graphs, using the eigenvectors of the Laplacian matrix.

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Laplacian Matrix

Square matrix representing the structure of a graph, essential in spectral analysis and defined as L = D - A where D is the degree matrix.

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Spectral Filter

Filter applied in the spectral domain to modify the frequencies of a graph signal, analogous to filters in classical signal processing.

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Aggregation Function

Mathematical operation in spatial GNNs that combines features of neighboring nodes, such as mean, max, or sum pooling.

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Chebyshev Polynomials

Orthogonal polynomials used to efficiently approximate spectral filters in GNNs, reducing computational complexity.

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Eigendecomposition

Fundamental matrix decomposition for spectral GNNs, computing eigenvalues and eigenvectors of the Laplacian matrix.

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Spectral Clustering

Partitioning method using eigenvalues of the Laplacian matrix to identify communities in graphs.

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Graph Isomorphism Network

Powerful spatial GNN architecture with strong theoretical expressivity properties, capable of distinguishing most non-isomorphic graphs.

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Graph Wavelet Transform

Alternative to graph Fourier transform offering simultaneous spatial-spectral localization for multi-scale analysis.

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Neighborhood Sampling

Neighbor sampling strategy in spatial GNNs to handle large graphs and reduce computational complexity.

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Spectral-Temporal GNN

GNN extension combining spectral analysis and temporal modeling to process evolving dynamic graphs.

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