Methoden vergleichen

	Mapper-Algorithmus	Spektrale Clusteranalyse
Fachgebiet	Topologie	Maschinelles Lernen
Familie	Machine learning	Machine learning
Entstehungsjahr	2007	2002
Urheber	Singh, Mémoli & Carlsson	Ng, A. Y.; Jordan, M. I.; Weiss, Y.
Typ	Graph-based topological summarization	Graph-based clustering (spectral method)
Wegweisende Quelle	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.	Ng, A. Y., Jordan, M. I., & Weiss, Y. (2002). On Spectral Clustering: Analysis and an Algorithm. Advances in Neural Information Processing Systems, 14, 849–856.
Aliasnamen	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma	NJW spectral clustering, graph Laplacian clustering, normalized spectral clustering, spectral graph clustering
Verwandt	2	5
Zusammenfassung	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.	Spectral Clustering is a graph-based unsupervised learning algorithm, formalized by Ng, Jordan, and Weiss in 2002, that maps data points into a low-dimensional eigenspace derived from the similarity graph's Laplacian before applying k-means. This spectral embedding makes it possible to recover clusters of arbitrary shape — rings, crescents, interleaved spirals — that Euclidean distance-based methods consistently fail to separate.