So sánh phương pháp

	Học Sâu Tôpô	Thuật toán Mapper
Lĩnh vực	Tô pô học	Tô pô học
Họ	Machine learning	Machine learning
Năm ra đời	2023	2007
Người khởi xướng	Topological deep learning literature	Singh, Mémoli & Carlsson
Loại	Higher-order message-passing framework	Graph-based topological summarization
Công trình gốc	Hajij, M., et al. (2023). Topological deep learning: Going beyond graph data. arXiv preprint.	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.
Tên gọi khác	TDL, Topological Neural Networks, Higher-Order Deep Learning, Topolojik Derin Öğrenme	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma
Liên quan	3	2
Tóm tắt	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.	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.