مقایسهٔ روش‌ها

	یادگیری عمیق توپولوژیکی	شبکه عصبی گراف	همولوژی پایدار
حوزه	توپولوژی	تحلیل شبکه	توپولوژی
خانواده	Machine learning	Process / pipeline	Machine learning
سال پیدایش	2023	2017–2018 (major variants)	2002
پدیدآور	Topological deep learning literature	—	Edelsbrunner, Letscher & Zomorodian
نوع	Higher-order message-passing framework	Deep learning on graph-structured data	Topological feature extraction algorithm
منبع بنیادین	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).	Edelsbrunner, H., Letscher, D., & Zomorodian, A. (2002). Topological persistence and simplification. Discrete & Computational Geometry, 28(4), 511–533.
نام‌های دیگر	TDL, Topological Neural Networks, Higher-Order Deep Learning, Topolojik Derin Öğrenme	GNN, GCN, GAT, GraphSAGE	Topological Persistence, Persistence Barcodes, Persistent Betti Numbers, Kalıcı Homoloji
مرتبط	3	5	2
خلاصه	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.	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.