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	Topologisk djupinlärning	Grafneuralnätverk	Mapper-algoritmen
Ämnesområde	Topologi	Nätverksanalys	Topologi
Familj	Machine learning	Process / pipeline	Machine learning
Ursprungsår	2023	2017–2018 (major variants)	2007
Upphovsperson	Topological deep learning literature	—	Singh, Mémoli & Carlsson
Typ	Higher-order message-passing framework	Deep learning on graph-structured data	Graph-based topological summarization
Ursprungskälla	Hajij, M., et al. (2023). Topological deep learning: Going beyond graph data. arXiv preprint.	Kipf, T.N. & Welling, M. (2017). Semi-Supervised Classification with Graph Convolutional Networks. International Conference on Learning Representations (ICLR).	Singh, G., Mémoli, F., & Carlsson, G. (2007). Topological methods for the analysis of high dimensional data sets and 3D object recognition. Eurographics Symposium on Point-Based Graphics, 91–100.
Alias	TDL, Topological Neural Networks, Higher-Order Deep Learning, Topolojik Derin Öğrenme	GNN, GCN, GAT, GraphSAGE	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma
Närliggande	3	5	2
Sammanfattning	Topological Deep Learning (TDL) is a framework that extends deep learning beyond graphs to higher-order topological domains such as simplicial complexes, cell complexes, and hypergraphs. Formalized by Hajij et al. (2023), TDL provides a unified mathematical language for defining message-passing schemes across cells of different ranks, enabling neural networks to model multi-way interactions that pairwise graph edges cannot capture. It is relevant to researchers working with relational, geometric, or biological data exhibiting group-level dependencies.	A Graph Neural Network (GNN) is a deep learning architecture that operates directly on graph-structured data by combining node features with structural information through iterative neighborhood message passing. The three canonical variants — the Graph Convolutional Network (GCN) introduced by Kipf and Welling in 2017, the Graph Attention Network (GAT) introduced by Veličković et al. in 2018, and GraphSAGE — differ in how they aggregate neighbor information: GCN applies a spectral convolution over the full adjacency, GAT weights neighbors by learned attention scores, and GraphSAGE samples and aggregates local neighborhoods inductively, enabling generalization to unseen nodes.	The Mapper algorithm is a method in topological data analysis (TDA) that produces a graph-based summary of the shape of high-dimensional point cloud data. Introduced by Singh, Mémoli, and Carlsson in 2007 at the Eurographics Symposium on Point-Based Graphics, Mapper constructs a simplicial complex — typically a graph — that captures the global topological and geometric structure of a dataset without requiring a fixed embedding or metric assumption.