قارن الطرق

	الهومولوجيا المستمرة	خوارزمية Mapper
المجال	الطوبولوجيا	الطوبولوجيا
العائلة	Machine learning	Machine learning
سنة النشأة	2002	2007
صاحب الطريقة	Edelsbrunner, Letscher & Zomorodian	Singh, Mémoli & Carlsson
النوع	Topological feature extraction algorithm	Graph-based topological summarization
المصدر التأسيسي	Edelsbrunner, H., Letscher, D., & Zomorodian, A. (2002). Topological persistence and simplification. Discrete & Computational Geometry, 28(4), 511–533.	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.
الأسماء البديلة	Topological Persistence, Persistence Barcodes, Persistent Betti Numbers, Kalıcı Homoloji	Topological Mapper, TDA Mapper, Reeb Graph Approximation, Eşleyici Algoritma
ذات صلة	2	2
الملخص	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.	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.