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	グラフニューラルネットワーク	Mapperアルゴリズム
分野	ネットワーク分析	位相幾何学
系統	Process / pipeline	Machine learning
提唱年	2017–2018 (major variants)	2007
提唱者	—	Singh, Mémoli & Carlsson
種類	Deep learning on graph-structured data	Graph-based topological summarization
原典	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.
別名	GNN, GCN, GAT, GraphSAGE	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma
関連	5	2
概要	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.