Vertaile menetelmiä

	Topologinen syväoppiminen	Mapper-algoritmi	Pysyvä homologia
Tieteenala	Topologia	Topologia	Topologia
Menetelmäperhe	Machine learning	Machine learning	Machine learning
Syntyvuosi	2023	2007	2002
Kehittäjä	Topological deep learning literature	Singh, Mémoli & Carlsson	Edelsbrunner, Letscher & Zomorodian
Tyyppi	Higher-order message-passing framework	Graph-based topological summarization	Topological feature extraction algorithm
Alkuperäislähde	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.	Edelsbrunner, H., Letscher, D., & Zomorodian, A. (2002). Topological persistence and simplification. Discrete & Computational Geometry, 28(4), 511–533.
Rinnakkaisnimet	TDL, Topological Neural Networks, Higher-Order Deep Learning, Topolojik Derin Öğrenme	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma	Topological Persistence, Persistence Barcodes, Persistent Betti Numbers, Kalıcı Homoloji
Liittyvät	3	2	2
Tiivistelmä	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.	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.