เปรียบเทียบวิธี

	Graph Neural Network	อัลกอริทึม Mapper	ความคงทนเชิงทอพอโลยี (Persistent Homology)
สาขาวิชา	การวิเคราะห์เครือข่าย	ทอพอโลยี	ทอพอโลยี
ตระกูล	Process / pipeline	Machine learning	Machine learning
ปีกำเนิด	2017–2018 (major variants)	2007	2002
ผู้ริเริ่ม	—	Singh, Mémoli & Carlsson	Edelsbrunner, Letscher & Zomorodian
ประเภท	Deep learning on graph-structured data	Graph-based topological summarization	Topological feature extraction algorithm
แหล่งต้นตำรับ	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.	Edelsbrunner, H., Letscher, D., & Zomorodian, A. (2002). Topological persistence and simplification. Discrete & Computational Geometry, 28(4), 511–533.
ชื่อเรียกอื่น	GNN, GCN, GAT, GraphSAGE	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma	Topological Persistence, Persistence Barcodes, Persistent Betti Numbers, Kalıcı Homoloji
ที่เกี่ยวข้อง	5	2	2
สรุป	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.	Persistent homology is a method in topological data analysis that quantifies the multi-scale topological structure of data by tracking connected components, loops, and voids as a scale parameter varies. Introduced by Edelsbrunner, Letscher, and Zomorodian in 2002, it encodes topological features through their birth and death scales, producing persistence diagrams or barcodes that serve as compact, coordinate-free descriptors of shape. The approach is robust to noise and provides a mathematically rigorous bridge between discrete data and algebraic topology.